Abstract. Anisotropy has been shown to be an influencing factor of many nonwoven

Transcription

1 Abstract Konopka, Amy Elizabeth. The Effect of Anisotropy on In-Plane liquid Distribution in Nonwoven Fabrics. (Under the direction of Behnam Pourdeyhimi) Anisotropy has been shown to be an influencing factor of many nonwoven structural properties such as the bending rigidity and the tensile strength. The effect on liquid distribution (a very important property in many nonwoven applications), however, has not been determined. In this study the effect on anisotropy on a material s in-plane liquid distribution is examined. By using the new NCRC GATS device, which enables the in-plane liquid distribution and the recording of the spread to occur simultaneously, it was determined that the liquid distribution was indeed influenced by the structural anisotropy. Also determined was the effect of the testing method on the wicking rate of the material. A comparison between conventional test methods and a newly developed test method, which utilizes the NCRC GATS and a hollowed plate, were made. It was determined from the results that the new method is the only method that measures the intrinsic wicking of the material.

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3 BIOGRAPHY Amy Konopka received her Bachelor s degree in 1999 in Textile Engineering from the Georgia Institute of Technology. Ms. Konopka has been working as a research assistant with NCRC and a Masters student for the past two years. Her research has been focused on the liquid movements in nonwovens. After graduation Ms Konopka plans on pursuing a PhD at Ensait University in France. ii

4 Table of Contents LIST OF TABLES... IV LIST OF FIGURES...V 1 INTRODUCTION...1 LITERATURE REVIEW CONTACT ANGLE...6. LUCAS-WASHBURN EQUATION DARCY S LAW ANISOTROPY TEST METHODS FOR LIQUID ABSORPTION/WICKING EXPERIMENTAL METHODS MATERIALS MATERIAL CHARACTERIZATION Orientation Distribution Function LED Lighting System Fast Fourier Transform Tensile Tests APPARATUS AND PROCEDURE NCRC GATS Conventional Specimen Stage New specimen stage LIQUID SPREAD ANALYSIS Thresholding Boundary Extraction & Tracking ANALYSIS Chi-Square Test Anisotropy Parameter RESULTS AND DISCUSSION /5 WOODPULP/POLYESTER BLEND SAMPLES ODF Liquid Spread Anisotropy Cos Anisotropy The Effect of Basis Weight on In-Plane Liquid Distribution Sample Stage NCRC Horizontal Test CARDED POLYPROPYLENE SAMPLES ODF Liquid Spread Anisotropy Cos Anisotropy Sample Stage CONCLUSIONS AND RECOMMENDATIONS CONCLUSIONS ODF Test Plate The Effect of Basis Weight on In-Plane Liquid Distribution Directional Absorption RECOMMENDATIONS REFERENCES...17 iii

5 LIST OF TABLES TABLE MATERIALS USED IN EXPERIMENTS...46 TABLE CHI-SQUARE TEST FOR ODF S FOR WOODPULP/POLYESTER...65 TABLE 4.1- CHI-SQUARE FOR LIQUID SPREAD VS. ODF FOR WOODPULP/POLYESTER...71 TABLE CHI-SQUARE TEST FOR ODF S FOR CARDED POLYPROPYLENE...85 TABLE 4.- CHI-SQUARE FOR LIQUID SPREAD VS. ODF FOR CARDED POLYPROPYLENE...9 iv

6 LIST OF FIGURES FIGURE.1-1 INTRINSIC CONTACT ANGLE...8 FIGURE.1- A) CONTACT ANGLE LESS THAN NINETY DEGREES B) CONTACT ANGLE GREATER THAN NINETY DEGREES...8 FIGURE.5-1 SCHEMATIC OF DOWNWARD WICKING TEST...4 FIGURE.5- GATS (NOTE THAT PLASTIC TUBE CONNECTING THE RESERVOIR TO THE PLATFORM NOT SHOWN)...43 FIGURE.5-3 POINT ABSORBENCY TEST PLATE...43 FIGURE.5-4 POROUS PLATE...44 FIGURE.5-5 NCRC DIRECTIONAL...45 FIGURE A) 5/5 WOODPULP/POLYESTER BLEND B) POLYPROPYLENE CARDED/CALENDARED WEB...46 FIGURE 3.-1 DEPICTION OF LED BACKLIGHTING SYSTEM...48 FIGURE 3.-- PICTURE OF ANNULUS...5 FIGURE 3.-3 EDGE WITH DISCONTINUITIES...5 FIGURE 3.-4 ABOVE PICTURE AFTER WINDOWING...51 FIGURE 3.-5 A) SIMULATION ODF AND FFT B) SIMULATION ODF AND FFT AFTER WINDOWING...51 FIGURE MODIFIED GATS MACHINE (NOTE PLASTIC TUBE NOT PICTURED)...53 FIGURE 3.3- TYPICAL IMAGES CAPTURED DURING LIQUID SPREADING...54 FIGURE BOTTOM PLATE (POINT TEST)...55 FIGURE HOOP PLATE...56 FIGURE HOOP USED TO MOUNT SAMPLE...56 FIGURE SIMPLE THRESHOLDING (ALL GRAY LEVELS TO THE LEFT OF THE LINE WOULD BE SHOWN AS BLACK AND ALL PIXELS TO THE RIGHT OF THE LINE WOULD BE SHOWN AS WHITE)...58 FIGURE 3.4- DUAL THRESHOLDING (ALL PIXELS THAT ARE FOUND BETWEEN THE TWO LINES WILL BE SHOWN AS BLACK AND THE PIXELS ON THE OUTSIDE OF THE LINES ARE SHOWN AS WHITE)...58 FIGURE TOP) FOUR CONNECTIVITY TOP AND BOTTOM) EIGHT CONNECTIVITY...59 FIGURE NUMBER ASSIGNMENTS OF PIXELS...6 FIGURE LIQUID SPREAD BOUNDARY...6 FIGURE MEASUREMENT OF LIQUID SPREAD PROPERTIES...61 FIGURE ORIENTATION DISTRIBUTION FUNCTION FOR SET A...65 FIGURE TENSILE DATA VERSUS ODF...66 FIGURE WOODPULP/POLYESTER 1.5 TOP) POLAR PLOT OF THE ACTUAL LIQUID SPREAD...68 FIGURE WOODPULP/POLYESTER 1.6 TOP) POLAR PLOT OF THE ACTUAL LIQUID SPREAD...69 FIGURE WOODPULP/POLYESTER 1.94 TOP) POLAR PLOT OF THE ACTUAL LIQUID SPREAD...7 FIGURE BOUNDARY OF TWO SEPARATE LIQUID SPREADS...7 FIGURE WOODPULP/POLYESTER 1.5 TOP) %SPREAD VS. ORIENTATION ANGLE W/ RESPECT TO TIME 73 v

7 FIGURE WOODPULP/POLYESTER 1.6 TOP) %SPREAD VS. ORIENTATION ANGLE W/ RESPECT TO TIME BOTTOM) COS ANISOTROPY VS. TIME...74 FIGURE WOODPULP/POLYESTER 1.94 TOP) %SPREAD VS. ORIENTATION ANGLE W/ RESPECT TO TIME...75 FIGURE COMPARISON OF THE EFFECT OF BASIS WEIGHT ON THE LIQUID DISTRIBUTION RATE...76 FIGURE PLOT OF ACTUAL LIQUID SPREAD ON EACH OF THE THREE PLATES...78 FIGURE ACTUAL LIQUID SPREAD AS SEEN DURING TESTING. NOTE THE TWO FRONTS IN THE BOTTOM TWO PICTURES...79 FIGURE AREA VS. TIME FOR HOOP, BOTTOM, AND BOTTOM W/ TOP PLATE...8 FIGURE ACTUAL SPREAD OF LIQUID DURING THE NCRC DIRECTIONAL WICKING TEST. TOP) SHAPE OF SPREAD AT THE START OF TEST BOTTOM) SHAPE OF SPREAD AT END OF TEST...81 FIGURE TOP) HOOP TEST BOTTOM) NCRC DIRECTIONAL ABSORPTION TEST...83 FIGURE 4.-1 ORIENTATION DISTRIBUTION FOR SET B...85 FIGURE 4.- CARDED POLYPROPYLENE 8 FPM TOP) %SPREAD AND %FREQUENCY VS. ORIENTATION ANGLE...87 FIGURE CARDED POLYPROPYLENE 15 FPM TOP) %SPREAD AND %FREQUENCY VS. ORIENTATION ANGLE...88 FIGURE CARDED POLYPROPYLENE 15 FPM TOP) %SPREAD AND %FREQUENCY VS. ORIENTATION ANGLE...89 FIGURE 4.-5 CARDED POLYPROPYLENE 8 FPM TOP)%SPREAD VS. ORIENTATION ANGLE W/ RESPECT TO TIME BOTTOM) COS ANISOTROPY VS. TIME...91 FIGURE CARDED POLYPROPYLENE 15 FPM TOP)%SPREAD VS. ORIENTATION ANGLE W/ RESPECT TO TIME BOTTOM) COS ANISOTROPY VS. TIME...9 FIGURE CARDED POLYPROPYLENE 5 FPM TOP)%SPREAD VS. ORIENTATION ANGLE W/ RESPECT TO TIME BOTTOM) COS ANISOTROPY VS. TIME...93 FIGURE 4.-8 CARDED POLYPROPYLENE 8 FPM % SPREAD AND % FREQUENCY VS. ORIENTATION ANGLE...95 FIGURE CARDED POLYPROPYLENE 15 FPM % SPREAD AND % FREQUENCY VS. ORIENTATION ANGLE...96 FIGURE CARDED POLYPROPYLENE 5 FPM % SPREAD AND % FREQUENCY VS. ORIENTATION ANGLE TOP)BOTTOM PLATE BOTTOM)BOTTOM W/ TOP PLATE...97 FIGURE CARDED POLYPROPYLENE 8 FPM A) LIQUID SPREAD WITH BOTTOM PLATE...98 FIGURE CARDED POLYPROPYLENE 15 FPM A) LIQUID SPREAD WITH BOTTOM PLATE...99 FIGURE CARDED POLYPROPYLENE 5 FPM A) LIQUID SPREAD WITH BOTTOM PLATE...99 FIGURE DIFFERENCE IN RATE OF AREA CHANGE BETWEEN THE BOTTOM PLATE AND THE TEST WITH THE BOTTOM AND TOP PLATE FOR 8 FPM...1 vi

8 FIGURE DIFFERENCE IN RATE OF AREA CHANGE BETWEEN THE BOTTOM PLATE AND THE TEST WITH THE BOTTOM AND TOP PLATE FOR 15 FPM...11 FIGURE DIFFERENCE IN RATE OF AREA CHANGE BETWEEN THE BOTTOM PLATE AND THE TEST WITH THE BOTTOM AND TOP PLATE FOR 5 FPM...11 vii

9 1 INTRODUCTION Nonwovens are textile assemblies made up of fibers that are neither interlaced nor interlocked, but instead they are held together through mechanical, thermal or chemical bonding 1. It is this unique way of producing the materials that results in the materials being highly anisotropic. Nonwovens are highly anisotropic materials and unlike woven and knitted fabrics where the properties of the material depend on the way in which the yarns are interlaced or interlooped, nonwoven s properties depend greatly on the way in which the fibers are oriented within the material which, can vary significantly from one product to another depending on the production techniques and any further processing that the product might experience. The anisotropy of a nonwoven is an important structural characteristic of the material because it allows the user to isolate the directional properties of the nonwoven and due to this the structure can be engineered such that the material serves a specific purpose. It has been found that important structural characteristics such as the tensile strength and the bending rigidity are directly influenced by the anisotropy of the nonwoven 3. There are other important properties of nonwovens that have not been correlated with the structural anisotropy. This includes the liquid distribution of the material. Nonwovens are used in such products as baby diapers, feminine products, geotextiles, medical equipment such as gowns and sterilization covers, and may someday be a common method for the production of clothing. In most of these areas one of the key properties of the material is its liquid transport ability and more specifically the in-plane liquid distribution. In-plane liquid distribution is the movement of liquid within the plane of the fabric as opposed to the movement of the liquid perpendicular to the plane of the fabric, which is referred to as transplanar distribution, which is also important, but will not be discussed here. The in-plane liquid distribution is used to distribute liquid over a given area so that either total evaporation of the liquid can occur more readily, such in the case of perspiration on clothing, or so that the product can be used to its maximum capacity, such in the case of the second layer of a baby diaper 4. If the connection between the anisotropy and the liquid distribution can be made then the liquid flow can 1

10 be modeled as a function of the anisotropy and from there the nonwoven materials can be made such that the liquid distribution is engineered to meet a specific purpose. It is necessary however, to first measure the intrinsic in-plane liquid distribution of the material. Presently there are many different ways in which liquid movement within the nonwoven is measured. These are normally divided into two categories: Liquid absorption from a limited and liquid absorption from an unlimited reservoir. The drop test is an example of a test from a limited reservoir. This paper, however, focuses on absorption from an unlimited reservoir because for many of the nonwoven applications the liquid that wets the material can be assumed to constitute an unlimited reservoir. Conventionally tests that have been used to measure liquid absorption from an unlimited reservoir are tests such as the vertical wicking test, the dunk test, and the Gravimetric Absorbency Test System (GATS). The results from these tests, however, are all inconclusive because of the way in which the tests are carried out. To resolve these problems a new system was developed. The new instrument is based on the GATS testing system and has been developed in order to measure and quantify the in-plane liquid distribution of nonwoven fabrics as well as absorbency, desorbency and pore size distribution. This system is able to accurately calculate the liquid distribution with the added feature of a camera mounted above the testing plate. A new plate was also developed so that the intrinsic liquid absorption rate could be determined. The new plate is a flat circular plate that is hollowed out. The material that is placed on the plate touches the plate only in the center where the liquid is distributed to the fabric and around the edges for support. Unlike the old testing plates this new plate adds no new capillaries to the system and therefore allows for the true intrinsic wicking of the material to be generated. With the new plate and the new machine the effect of fabric anisotropy on liquid distribution can easily be determined. Anisotropy has been shown to influence many of the properties of a nonwoven material. For this reason and the fact that liquid distribution in nonwoven materials is so

11 significant, the effect of anisotropy on liquid distribution is investigated in this study. Also examined is the influence of test method on liquid absorption/wicking results. 3

12 LITERATURE REVIEW Liquid uptake into a material involves many processes and parameters. Initially, the process of wetting, the exchange of a fiber air interface with that of a fiber liquid interface, must take place. Directly resulting from wetting is the contact angle. The contact angle has been shown to play an important role not only in the determination of whether a liquid from an infinite reservoir will penetrate a material, but also in determining the rate of liquid flow within the material and the amount of liquid absorbed into the material. If the contact angle is less than ninety degrees the liquid will begin to flow into the material. If this flow is spontaneous, i.e. no outside pressure difference resulting in the imbibition of the material, then the flow is referred to as wicking. Wicking is caused by a pressure difference within the capillary and capillary forces are responsible for the bulk of the liquid uptake into the system. Hollies et al 5 performed experiments on the liquid absorption rate in yarns with varying twist levels and surface roughness. It was found that increasing either of these values decreased the rate of absorption. This was attributed to the capillary size decreasing with increasing twist and the increase in surface roughness resulting in discontinuities within the capillaries. This finding supports the theory that the capillaries are the major factor in liquid movement through the material. Capillaries are not always the only force that drives liquid into the material. Along with wicking, the process of absorption can occur. Although these two terms are sometimes used interchangeably, they are actually two separate processes. Whereas wicking is liquid uptake by the capillaries (interstices) formed by the yarns and fibers, absorption is the uptake of liquid into the fibers themselves. Typically, materials such as polyester are coated with a hydrophilic finish and only move liquid through the material by wicking, but materials such as cotton are naturally absorbent and therefore, both wicking and absorption occur. Fiber swelling due to absorption can actually hinder the capillary flow because it changes the capillary geometry. In addition to absorption and wicking a third 4

13 process of liquid movement can occur. This process is referred to as adsorption, which is the movement of a thin layer of liquid on the outside of the material. Liquid flow into a porous material is described by the Lucas-Washburn equation. The Lucas-Washburn equation is used primarily to describe flow into vertically hung materials and has been shown to be a good estimate of the flow rate within many textile materials. Even in systems where surfactants are used, if the dynamic balance of the absorption of the surfactant by the fiber at the advancing meniscus and the replenishing of the surfactant by the bulk solution is established quickly, the experimental values may comply with the linear relationship of the Lucas-Washburn equation. Inherent in the Lucas-Washburn equation are many assumptions and it is therefore, not surprising that some systems deviate from this linear relationship. Also, the experimental results may be dictated by events other than solely by the effect of wicking within the capillaries and therefore, may not follow the Lucas-Washburn equation. Depending on the system, there are many different factors that could contribute to the results deviating from the Lucas Washburn equation. For instance, the liquid absorption results results could be a combination of not only the wicking of liquid into the inner capillaries, but also to a large amount of liquid adsorption onto the surface of the material. This can occur when the alveoli, the indentions in the material formed by the crossing of yarns, are large. Or it could be due to liquid wicking into the inner capillaries plus the surface tension exerted on the material by the liquid. Other experimental results deviate from the calculated results because the radii of the capillaries are so large that one can no longer assume a constant equilibrium contact angle. Still, other results, which do not follow a linear path, might follow the Lucas-Washburn equation if it was not for its inherent linear nature between t vs. x, where x in this case is the height of the liquid column at time t. When the equation s coordinate system is altered, the form of it becomes nonlinear and therefore may be better suited to describing the experimental results than the original linear relationship. Darcy described steady-state unidirectional flow through an isotropic medium in Darcy s law is used to determine liquid flow into a porous solid and relates the flow rate 5

14 and pressure difference with respect to permeability, K, in units of length and fluid viscosity, µ. The permeability of a material is usually unknown and therefore, has to be determined separately. One approach is to model the constant as a function of the materials properties. The Carmen-Kozeny approach is one such model. The Carmen- Kozeny approach is a hydraulic radius theory that relates the permeability of the material to the porosity of the material and the fiber diameter. Another approach that has been described relates the permeability constant to the inter-network geometry of a woven material and therefore the geometry of the material is used to define the flow properties through the material. On the other hand, flow properties through the material have been used to describe the permeabilities of the material. These flow properties can help define the maximum and minimum permeabilities and can even help define the local permeabilities of the material, which are determined by the local heterogeneities of the material caused by processing and handling. In this section, the literature that is reviewed covers the spontaneous movement of liquid into a material from an unlimited reservoir. This will include discussions dealing with the contact angle, Lucas-Washburn equation and Darcy s Law. Also described will be the conventional test methods used for the measurement of the liquid uptake and the drawbacks to these systems..1 Contact Angle The contact angle is a value that is used to determine whether or not a liquid will wick into a material. Although sometimes it is thought that the contact angle is the cause of wetting, it must be noted that it is actually the result of wetting and not the cause of it 6. The contact angle is most often described by the simple Young s equation, where, γ cosθ = sv γ γ lv sl 6

15 γ γ γ sv sl lv = = = the interfacial tensions between the solid and the vapor the interfacial tensions between the solid and the liquid the interfacial tensions between the liquid and the vapor where the cosine of the contact angle is related to the equilibrium interfacial tensions between the solid, liquid, and vapor. Young s equation assumes that the solid is smooth, non-deformable, homogeneous, and impermeable. When γ sv is greater than γ sl the contact angle must be between zero and ninety degrees and wicking will occur. As the contact angle approaches zero the solid approaches complete wet out. On the other hand, when γ sv is less than γ sl the contact angle must be between ninety and one hundred eighty degrees, which is when wicking does not occur for most systems. Marmur 7 describes a situation when penetration into a capillary can occur even when the contact angle is greater than ninety degrees. Partial penetration of the capillary can occur at contact angles that are greater than ninety degrees when the pressure within the bulk of the liquid is substantial enough to force the liquid into the capillary. This occurs only when the liquid reservoir is small i.e. a drop of liquid. In a drop of liquid the radius of curvature of the drop can be high enough such that the pressure directly outside of the capillary is increased and thus the pressure difference, which is the driving mechanism in capillary penetration, is increased and therefore penetration may occur. This occurrence has been noted for contact angles as great as 115 degrees. Capillary penetration of liquid drops into a porous medium has been modeled extensively in the literature However the research contained within this work is focused on liquid wicking from an unlimited reservoir and therefore, the topic of limited reservoirs will not be discussed. The contact line is the location were the solid, liquid, and air all meet. The intrinsic contact angle is the angle formed from the tangent line at this point. (See Figure.1-1) 7

16 θ Intrinsic contact angle Figure.1-1 Intrinsic Contact Angle The intrinsic contact angle is the angle used by Young in his equation. However, the contact angle measured in experiments does not usually equal this value due to the inherent roughness of most surfaces. This contact angle is referred to as the apparent contact angle. The difference in value of the apparent contact angle and the intrinsic contact angle varies depending on the degree of surface roughness. Additionally, the fact that the interfacial tensions are supposed to be evaluated at the contact line, which is not presently possible, Young s equation should only be used as an approximate guide. The contact angle also determines the shape of the meniscus within a capillary, which is concave for contact angles less than ninety degrees and convex for angles greater than ninety degrees. (See Figure.1-) 1 3 Figure.1- a) contact angle less than ninety degrees b) contact angle greater than ninety degrees 8

17 For rise in a capillary to occur, the pressure at point 1 (see figure above) must be less than the pressure at points and 3. This pressure difference can be described by the Young- LaPlace equation, where, P = γ cosθ r P = capillary pressure γ = liquid surface tension θ = contact angle r = pore radius which in this case is written in the form for the specific case of spherical meniscus inside a cylindrical capillary. According to this equation, the smaller the pore size the greater the pressure within the capillary. Therefore, when external pressure is applied to a dry fabric and is slowly decreased until liquid begins to penetrate, the smaller pores will fill first and conversely when the external pressure, applied to a wet material, is increased, the smaller pores drain last. When there is no longer a pressure difference across the meniscus of the liquid in the capillary, equilibrium has been achieved and wicking ceases. This can be caused by the meniscus reaching the edge of the capillary or by a drastic change in the radius of the capillary. In the case of vertical wicking in a capillary, wicking can end due to the balance of a hydrostatic head with the capillary pressure head 1. This balance is described by the well-known Lucas-Washburn equation, which will be discussed later in this chapter. As stated previously, the contact angle determines whether or not a liquid will wick into a material from an infinite reservoir. It is obviously a very important parameter and is one, which is often manipulated by lowering the surface tension of the liquid to increase the liquid wicking rate into a material. 9

18 The Lucas-Washburn equation gives the dependence of the liquid uptake into the material to be in direct correlation with the product of γ cos θ. It is commonly thought that decreasing the surface tension of the liquid will increase the rate of absorption into the material. Miller et al. 13 discussed this matter and showed that this is not always the case. Decreasing the surface tension will only increase the rate of absorption if the contact is also decreased significantly. Miller et al. tested the absorption rates for four fabrics: cotton, silk, Nylon, and Thermax (a flat elliptical fiber produced by DuPont in order to increase thermal insulation). Water and a surfactant solution (lower surface tension than water) are used to compare the rates for liquids with different surface tensions. Silk, Nylon and Thermax all show an increase in the rate of absorption with the use of the surfactant solution. The rate for Thermax increased by almost ten times its rate with water. Cotton s absorption rate, however, decreased with the decrease in surface tension of the liquid. These results can all be attributed to the original and final contact angle. The original contact angle being the angle formed with water and the final contact angle being the one formed with the surfactant solution. Miller et al. found that for cotton, the contact angle between it and water is already so small that any reduction in the surface tension would have little to no effect on the contact angle. Therefore, a decrease in the absorption rate is observed. As for Thermax, the contact angle with water was greater than 85 ο. Therefore, there was a significant decrease of the contact angle and a large increase, times greater, in the cosine theta. This resulted in a large difference between the uptake rates of the two solutions. Thus, if the contact angle is already small, other measures, besides decreasing the surface tension to increase the absorption rate, must be taken in order to increase the absorption rate to occur. Not only is the absorption rate dependent on the contact angle, the absorption capacity is also dependent on this property. Hsieh 14 performed experiments on woven fabrics to determine the influence of fabric properties on the retention of liquid throughout the 1

19 structure. Vertical wicking tests were carried out on polyester and cotton fabric strips to determine the maximum absorption capacity of the fabrics. The two materials were made to have very similar woven structures, weights, and thickness. The differences between the two sets were the inherent fiber properties such as the cross sectional shape and fiber density. Polyester fibers are cylindrical and vary little from fiber to fiber and therefore have a high packing density, cotton on the other hand has a bean shape like cross section and varies significantly from fiber to fiber and therefore does not pack as well as polyester. Therefore, the pores in cotton will be larger and more abundant than the ones in the polyester fabric. Hsieh utilized two liquids for the tests. These were water (surface tension of 7.8mN/m) and hexadecane, because of its low surface tension (surface tension of 7.47mN/m) 15, density and viscosity. The experimental setup was like most vertical wicking test configurations. A piece of material was cut into strips ranging from 6.35mm x 8mm to 6.35mm x 1mm. These strips were then hung, using a film tab, from a microbalance that was used to record the change in weight during the test. The liquid reservoir was placed below the strip and then electronically moved upwards until the balance recorded a change in weight. At this point the reservoir stopped and the test proceeded until there was no change in weight recorded by the balance, indicating that the material had reached its maximum absorption. The liquid reservoir was then lowered until the material was no longer immersed within the liquid so that the final weight of the material could be measured without the interference of the force of the liquid on the material. The pores within the structure are responsible for liquid flow through a material and the size and connectivity of the pores in the fabric influence how fast and how much liquid is transported through the material. The porosity (ϕ ) of a material is defined as the fraction of void space within the material 16. ρb ϕ = 1 ρs ρ = fabric density b ρ = fiber density s 11

20 The fabric density can be found by: fabric weight ρ b = thickness and the maximum absorption capacity can be found with: where, C m ρl ϕ = ρ 1 ϕ ρ = liquid density l s Hsieh using the above equation for each of the materials found the maximum holding capacity for the materials. Polyester was found to have a 17.6% less calculated absorption capacity than cotton. However, when tested with hexadecane, polyester had.7% less absorption capacity than cotton. This variation is attributed to the way in which fabric thickness is measured due to the fact that this measurement results in a slight compression of the material thus, the thickness is slightly underestimated. So although the material properties are the same, weights, thickness and structure, the packing density had a great affect on the how much liquid was absorbed. Hsieh illustrated that the density of the material plays a key role in the absorption capacity of the material, however, if the contact angle is large it will cancel out any benefits brought about by the density. The experiment was performed a second time with water. This changed the liquid-solid contact angle for cotton and polyester to 41.5 ο and 7. ο respectively. As stated before, the measured difference in maximum absorption capacity for the two materials was 17.6%. However, when the experiment was carried out using water, polyester was found to have 78% less absorption capacity than cotton. This was attributed to the large contact angle for polyester. 1

21 It has been demonstrated that the contact angle plays an important role in the driving mechanism for bulk liquid uptake into a material. It can affect both the amount absorbed and the rate of absorption. This rate is described by the Lucas-Washburn equation, which incorporates the contact angle into its definition. This is discussed below.. Lucas-Washburn Equation The flow in a porous medium is usually envisioned as flow through a network of interconnected capillaries. One of the most famous equations used to describe this movement is the Lucas-Washburn equation, where, dl dt rγ cosθ = 4ηl l = distance the liquid has traveled at time t η = fluid viscosity t = time This equation is based on the Poiseulle s law of flow through a tube When vertical wicking is being examined the following form of the equation must be used in which the influence of gravity is taken into account. dl dt = rγ cosθ 4ηl r ρg 8η where, ρ = liquid density g = gravitational constant 13

22 The first term on the right side of the equation accounts for the spontaneous uptake of liquid into the material while the second term accounts for the gravitational resistance. There are many examples of systems that follow the Lucas-Washburn equation. One such example is a study done on the effect of surfactants on the liquid uptake into the system. Hodgson and Berg 19 reported on the effect of surfactants on the relationship of the actual wicking rates to those given by the Lucas-Washburn equation. This was done because the relationship between the Lucas-Washburn and pure liquids had already been established while the relationship between multi-component liquids and Lucas-Washburn had not been reasonably established. To do so, they first separated the dependence of wicking rates on surface tension into two categories: those whose liquid completely wet out the solid i.e. the contact angle equals zero and those whose liquid only partially wets out the solid. Then using the integrated form of the Lucas Washburn equation, where, 1 rσ cosθ h = t = k τ µ σ = liquid surface tension τ = tortusity factor h = height of liquid rise t k is either equal to the following when the contact angle equals zero i.e. cos θ = 1, rσ k = τ µ 1 14

23 or substituting Young s equation, k is found to be the following when the contact angle is greater than zero. k = r 1 ( σ σ ) SG τ µ SL Using these equations the role of surface tension was determined by measuring the contact angle separately. The contact angle was measured using a technique based on the Wilhelmy principle, which expresses the wetting force as a function of the surface tension, perimeter of the object being measured and the cosine of the contact angle. Basically a fiber is extracted from a piece of the material that will be used for testing. One edge of the fiber is then immersed in the liquid and the other is hung from a balance. The wetting force of the liquid on the fiber can then be determined. Since the surface tension and the perimeter of the object are already known values the cosine of the contact angle can then be calculated. The advancing contact angle was measured. With this established the equilibrium surface tension, the surface tension that occurs when the system is at equilibrium, could be compared to the wicking-equivalent surface tension, the actual surface tension that occurs during the liquid absorption. This enabled Hodgson and Berg to determine the parameters, which influenced the results. The wicking equivalent surface tension is equal to: σ = σ ref cosθ ref cos θ µ µ ref k k ref For a pure liquid the equilibrium surface tension and the wicking-equivalent surface tension should be equal. The actual test was a version of the vertical wicking test where a strip measuring 1cm X 1 cm was cut and hung from a wire and the lower edge of the strip was placed into the liquid so that the tip just contacted the liquid. The time for the liquid to reach previously marked heights on the material was recorded. The strips that were used were porous papers that were made of four different types of cellulose fiber. 15

24 The first group of surfactants that was chosen represented anionic, cationic and nonionic types and the second group represented surfactants commonly used in the pulp industry, which were Berocell 564 and Berocell 584. For the systems in which the contact angle was equal to zero it was found that the wicking-equivalent surface tension was much greater than the equilibrium surface tension except at very high surfactant concentrations. Even so, this group was found to obey the Lucas-Washburn equation. These results were attributed to a rapid establishment of the dynamic balance amongst the adsorption of the surfactant by the fiber at the advancing meniscus and replenishing of the surfactant by the bulk solution. Hodgson and Berg had to use a slightly different approach for the systems where the contact angle was greater than zero. Because it was known that the surface tension and the contact angle would never be at equilibrium, the magnitude of disequilibrium was measured by comparing the difference between the wicking equivalent adhesion tension: ( σ σ ) SG SL * 7 k. = kwater and the equilibrium adhesion tension ( σ SG σ SL ), which were also found to very different except at high concentrations. The systems that only partially wet out the solid were also found to be in good agreement with the Lucas-Washburn equation. As stated earlier, a number of assumptions are inherent in the Lucas-Washburn. These assumptions are: The flow is at steady state The flow is fully developed The fluid is Newtonian There are negligible inertia effects 16

25 The contact angle that is represented in the Lucas-Washburn equation is the angle at constant equilibrium; meaning one constant angle is used during the entire duration of the test. In previous experiments, deviations from the linear relationship of the Lucas- Washburn equation have been attributed to the fact that the contact angle during experiments is actually a dynamic contact angle and therefore is ever changing. It has also been attributed to an uneven distribution of pore sizes throughout the porous solid. Labajos-Broncano et al performed experiments on silica gel to determine other reasons for why experimental results might deviate from the linear relationship of the Lucas- Washburn equation. The weight of the liquid is related by the equation: where, ρ = liquid density w = ερx1x x w = weight of the liquid x = length of liquid front ε = porosity x & x 1 = dimensions of the lower base of the layer If this equation is substituted into the Lucas-Washburn equation the result is: where, η = viscosity w t = penetration time P = ( ερx x r) 1 = 4η P t pressure difference across the liquid - vapor interface Like the original equation where a linear relationship between x vs t is established, this equation establishes a linear relationship between w vs t. 17

26 Labajos-Broncano et al. s tests were accomplished using rectangular plates of silica gel, for the porous solid, and formamide for the penetration liquid. The formamide liquid was chosen because its properties had been formerly established. The silica gel was hung vertically from a balance that would be used to measure the change in weight of the liquid within the porous solid. The liquid rested in a reservoir under the gel and was raised until just the edge of the gel was in contact with the liquid. Four separate groups of experiments were performed. First, the silica gel, exposed to air, was hung vertically and placed in the liquid. Second, the silica gel was covered on either side with glass plates, measuring the same in dimension as the gel, and placed in the liquid. Third, the glass plates were placed in the liquid without silica gel to show the effect of surface tension on a solid. Finally, the glass plates were placed in the liquid with only 1mm of gel at the bottom to try and determine the force exerted on the silica gel. The results from the Labajos-Broncano et al. experiments using the silica gel exposed to air produced a graph of w vs. t in which the first part of the curve changed as t increased, a middle section which was linear and a third section which leveled off and became constant due to complete saturation of the gel. This graph shows only that the middle section obeys the Lucas-Washburn equation. It was found that the resulting graph from the experiments correlated well to a graph that was the sum of three values: the graphs of w vs. t for the Lucas-Washburn equation, the constant value for the force exerted on the plate due to surface tension, and w const w imb (w const = constant weight of the force obtained from the glass plate with the silica gel w imb = the weight of the penetrating liquid). Therefore, it was concluded, that not only did the liquid movement within the capillaries dictate the results, but it was also due to a combination of inner and outer forces related to the material and the liquid in the reservoir. There was still a slight deviation between the two graphs near the end, which was attributed to evaporation. Additionally, other researchers found further reasons for deviation from the Lucas- Washburn equation. Pezron et al. 1 tested the validity of the Lucas-Washburn equation by performing vertical wicking tests. The mass of the liquid vs. time was recorded. 18

27 Untreated cotton samples were used for the experiment. They were woven such that the alveoli, small indentions formed by the under-over weaving of the yarns, formed on the outside of the material measured about 4 µm and were connected by tiny channels. The material was cut into strips,.5 cm in width,.75 mm in thickness, and between.5 and 3 cm in height. The strips were only cut in a direction parallel to the warp direction due to the fact that this is the direction in which most of the liquid is absorbed. Because the material is hydrophobic (the wax coating on the cotton had not been removed), the liquids used for penetration were hexadecane, decanol, and silicone oil. It was found using the Wilhemy principle, the principle that relates the wetting force to the surface tension, perimeter of the object being measured and the cosine of the contact angle, that the contact angles between the liquids and the material were equal to zero, i.e. the liquids completely wet out the material. First, to test the validity of the experiments, Pezron et al. performed experiments on a porous membrane. This hydrophobic porous membrane had a porosity of 7% and a pore diameter of.45 µm. The samples were hung vertically in a tensiometer and the material was placed in contact with the liquid. The mass of the sample with respect to time was recorded. When the mass became constant, complete saturation had occurred and the test was stopped. The fabric was then raised very slowly out of the liquid, to avoid excess liquid being attached onto the fabric due to the work of adhesion, and the weight of the liquid absorbed was recorded. The porous medium was tested using decanol and was found to be in good agreement with the Lucas-Washburn equation. From this result, the effective capillary radius r * and the effective cross section S v were obtained. r r * = k where, r = mean capillary radius k = tortuosity factor and 19

28 where, S v m a S v ma = ρh = cross section through which the liquid passes = mass of liquid at saturation o The values for these variables established the legitimacy of the experiment because they correspond to the given values for the structure of the membrane. Pezron et al. then performed experiments on cotton strips and the graph for m vs.t displayed a nonlinear relationship. M vs. h was also graphed and it was found that the values obtained could be represented by two straight lines. It was felt that this might be due to, in addition to the inside capillaries absorbing liquid, the alveoli at the surface of the material absorbing liquid because if the alveoli were absorbing they could not absorbed to as great of a height as the capillaries inside of the material due to their large size. Thus, this would cause the results for the m vs. h graph to be represented by two lines. The first line would represent the absorption if both the capillaries and the alveoli were wicking liquid to the top of the material. The second line represents wicking if only the capillaries were wicking. This theory was tested by first coating the outside of the woven material with a gel to rid the system of the alveoli. The ends were then cut to 1 expose the cotton to the liquid. The graph of the m vs.t displayed a linear relationship between the two values. Therefore, it was concluded that the inside of the material followed the Lucas Washburn equation. A second test was performed to test the effect of the alveoli by fully saturating the material and then drying the material at the surface by placing the material on an absorbent material. The resulting mass versus time added to the mass versus time of the gelatinized fabric resulted in the original mass obtained from the first experiment. It was therefore, concluded that two separate processes were proceeding during the test. First was the wicking of the liquid inside of the material, which followed the Lucas-Washburn equation, and secondly the wicking of the liquid on the outside of the material caused by the alveoli. It has been suggested by Berg that the largest radius in a capillary system for which the Lucas-Washburn equation is relevant 1

29 for is 5µm. It would of interest to see what would happen if the alveoli were smaller than this value to see if they would wick the liquid as high as the inside or if the outside air would have some sort of effect on the outcome. The reasons for divergence from the Lucas-Washburn equation are usually attributed in some way to the liquid properties or to the surface characteristics of the material. However, one team has tried to understand this divergence in terms of mathematical relationships. Labajos-Broncano et al. 3 look to the mathematical relationship provided by the equation for the answers. The experimental procedure that was carried out was almost the same as the one described previously for the Labajos-Broncano experiments earlier in this section. The materials for both the porous substrate and the liquids were the same. This process, however, involved a flannel wick that delivered the liquid to the silica gel. From the graphs of the t vs. x,determined from the experiments by Labajos-Broncano et al., where x in this case is the height of the liquid column at time t, a linear relationship, such as described by the Lucas-Washburn equation, cannot be found that quantifies all of the data points. The Lucas-Washburn equation, however, can be fit to the largest values for x. To understand this trend the equation is examined. It must be noted that the Lucas- Washburn equation is of the form: t = ax This of course,results in the linear relationship for the graphs of t vs x. If the coordinate system is altered, that is if the origin begins at some point after the initial contact of the material with the liquid at point x o, then a different relationship can be obtained. where, x = x x t 1 1 = t t o o 1

30 x = liquid height at some arbitrary time t from the point x x o = distance between original origin and new origin o The new form of the equation can then be written as t 1 = ax1 + axox1 There is no longer a linear dependence between t vs x. Labajos-Broncano et al. carried out new experiments varying the origin between and 1.5cm. The new relationship was found to correlate well with the new data. As stated earlier, one of the problems with the Lucas-Washburn equation is that it assumes a constant equilibrium contact angle. It is well known that there exists a contact angle hysteresis between absorption and desorption 4 5. And that the contact angle may be changing significantly in some cases during absorption and desorption. Therefore, an argument can be made for the need for the using a dynamic contact angle instead. Joos et al. 6 discussed the need for a dynamic contact angle and proposed the following equation: where, cosθ d = cosθ 1 η = liquid viscosity σ = surface tension o ( + cosθ ) θ = dynamic contact angle d υ = velocity of the meniscus o ηυ σ 1 θ = static advancing contact angle o thus, the equation for the rate of capillary rise becomes:

31 dx dt σr η dx = 1 4 4ηx σ dt 1 ρgr 8η In their study, they only considered fluids, which fully wet the capillary. These are highly viscous silicones. They assume that the radius of the porous medium is spherical at all times and therefore, can neglect the influence of gravity. Joos et al. conducted experiments with vertical capillaries of varying radii from.5cm to.36 cm and using silicone oils of varying viscosities for the liquid (note that the smallest capillary is at the largest value proposed by Berg for which the Lucas-Washburn equation has been suggested to be valid for). They compared the calculated results obtained from the Lucas-Washburn equation and those obtained from their theory to the results from the experiment. The results predicted from the proposed equations fit the resulting data more accurately although the Lucas-Washburn equation provided a close estimate for the smaller radii. With increasing pore radius, the difference between the predictions made by the Lucas-Washburn and the actual results increased. Darcy s law is another way in which flow through a porous medium is quantified. This equation is discussed in the following section..3 Darcy s Law A porous medium can be defined as a solid matrix consisting of interconnected empty spaces. This matrix has a dimension known as the porosity of the material. The porosity is the percent of the material that is empty space and is usually represented byϕ. Of interest is not only the total porous area of the material, but actually the pore size distribution. The technique of measuring this size distribution is discussed below. Liquid flow analysis has been used in many ways to describe structural characteristics of textile materials. Rebenfeld and Miller 7 describe ways in which to measure both the 3

32 pore dimensions and the directional permeabilities of the material. They argue that the average porosity of a material can be a deceptive value. That two materials with the same overall porosity could behave quite differently because of differences in the directional porosities and also because the pore size can vary greatly within a single structure. Therefore, quantifying the pore size distribution can help in understanding the behavior of the material. A more appropriate method is the liquid porosimetry in which pore dimension distributions are determined using liquids. The most widely used technique is that of the Mercury intrusion method. This method is not valid for many textile structures because of the compression loading which can cause damage to the structure. Furthermore, it can only measure pores accurately up to 5µm; textile structures can have pores that are as large as 1µm. The method described by Rebenfeld and Miller a pre-saturated material is placed on a membrane in a chamber. The chamber is then filled with pressurized gas in incremental amounts over time and the pores begin to drain starting with the largest ones first. A computer controls this process. A balance monitors the liquid that is drained from the material. The process in measuring the in-plane flow of the liquid, also described by Rebenfeld and Miller, is much like that of the liquid porosimetry in that pressurized air is used to force liquid into the material. A highly viscous fluid is chosen so that the flow is a function of material structure only and not that of the intrinsic wetting properties of the material. The flow is monitored by a video camera and then analyzed using an image analysis system. The Darcy flow can then be determined using the analysis of the images. Darcy described steady-state unidirectional flow through an isotropic porous medium in and can only be applied to systems for which slow laminar flow is found. This equation describes the relationship between flow rate and the pressure difference. K P u = µ x 4

33 where, K = permeability P = pressure gradient in the flow direction x µ = fluid viscosity It should be noted that K is independent of the properties of the fluid and instead is controlled by the structural characteristics of the material. The quantification of K for simple structural parameters has been the focal point of many studies. The Carman- Kozeny approach is a hydraulic radius theory that defines K for a bed of particles or fibers to be 9 : where, φ = porosity 3 φ k = k' S ( 1 φ ) k' = Kozeny constant S = surface area of the channel Although the Carmen-Kozeny constant is a popular approach for measuring permeability, others have tried to quantify it in terms of the geometry of the material. Ariadurai and Potluri 3 have examined the flow of liquid through woven geotextiles and tried to model the flow with the intentions of increasing liquid movement through the materials. Ariadurai and Potluri based their model for fluid flow through a woven geotextile on the actual structure of the woven material and its yarn. The geotextiles studied in this work can be assumed to be infinitely wide and therefore it was only necessary to study the unidirectional flow through the warp direction. This model is based on the Poiseuille s equation for volumetric flow rate flow through noncircular channels and is written as: Rh P Q = Aε kµ L 5

34 where, R h = hydraulic radius µ = viscosity k = shape constant resulting from the shape of the channel A = cross sectional area of the capillary ε = porosity L = length of capillary And where the specific permeability can be written as: B = R k h ε The foundation for the hydraulic radius for the woven structure is based on the basic geometry of the material. The hydraulic radii (the cross sectional area of the liquid moving through a capillary divided by the wetted perimeter) for the yarns are determined by assuming that the yarn has a racetrack sectional geometry. Thus, the volumetric flow rate and specific permeability can be determined by using these equations if the shape constants can be determined. Finally, the hydraulic transmissivity (in-plane permeability) can be found. Ariadurai and Potluri s tests, carried out to analyze the equations, were conducted with compliance to British and ASTM standards for determining transmissivity values. The results were found to correlate well with the proposed model. Rebenfeld et al describes in many papers a way to quantify in-plane liquid distribution within a porous network and how this applies to the directional permeabilities. The process by which the experiments are carried out is the process described earlier on page 4 for measuring in-plane flow. This process forces a liquid into the material and the flow front is recorded using a video camera. An isotropic material will be expected to have a circular fluid front while an anisotropic material will have a fluid front that deviates from a circular front. Due to the nature of the fluid front 6

35 the image can then be analyzed to determine the dominant directional permeabilities of the material. The process for analyzing these fronts is based on Darcy law, where the equation is written in the form: k q = PA µ where, q = volumetric flow rate µ = fluid viscosity P = pressure gradient A = area normal to flow µ k = in - plane permeability = k p ρg k p = in - plane coefficient of permeability ρ = fluid density g = gravitational constant For the analysis of a flow in a medium, the continuity equation and Darcy s Law are combined to give, where, v = v = superficial velocity vector and P k + x1 k 1 P = x 7

36 In the above equation 1 and are the principal flow directions. For an isotropic flow k front = 1 and analyzing the front at R = R f the corresponding Darcy s equation is k 1 equal to: k P 1 dr ν or = = ε µ R f dt R f ln R f where porosity, ε, is equal to: where, W = ε =1 total mass of W ρha the fibrous network ρ = material solid phase density h = total in - plane flow thickness A = area of the fibrous flow plane The permeability of the material can then be calculated by obtaining the slope of the least square line, m, through the graph of d ( R ) dt f vs 1 R ln f R permeability for the isotropic flow front k is found using the following: mεµ k = P o. Once this is obtained the An exact solution from the above equations cannot be determined for anisotropic flows. Instead, Rebenfeld et al. used finite elemental analysis and analytical expansion to determine the solution for k 1 and k from experimental data 35. It was determined from these studies that the directional in-plane flow of liquid is not determined by the fluid 8

37 viscosity, driving pressure, or surface wettability, but in fact was influenced by the structure of the material. While in this study Rebenfeld et al. examined the in-plane permeabilities in the main flow directions, in another study Rebenfeld et al. 36 examined the local flow rates to determine the local permeabilities, which are a function of the local heterogeneities. For example, even though a fluid front may have an overall circular shape, the local curvature will not be perfectly smooth due to local imperfections in the fabric. Processing and handling of the material can cause these local imperfections. Rebenfeld et al. determined a process by which the local permeabilities of the material at given angles could be estimated by examining an image recorded during testing. Again the experimental set-up and test procedure are the same as these reported in previous experiments. Also, like past studies this one is based on Darcy s law. The liquid fluid front boundary is extracted at given intervals. This boundary is then subdivided into tendegree intervals and placed on a grid so that sections of the pie could be analyzed. For each slice, the average permeability is calculated between every two-boundary intervals using the following form of Darcy s Law where, P εk v = r µ v = fluid velocity When a liquid front is moving through the plane of a material due to an applied pressure, there is a pressure drop across the face of the material. This model, however, is a simplification of the movement of the liquid because it assumes that there is no pressure drop in the angular direction. A computer simulation of the fluid front using this model showed that the results using this assumption and the results obtained from the actual 9

38 fluid front correlated well. Once the permeability of the slice is known, the average permeability of each grid square can be obtained by: k h m i i= 1 = h k i With this method, not only are the principal flow directions analyzed, but the local flow directions are also analyzed. The local flow properties reflect the fabric s local heterogeneities, which are inherent in any nonwoven fabric. The results could be misleading if only the maximum and minimum flow directions or the overall flow permeability were analyzed. These results may give the impression that the shape of the liquid front is a homogeneous ellipse, when in fact it is not. A smooth homogeneous ellipse almost never occurs due to process and handling. Nederveen 37 studied the relationship between different theoretical models for liquid flow in a porous material with that of the actual experimental results. The models are based on the Lucas-Washburn equation and Darcy s permeability. The Darcy expression for permeability is: where, P D = S D = Darcy permeability P = porosity S = surface area of the channels 3 This equation assumes that the capillaries are straight and parallel to one another. However, because not all of the channels are parallel to one another and their path is tortuous, the in the denominator of the above equation is replaced with the Kozeny 3

39 constant, k. This constant takes into consideration both of these effects within a porous medium. For porosities less than.6, the Kozeny constant was found to be between 4 and 6. If the porosities are greater than.7, the Davies expression, discussed below, can be used to determine the Kozeny constant and the expression for this constant is as follows: where, { 1+ b( ) } 3 3 k = ap ( 1 P).5 1 P a = 4 b = 56 If an ideal structure, defined as a material with constant fiber radius where all fibers are parallel to the direction of flow, is considered, the Darcy permeability combined with the Davies expression, could be re-written as: D d ( R )( 1 ) 1.5 { 1 57( 1 ) } P + 1 = P 14 Iberall proposed a model based on the forces applied to the structure during steady flow. If the velocity is very small, the equation is written as: D I =.75PR ( 1 P) For liquid rise in a capillary tube, the Lucas-Washburn equation is frequently used to describe the flow. For this purpose this equation has the form: h ( dh ) = D [ ( σ cosθ ) ρgh] dt η r t T ( h ) ln ( h ) = 1 H H 31

40 where, H = σ cosθ T = ηh ( ρgd) ( ρgr) The models tested by Nederveen for liquid rise in a porous medium are referred to as model one and model two. Model one assumes that the number of capillaries within the medium is twice that of the number fibers. The equation for this model is once again the general solution found for the Lucas-Washburn equation except that there is a change in T and H H T = ηh 1 ( 8 8P) ( σ cosθ ) ( ρgd) ρgrp 3 = Model two does not assume a particular amount of capillaries. Instead, it is based on the circumference of the fibers. The same ideal structure assumed for Iberall s equation is assumed for model two. The upward tension for this model is written as: p c = { ( 1 P) σ cosθ} R Therefore, the value for T is the same as for model one, but the value for H changes to: H ( 1 P)( σ cosθ ) ( PρgR) =. To test the validity of these models two separate tests were conducted testing the permeability in one and the liquid rise in the other. Both tests used fibrous mats made from a polyester fiber treated with a hydrophilic finish. These fibers did not swell. The material for the permeability test was clamped between two horizontal plates one end of the material was exposed to a liquid reservoir while at the other end there was a balance. 3

41 The liquid moved through the structure and was collected on the balance at the other end. The readings were taken every minute for an hour. The material for the liquid rise was also clamped between two plates, but the material was positioned vertically. The plates were tightened more on one side so that the material s density varies over the width of the material. This enabled the measurement of different densities during one trial. The bottom of the material was placed in the liquid and the level of the liquid was marked on the plate at specific times. The results from the permeability tests compared the results from the experiment to the permeabilities of the Iberall equation and the Davies equation. Neither of the equations predicted the experimental values closely although the Davies equation was closer match. The maximum height for the vertical rise experiments were recorded and compared to the two models. Model one predicted values much higher than the maximum and model two seemed to be very close to the actual value. Thus, it was concluded that using model two as a modification of the Lucas-Washburn equation results in an accurate prediction of the vertical rise of liquid through a porous medium with negligible swelling. Tests were also performed on cotton and on viscose fibers. These fibers tend to swell when exposed to liquid. The results from these tests did not correlate well with the theoretical values..4 Anisotropy Nonwovens are highly anisotropic materials and unlike woven and knitted fabrics where the properties of the material depend on the way in which the yarns are interlaced or interlooped, nonwoven s properties depend greatly on the way in which the fibers lay within the material. The method in which the fibers are laid down and any further processing determine the anisotropy of a nonwoven. The anisotropy of a nonwoven is an important structural characteristic of the material because it allows the user to isolate directional properties of the nonwoven and, because of this, the structure can be engineered such that the material serves a specific purpose. 33

42 Properties of nonwovens have been studied extensively to determine if they are in fact directionally dependent properties. Hearle and Stevenson 38, among other things, studied the effect of anisotropy on the tensile properties of the material. Three test groups were examined whose difference was the directional percentage of fibers. The first group was random laid, the second cross laid, and the third parallel laid. The anisotropy of these materials were measured using a visual technique that consisted of projecting the image of the material onto a screen and manually determining the anisotropy. Tensile tests were also carried out by using a standard test on an instron machine. The angles tested varied between zero degrees (machine direction) and ninety degrees (cross direction) in 15-degree intervals. They found that the random group had the highest strength to break in the machine direction and that it this value decreased slightly as it got closer to the cross direction. Although it might be expected that the breaking strength would be the same in every direction given that it is a random laid material and thus essentially isotropic, the processing tends to slightly align the fibers in the machine direction resulting in a slightly higher value in this direction. The cross laid material was found to have the largest breaking strength in the cross direction as expected and then a decreasing value until it reached the machine direction. The parallel laid material on the other hand had the largest breaking strength in the machine direction and decreased until it reached the cross direction. The trends that both the cross and parallel laid materials displayed were expected because it is intuitive that the greater number of fibers in a given direction would result in higher strength. However, the difference in strength in the machine direction and cross direction of the parallel laid materials was much larger than it was for the cross laid materials. Once again this is probably due to the processing parameters. Hearle and Stevenson showed that the fiber orientation directly influences tensile properties of nonwovens. It is not surprising that tensile tests are used to determine a material s anisotropy. 34

43 The effect of anisotropy on other properties has been examined as well. Pourdeyhimi and Kim 39 investigated the effect of bonding temperature and also anisotropy on the bending rigidity of nonwoven materials. The material utilized for the test was dry staple unidirectional carded webs. The bonding temperature varied between 14 o and 18 o C. It was found that as the temperature of the bond increased the bending rigidity also increased. What was also found is that although the bending rigidity increased due to bonding temperature it still directly correlated with the material s anisotropy. The effect of anisotropy of a nonwoven has been shown to be a determining factor on many of its properties. To accurately determine the effect of anisotropy on liquid distribution a suitable test method must be determined. Conventional test methods for testing liquid distribution are discussed below..5 Test Methods for Liquid Absorption/Wicking There are many tests that are used for measuring the absorption rate of a material. These tests include the vertical wicking test, downward wicking test, the basket test, GATS test and the NCRC directional absorbency test. Strip tests are generally used to measure absorption in a given direction while the other tests, basket, GATS, and NCRC directional absorbency test, are used to measure the bulk of liquid uptake into a system whether that is transplanar or in-plane liquid uptake. Although many may argue reasons to use the previously mentioned tests they all possess inherent problems. The test methods and the problems associated with each one are discussed in the following section. The vertical wicking test, as the name implies, is an absorbency/wicking test carried out with the specimen being tested vertically. This is referenced in the Association of Nonwoven Fabrics Industry s (INDA) standard test method 1.1. For this test, a strip of material is cut in a given direction (usually the machine or cross direction) and one end of the material is suspended while the other end hangs vertically down into a liquid reservoir. The test fabric is preconditioned at o C and 65% RH. The time it takes for 35

44 the liquid to rise to a given height is timed. There are different standards for those materials that are considered to wick slowly and those that are considered to wick at a rapid rate. For the slow ones the time allotted is 4 hours and the ones that wick fast are allotted five minutes maximum. Many people include an additional piece of equipment during testing that measures the change in weight of the material as the liquid is absorbed into the system. Although this is not included in the standard test method it is often a useful technique of measuring liquid absorption. This has been referenced in earlier sections in the discussions on the contact angle and the Lucas-Washburn equation As described in earlier sections the material can be hung from a device in which the weight of the material during uptake is recorded. This is a direct measurement of the amount of liquid being absorbed into the material. When the material is fully saturated, the weight balance will show a constant value and the test is ended. Hsieh and Yu 43 have experimentally observed varying parameters for the test such as fabric length immersed in the liquid and direction of cut. They describe a technique in which both wetting and retention characteristics of single component materials can be measured simultaneously. They also discuss the effect that different testing parameters have on wetting and retention. The wetting force of a liquid on a solid body is often described by the Wilhelmy principle. This equation results in an accurate measure of the wetting properties of single fibers. However, determining the wetting characteristics of fibrous assemblies is not as easy because not only is wetting occurring, but also wicking and sometimes absorption into the fiber themselves. Hsieh and Yu describe a technique in which both wetting and retention characteristics of single component materials can be measured simultaneously. They also discuss the effect that different testing parameters have on the wetting and retention characteristics. 36

45 Hsieh and Yu s experimental setup was like many vertical wicking test configurations. A strip of material was cut into strips ranging from 6.35mm x 8mm to 6.35mm x 1mm. These strips were then hung, using a film tab, from a microbalance that was used to record the change in weight during the test. The liquid reservoir was placed below the strip and then electronically moved upwards until the balance recorded a change in weight. At this point, the reservoir stopped and the test proceeded until there was no change in weight recorded by the balance, indicating the material had reached its maximum absorption. The liquid reservoir was then lowered until the material was no longer immersed within the liquid. This was done so that the final weight of the liquid in the material could be measured without the interference of the force of the liquid on the material. The materials tested in this experiment were single component materials consisting of cotton, polyester, Nomex, nylon 66, acetate, or rayon. Hsieh and Yu determined the wetting force from the results of the test using the following equation: F = Adv. St. w W t where, F w = wetting force Adv. St. = AdvanceSteady State W t = total liquid retention The advance steady state of the material occurs when the material has reached its maximum capacity. At this point the force recorded using the microbalance is a combination of the steady state wetting force and wicking. Once the interfacial dimensions between the liquid and water were determined the contact angle was then calculated using the Wilhelmy principle. Once the methodology for determining the wetting and wicking of the material was decided, many different configurations were studied to validate the method. The length of fabric exposed to the liquid and fabric directions were examined. 37

46 The wetting force and wicking characteristics did not change with the increase in amount of fabric exposed to the liquid. This conclusion leads to the ability of the method to be applied to many different systems because for many materials when they become exposed to liquid the increase in force during the experiment will actually lead to the material becoming more emerged within the liquid reservoir. Strips of material cut at different angles were also tested to determine the effect of configuration on the retention properties and contact angle. The water retention properties were found to vary depending on the direction of the cut in the anisotropic materials. This is due to changes in pore dimensions within the materials. The contact angles were found to be the same for all fabric directions measured even though the fill interface dimensions for the fill direction were greater than those for the warp direction. The wetting force reflected this difference so therefore the contact angles remained the same. The intrinsic contact angle was also observed to be the same for the individual fibers and the single component fabrics. Although the vertical wicking test is used extensively for liquid absorption/wicking tests, it posses some inherent problems. Miller 44 discussed some of these problems and proposed a solution. Miller compares two different approaches to measuring liquid absorption/wicking rates. The first one is the vertical wicking test already described and the second one is the downward wicking test. As stated earlier, the Lucas-Washburn equation is used to describe vertical wicking systems. Of course, the equation with the opposing hydrostatic term, utilized. dl rγ cosθ r ρg = dt 4ηl 8η PH, must be 38

47 where, l = distance the liquid has traveled at time t η = fluid viscosity t = time ρ = liquid density g = gravitational constant θ = contact angle γ = surface tension In any two vertical capillary systems, where the only difference between the two materials are the pore sizes, the absorption rates will differ according to time. At first, the rise of height in the material with the larger pores will be greater. Then, after a given period of time, gravity will have a greater influence on the rise in the larger pores and therefore the liquid rise will slow down. Finally the liquid height in the smaller pores will overcome the height of the liquid in the larger pores. It will be recalled that equilibrium is achieved in a vertical capillary when an opposing pressure head, which is caused by the height of the liquid column, balances the capillary pressure. Larger pores will achieve this equilibrium more readily due to more liquid being held within the capillary. Because of this effect, both systems can be deemed to have the faster absorption rate depending on the time that is considered for evaluation. Therefore, Miller suggests a downward approach to measuring the rate of liquid absorption. The downward wicking configuration, pictured in Figure.5-1, begins with an initial upward wicking. The beginning of the test is started at the point where the downward wicking begins. 39

48 Roller L L α Liquid Reservoir Clamp Balance Load Figure.5-1 Schematic of Downward Wicking Test 45 It will be recalled that the form of the Lucas-Washburn equation for vertical wicking is: dl dt R γ P 8ηL R = H where, P H = ρgl For downward wicking, the term for the hydrostatic pressure head changes to P h ( L L) = ρg cos β o 4

49 Thus the equation for the rate becomes: dl dt ρgk Lc = η L o cos β + L Lo + L The advantage of the downward wicking is seen when L o = L or when constant flow rate is achieved. Therefore, the effect of pore radius on wicking rate that occurs in vertical wicking does not occur in downward wicking. Also when L o = L occurs, the equation becomes: dl ρgk L c = + 1 cos β dt η Lo From here, the ratio of two flow rates can easily be found which is used to find L c, the capillary pressure and permeability. Problems with both the vertical and downward wicking test are edge effects. As stated earlier in the section discussing the contact angle, this edge effect is due to the equilibrium that occurs when the liquid reaches the edge of the material 46. The liquid front ceases at these edges and therefore, can cause a change in rate of the overall velocity within the material. Therefore, the actual velocity in each direction may not be known. Also a problem is the inability to accurately compare the wicking rate of one direction to that of another. Because equilibrium occurs at the edges the differences in the rates per angular direction may potentially be affected and therefore the true difference in rates for each direction may not be known. Although there are these problems with the vertical wicking test, some feel there are reasons for which the test should be used. Marmur and Cohen 47 have made a case for the vertical wicking test. They believe that the test should be used if an independent 41

50 calculation of θ from the test results is desired. In most cases, the contact angle is calculated prior to the beginning of the experiment. As stated earlier, other tests for measuring wicking and/or absorption are the basket test, the Gravimetric Absorbency Testing System (GATS), and the NCRC directional wicking test. The basket or sink test as it is sometimes referred to, is used to measure the total liquid uptake into a material over a period of time. This is referenced in the Association of Nonwoven Fabrics Industry s (INDA) standard test method 1.1. This test is executed by cutting out a strip of material weighing 5 grams and then rolling it up and placing it into a basket. The basket is then placed into a liquid reservoir and the time it takes for the material to sink is recorded. When the basket is recovered from the liquid the excess liquid is allowed to drain off and then the weight of the material is measured by subtracting from the total weight the weight of the basket. There are a number of problems associated with this test method, which may make the test unsuitable for real world applications. First, the rolled up material forms extra capillaries between its layers. These capillaries have the potential of holding liquid thus the reading for the weight may be a greater than the actual amount of liquid that the material could absorb for a given period of time. Second, the absorption rate cannot be modeled by using this test procedure. Another way to measure absorption versus time is the GATS machine. (See Figure.5-) The Gravimetric Absorbency Testing System or GATS is a method of measuring the wicking rate of a material over a period of time. It consists of a liquid reservoir that is connected to a platform via a plastic tube. The plastic tube enters the plate from the bottom and this is how the liquid is delivered to the material. The liquid reservoir rests on top of a balance, which is connected to a computer. The material, a circular piece of fabric, is placed on the platform and the test is initiated by using an automatic start switch. The material then begins to absorb the liquid delivered to it through the plastic 4

51 tube. As the liquid in the reservoir drops the value on the balance also drops and this is recorded by the computer as the amount of liquid absorbed by the material per unit time. Figure.5- GATS (note that plastic tube connecting the reservoir to the platform not shown) GATS employs one of two possible plates for which the sample rests. First, there is a plate with a small hole in the center referred to as the point absorbency test (See Figure.5-3). Figure.5-3 point absorbency test plate 43

52 This test is used to measure in-plane absorbency/wicking over a period of time. In this test, the liquid is absorbed only from the small hole and then is allowed to spread over the entire area of the material. The test is stopped either after a given period of time or when the sample is fully saturated. The sample is considered to have reached full saturation when there is no notable difference in the change of the liquid in the reservoir indicated by no change on the balance. The other plate utilized for this test is the "porous plate. (See Figure.5-4) Figure.5-4 porous plate The sample that is placed on this plate absorbs liquid over the entire surface of the material and is used to measure the total absorbency of the sample. This is widely used for thicker samples were transplanar wicking as well as in-plane wicking is occurring or when total absorbency is to be determined. There are some inherent problems with the GATS test method. First, an extra capillary may form between the plate and the material, especially when using the point test plate. This may result in faster absorption times than would normally be associated with the intrinsic wicking ability of the material. Second, the platform is at a constant height. Therefore, as liquid is absorbed into the material the pressure head changes due to the liquid in the reservoir receding. This causes errors in the data. Third, there are some problems with the machine itself. The automatic start does not work so the user has to place the sample on the platform at the same time that the test is begun. Of course, this 44

53 results in errors due to human involvement. Finally, the directionality of the wicking cannot be isolated. This means that although the total absorption of the material can be measured, the rate of wicking in a given direction is not known. NCRC developed a plate that would enable the directionality of the liquid spread to potentially be isolated. The test method that NCRC developed utilizes the GATS equipment, but uses a plate that is rectangular in shape (See Figure.5-5) and measures the liquid spread of a strip of material cut in a given direction (such as the cross or machine direction). Figure.5-5 NCRC directional This test is similar to the vertical and downward wicking test except now the test is executed in a horizontal position. The material is only in contact with the plate in the center and along the edges. This eliminates the extra capillaries formed between the plate and the fabric. One of the problems that arise with this test is overflow of the liquid into the trough of the plate. This in turn, results in inconclusive results because the data that is being recorded is not only a function of the liquid being absorbed by the material, but also a function of the liquid that is filling the trough. Also, like the vertical wicking test there are edge effects. A solution to the problems that are caused by the conventional test methods is discussed in the following chapters. 45

54 3 EXPERIMENTAL METHODS 3.1 Materials Two sets of materials were tested. The sets are designated as Set A and Set B. Set A consists of three subsets all of which are a hydroentangled 5/5 woodpulp/polyester blend and vary in basis weight. Woodpulp is a highly absorbent material and is used in many textile applications where liquid absorption is necessary. Set B also contains three subsets. The three subsets for set B is comprised of Polypropylene webs that were carded at varying speeds and calendared with a basic diamond pattern at 158 ο Fahrenheit. The fibers were coated with a hydrophilic finish because polypropylene is naturally hydrophobic. Table gives a description of each material used and an example picture from each set is shown in Figure Table Materials used in experiments Subset Set A 1 5/5 Woodpulp/Polyester blend -1.5 ounces per square yard 5/5 Woodpulp/Polyester blend ounces per square yard 3 5/5 Woodpulp/Polyester blend ounces per square yard Set B 1 Polypropylene web that was carded at 8 feet per minute Polypropylene web that was carded at 15 feet per minute 3 Polypropylene web that was carded at 5 feet per minute Figure a) 5/5 Woodpulp/Polyester Blend b) Polypropylene Carded/Calendared Web 46

55 3. Material Characterization 3..1 Orientation Distribution Function The comparison of the fabric s anisotropy to the anisotropy of the liquid distribution required that the orientation distribution function (ODF) of the fabric be determined. The ODF was determined by first digitizing an image of the fabric using an LED backlighting system. Then, a median filter was applied to the image to eliminate high frequency noise and an FFT procedure was used to determine the ODF. A nonwoven is considered to be a highly anisotropic material. To study the fabric s anisotropy, the orientation distribution function (ODF) was measured. The ODF ψ is a function of the angle θ. The integral of the function ψ from an angle θ 1 to θ is equal to the probability that a fiber will lie between the angles θ 1 and θ 48. The function ψ must additionally satisfy the following conditions: ψ ( θ + π ) = ψ ( θ ) π ψ ( θ ) dθ = 1 It can easily be seen from the above definition that the ODF is dependent on the anisotropy of the material. To determine a material s dominant orientation angle the following formula is used: θ = 1 tan -1 N i=1 N i=1 f ( θ ) sin θ i i f ( θ ) cosθ i i and the standard deviation is given as: ( 1 cos( θ θ )) N 1 σ ( θ ) = f ( θ i ) i N i=1 1/ 47

56 3.. LED Lighting System An LED (light emitting diode) backlighting system provided the light for the material image capturing. (See Figure 3.-1) Figure 3.-1 depiction of LED backlighting system 49 Unlike other forms of light, which have a broad-spectrum range, an LED is almost monochromatic and therefore, the LED s spectrum ranges are limited 5. Because of this the light has less of a chance of being absorbed by the material, which can cause distortions in the image. Although an LED has less luminosity than a halogen light source, and therefore, many must be used in order to create the required brightness, they have the advantage of being small and therefore can be packed into relatively small spaces and directed to enhance contrast 51. Also, the light source uses relatively less power than the halogen light and so the energy cost does not increase when using many LEDs compared to a halogen source. The actual LED lighting unit used consists of many LED lights densely packed together. These lights are placed behind a diffuser that reduces the directionality of the light and instead scatters it so that a more uniform lighting is achieved. A digital power unit controls the intensity of the lights. This type of power supply offers good repeatability and linearity 5. 48

57 3..3 Fast Fourier Transform The ODF of the digitized images was calculated using a Fast Fourier Transform (FFT) procedure. FFT is an indirect method of measuring the ODF, but has been shown to be very effective 53. A brief description is given below. An image is represented by transitions in the gray scale from light to dark and dark to light. These transitions represent the fibers and the spaces between them. The rate of transition is related to the orientation of the fibers. The FFT performs the transform by processing all of the rows one at a time and then by doing the same for the columns. This results in a two-dimensional set of values each with its own magnitude and phase. The orientation of the fibers is related to the transform because changes in the horizontal gray scale encompass vertical elements and vice versa. The equation of the direct and indirect Fourier transforms in two dimensions is the following: where, Fuv (, ) = f( xy, )exp[ jπ( ux+ vy)] dxdy f ( x, y) = F( u, v)exp[ jπ( ux + vy)] dudv f F ( x, y) ( u, v) = the image = the image's transform u = frequency along the x direction v = frequency along the y direction A detailed description of these equations can be found in the references 54. The transform s reference is in the center of the image and therefore the orientation can be directly found for an annulus of a given width w and radius r (See Figure 3.-). A given width is necessary for the annulus because if only a point was examined instead of an area there would be too much noise in the results and for that reason the data is averaged over a given width. 49

58 Figure 3.-- picture of annulus 55 The image is scanned radially to determine the ODF and the average intensity is found for a specified angular range. The images that were scanned for this study were examined in a ten-degree angular range. There are problems with using only an FFT function for given images. The FFT assumes periodicity, which means that when the image is scanned horizontally or vertically the resulting function will be periodic. Unfortunately most images are not periodic due discrepancies at the edges of the image. These discrepancies are caused by the right edge of the image not matching perfectly with the left side of the image or the top of the image not matching perfectly with the bottom of the image. (See Figure 3.-3) Figure 3.-3 edge with discontinuities 56 5

59 To reduce the problem windowing is introduced. In windowing the FFT function is multiplied by a given function to alleviate edge discrepancies. The -D power spectra after windowing are shown in Figure Figure 3.-4 above picture after windowing 57 The data from the FFT without windowing can have a great affect on the standard deviation of the ODF. This is shown in Figure Orientation: 9, 1 Density: 5% Thickness: Crimp: % Simulation FFT 6 5 Orientation: 9, 1 Density: 5% Thickness: Crimp: % Simulation FFT Frequency 4 3 Frequency Orientation Angle Orientation Angle Figure 3.-5 a) simulation ODF and FFT b) simulation ODF and FFT after windowing 58 In these pictures the actual simulated ODF is compared with that of the ODF obtained from the FFT transform with and without windowing. The picture illustrates that the ODF s standard deviation is more accurate after windowing than the ODF s standard deviation before windowing. The standard deviation is still slightly overestimated. 51

60 3..4 Tensile Tests Traditionally, tensile tests have been used to describe the anisotropy of a material. These tests have been proven to produce accurate results. They are not used as the principal form of determining the anisotropy for this work because they are very time consuming. To confirm that the LED backlighting system and FFT process indeed result in an accurate measurement of a fabric s ODF a random subset was chosen and tested at angles between and including and 9 degrees. Symmetry was assumed so the angles between and 18 degrees did not need to be examined. The material was cut into strips 1 inch in width and eight inches in length at the designated angle. For this test, ten-degree intervals from zero to ninety were decided upon so that it would correspond with the ODF intervals. An instron machine was used with a gage length of four inches because that corresponded to the standards set by ASTME. 5

61 3.3 APPARATUS and PROCEDURE NCRC GATS Tests for this study were carried out on a modified GATS machine. This machine is pictured in Figure Figure Modified GATS Machine (note plastic tube not pictured) Like the GATS, described earlier, this instrument is set up with a liquid reservoir that is placed on top of a balance and is connected to the bottom of a plate using a plastic tube. In addition to this configuration, a camera is mounted above the plate and is used to record the spreading of the liquid. Previously, when no camera was attached above the plate only the amount absorbed not the direction in which it spread could be determined. 53

62 Figure 3.3- shows typical images captured during the progression of the absorption test. These images are digitized at a preset time interval. The images are then analyzed to determine the properties of the spread s properties such as anisotropy and area spread per unit time. Figure 3.3- Typical images captured during liquid spreading The new instrument also has the ability to move the platform automatically during testing. This allows for a constant pressure or a change in pressure to be achieved throughout the test. For example, if a zero hydrostatic pressure head is desired the platform will actually move down as liquid is absorbed so that the level of the liquid in the reservoir and the level of the platform are kept even. The platform is able to move because it employs a stepping motor that drives the shaft that the platform is mounted on. The camera that is mounted above the platform is attached to the same platform and therefore, moves with the platform. Moving the camera with the platform provides a constant distance and magnification. 54

63 3.3. Conventional Specimen Stage Figure shows a schematic of one of the plates used in testing the sample. This plate was shown previously when discussing the GATS machine. Figure Bottom Plate (point test) This is the plate that was mentioned earlier as the point test plate and which will subsequently be referred to as the bottom plate. Two different methods of testing were executed on this plate. In the first method a piece of material that was to be tested was placed on the plate and a thin ring was placed around the outer edge of the material to weigh it down. In the second method, which will subsequently be referred to as top and bottom plate, the piece of material was placed on the plate and another clear plate was placed on top of the material. The second plate is used to ensure complete contact with the plate and is commonly used in absorption testing. There are some inherent problems with these test methods as described above. The problems with these methods arise because of the added capillaries that are formed when the relatively rough surfaces of the fabrics are place on the platform and also when the extra plate is placed on top of the material. These one or two added capillaries cause the data from the test to be skewed and will be discussed later in the study. 55

64 3.3.3 New specimen stage Figure shows a schematic of the new specimen stage used for the tests. Figure Hoop Plate Figure the plate is hollowed out in the middle. The plate is described as the hoop plate due to the use of a hoop that holds the fabric tightly when placed on the plate for testing. The cylinder in the middle of the plate is where the liquid enters the system. This is the initial point of absorption /wicking and is also the only point at which the fabric is touching the plate during the test. The point of contact measures cm in diameter. A weight was placed on the sample at this point to ensure complete contact and no overflow of the liquid into the trough. Although the fabric is in contact with the plate around the outer edge this area of the fabric is not considered in the test and therefore, has no effect on the results. Figure shows the hoop sample holder used in the test. The fabric is slipped in between the inner ring and the outer ring and the inner ring is expanded to hold the fabric in place. A slight tension is placed on the material, but it is felt that this has no affect on the results from the test. This hoop is slightly larger in diameter than the plate so that the fabric rests in intimate contact with the center cylinder and outer edge of the plate. Figure Hoop used to mount sample 56

65 3.4 Liquid Spread Analysis As mentioned earlier, the new device based on the GATS machine incorporates a camera into the testing process to capture the images as the liquid is spreading in the material. These images are stored digitally and are later analyzed for their liquid spread properties using image analysis. The process for analyzing these images is more complicated than the process for finding the ODF of the material. This process demands that a filter be applied, the image to be thresholded, the boundaries to be isolated, tracked and then finally the center to be found. From this all the necessary elements of the spread could be found Thresholding Thresholding, also referred to as segmentation, is the process by which a gray scale image is converted into a binary one. This step is necessary for tracking boundaries because a black and white image is needed to fully distinguish the object being measured from the background. Some examples of thresholding are edge thresholding, simple thresholding, and dual thresholding Edge thresholding is applied to images where the contrast between the image and its background is not sufficient enough to separate the two into groups. This is often used when individual fibers need to be separated from the background. For edge thresholding an edge detector is used to identify local changes in the intensity. A region of the image is considered to be an edge when there is an abrupt change in the intensity. If there is no abrupt change then the pixel is considered to be part of the background. For images with good contrast simple thresholding can be applied. Simple thresholding is a technique where the pixels are grouped into two classes and unlike edge thresholding without the consideration of their neighbors. (See Figure 3.4-1) The threshold cut off has been predetermined and is usually the mean intensity. This method works best when the images are bimodal. If the contrast is not as high, but the images are not small objects dual thresholding may be used. 57

66 Figure Simple Thresholding (all gray levels to the left of the line would be shown as black and all pixels to the right of the line would be shown as white) Dual thresholding is similar to simple thresholding in that it takes the gray levels and separates them into two groups. Unlike simple thresholding it does not use the mean intensity to differentiate between the two groups. Instead it selects a range, which, such as in this case, may be designated black, and then everything above and below that range would be white. (See Figure 3.4-) Depending on the quality of the image either simple thresholding or dual thresholding was used to clean up the images. Figure 3.4- Dual Thresholding (all pixels that are found between the two lines will be shown as black and the pixels on the outside of the lines are shown as white) 58

67 Sometimes images can appear to have high contrast when actually they do not. In this case just applying a simple threshold would mean some of the data would be lost. To improve the results of simple thresholding the local contrast is often improved prior to thresholding. Once again depending on the quality of the picture many different techniques were used to improve the quality of the image prior to thresholding and are too vast in number to describe in this paper Boundary Extraction & Tracking Images are representation of objects, which in this case is the liquid spread. All images can be represented by chain code. This is the key for tracking the boundary of the liquid spread. The chain code is the relationship of the center pixel to all of the pixels that are connected to it. There are two definitions for connectivity, four connectivity and eight connectivity. Four connectivity considers a pixel to be touching the center pixel only if that pixel is immediately to the right, left, upwards or downward from the center pixel. Eight connectivity also includes the four pixels diagonal from the center pixel. (See Figure 3.4-3) For tracking, the boundaries eight connectivity was used. Figure Top) Four Connectivity Top and Bottom) Eight Connectivity 6 As seen in Figure each of the pixels surrounding the center pixel is assigned a number zero through seven. 59

68 Figure Number assignments of pixels 63 These numbers are used to represent the movement from the center pixel to another pixel in a given direction. For example if the next pixel in the boundary was directly to the right of the starting pixel this movement would be designated seven. This new pixel would now be considered the center pixel. Then if the boundary moved diagonally up and to the right this movement would be designated zero. Thus the chain code that represents both of these moves is 7, 64. As mentioned earlier to track the boundaries the image must first be converted into a binary image. This was achieved through thresholding. Although not required the black area represented our liquid spread and the white area represented the background. The opposite could of course been used. Figure shows a typical liquid spread after the boundaries are extracted from the thresholded image. Figure Liquid spread boundary 6

69 Boundaries were extracted from the thresholded images by a morphological operation. From here the image was scanned from the bottom up until the first black pixel was reached. An arbitrary direction was chosen and then the boundary was tracked and then recorded using chain code. The gravitational center was then found and from this point the liquid spread properties were determined. The liquid spread properties, such as the area spread in a given direction or the dominate angle, were determined by starting at the center of the binary image and then calculating the distance from the center to the boundary in a given direction. (See Figure 3.4-6) 9 o 18 o o 7 o Figure Measurement of liquid spread properties The result from a given angle was actually an average of the angle and the angle plus 18 degrees. 3.5 ANALYSIS Chi-Square Test The relationship between two sets of ODF distribution data can be determined by applying the Chi-Square test. In this paper the Chi Square test was used to compare the ODF s of the subsets in each sample set and its was also used to compare the liquid spread anisotropy to the same sample s ODF so that a relationship might be established. The values obtained from the test are then correlated to a given probability found in a chisquare table which list the chi-square values and their corresponding probabilities. The 61

70 values for the probabilities range from zero, where the sets are not the same, to one, where the sets are exactly the same 65. The formula for the test is the following: X ( O E ) n i ν = i= 1 Ei i E i is the expected value and O i is the observed value Anisotropy Parameter A simple anisotropy parameter can be defined as the following: Machine / CrossAnisotropy = Machine Frequency (over a range) Cross Frequency (over a range) This equation is often used to described anisotropy, but is not accurate because it only considers the machine and cross directions. The basic equation for the anisotropy shown above is only valid for liquid distributions that maintain a shape that is a perfect ellipse (meaning no rough edges or variance from the path that the radii describe) that is oriented in either the machine or cross direction. If the shape of the ellipse varies from its original path or is not ellipse at all the results from this equation will be an inaccurate description of the spread. For example if the distribution was bi-modal, say with dominant angles in both the machine and cross direction, the number calculated using the above equation would be one. This number would give the impression that the spread was circular, but in fact the spread is non-circular. Also the equation only determines what is happening at the global level while many changes in the material occur at the local level. For these reasons the cos anisotropy is utilized for this study. 6

71 The cos anisotropy was used to compare the change in the anisotropy as a function of time. The value for the cosine anisotropy can be evaluated using the following equations. f p = cos θ 1 cos θ = π ψ ( θ )cos π ( θ ref ψ ( θ ) dθ θ ) dθ i Where Ψ is the orientation distribution function and the integration of Ψ between θ1and θ is equal to the probability that a fiber will lie in that interval. The value for the cosine anisotropy varies between 1 and 1 with 1 in this case pertaining to perfect alignment in the machine direction and the value of 1 pertaining to a perfect alignment in the cross direction. A value of zero always indicates a random distribution leading to an isotropic flow with a circular front. 63

72 4 Results and Discussion 4.1 5/5 Woodpulp/Polyester Blend Samples ODF The ODF is a function of the angle θ and when this function is integrated between two angles the result is the probability of a fiber lying in that direction. This function was used to determine the orientation of the fibers within the material. The ODF was found by using an LED backlighting system and the FFT process. The definition of ODF states that the angles between and 18 degrees are the same as the angles between 18 and 36 degrees. Therefore, symmetry is assumed for the liquid spread and only the angles between and 18 degrees are examined. The angles were not examined individually, however, instead they were divided into bins of ten degrees. So when an angle is referred to as the zero degree angle for the ODF it actually represents the ODF between the angles zero and ten and then of course if referring to the ten degree angle it actually is the ODF between the angles ten and twenty degrees etc. The y-axis is labeled %frequency. %Frequency refers to the amount of fibers assumed to lay in that direction with respect to the whole. The ODF for the Woodpulp/Polyester blend is shown Figure The ODF is oriented around the 9 o axis, which in this case is the machine direction. This is expected, as many nonwovens are oriented in this direction due to processing. It can be seen from this graph that the ODF s are the same and it is concluded that the increase in basis weight had no affect on the ODF. 64

73 1 1 % Frequency Avg ODF 1.5 Avg ODF 1.6 Avg ODF Angle (degrees) Figure Orientation Distribution Function for Set A To further examine the relationship between the three sets of ODF s a Chi Square test was performed. The Chi-Square test, as discussed earlier, gives the probability of how alike two sets of data are. The results from the Chi-Square test are shown in Table Table Chi-Square Test for ODF s for Woodpulp/Polyester Sample Set A 1.5 vs vs vs. 1.5 Chi Square Probability All of the Chi-Square probabilities are equal to one and therefore all of the ODF s are considered equal. To ensure that the results of the ODF from the imaging process were accurate tensile tests were performed on one of the subsets. Tensile tests have been proven to be good 65

74 indicators of a materials anisotropy. Figure 4.1- shows the result of the tensile tests on Sample set A subset 1. This particular subset was chosen randomly from the six subsets. From the graph one can see that the trend for both the imaging and the tensile tests are the same. Therefore it is concluded that the ODF determined optically represents the sample anisotropy correctly. 1 1 %Frequency Tensile 1 1 Frequency (%) Normalized Strength Orientation Angle Figure Tensile data versus ODF 4.1. Liquid Spread Anisotropy The relationship of the structure on the way in which liquid moves through the plane of the fabric is very important in many applications. To relate the two the ODF of the fabric was determined and then compared to the %spread of the liquid distribution. The %spread refers to the area of liquid spread in a particular direction when compared to the liquid spread as a whole. The anisotropy of the liquid spread was generated from the images digitized during testing. Once again, only the values for the angles between and 18 degrees were recorded. However, these were actually an average of the angles between o and 18 degrees and 18 and 36 degrees. The % spread was evaluated in bins of ten degrees where reference to the zero degree angles is actually the average between zero and ten as explained for the ODF. The figure on the top Figure 4.1-3, 66

75 Figure 4.1-4, and Figure displays the figure a polar plot of the actual boundary of the liquid spread and the figure on the bottom displays the % spread and % frequency versus angle. The Polar plot shows that the liquid spread is elliptical with a dominant orientation around the 9 o axis. The shape of the graph does not change significantly over time. The graphs on the bottom compares the distribution acquired from the polar plots and shows that not only is the liquid spread dominant with respect to the 9 o axis as is the ODF, but that it follows the same trend as the ODF for the remaining angles. 67

76 8 sec 4 sec sec 6 sec 1 sec 1 sec Dynamic Liquid Distribution Angle % Spread Avg Avg ODF 1 8 Frequency (%) Spread (%) Orientation Angle Figure Woodpulp/Polyester 1.5 top) polar plot of the actual liquid spread bottom) %spread and %frequency vs. orientation angle 68

77 8 sec 4 sec sec 6 sec 1 sec 1 sec Dynamic Liquid Distribution Angle % Spread Avg Avg ODF 1 8 Frequency (%) Spread (%) Orientation Angle Figure Woodpulp/Polyester 1.6 top) polar plot of the actual liquid spread bottom) %spread and %frequency vs. orientation angle 69

78 8 sec 4 sec sec 6 sec 1 sec 1 sec Dynamic Liquid Distribution Angle % Spread Avg Avg ODF 1 8 Frequency (%) Spread (%) Orientation Angle Figure Woodpulp/Polyester 1.94 top) polar plot of the actual liquid spread bottom) %spread and %frequency vs. orientation angle 7

79 Further evaluation of the change of shape in the liquid spread can be found in the Cos Anisotropy section of this chapter. A Chi-Square test was also performed to see how close the relationship of the liquid spread was to the ODF. (See Table 4.1-) Table 4.1- Chi-Square for liquid spread vs. ODF for Woodpulp/Polyester Sample Set A Subset 1 Subset Subset 3 Chi Square Probability The test results in a probability of one. The liquid spread exactly follows the path of the ODF. This is important because this shows that regardless of the material used the shape of the liquid spread is dictated by the structure of the material not the materials themselves Cos Anisotropy It will be recalled that it is standard practice to define the structure anisotropy as the machine frequency over the cross frequency. This number, that is used to describe the general trend of the liquid spread, can be misleading due to local heterogeneities of the material that cause irregular shapes to form. It is also misrepresentative if the liquid spread is not centered on the machine or cross direction such is the case with a bi-modal distribution. When examining the pictures found in Figure 4.1-6, it can easily be seen that the two spreads are different. However, if only the conventional method of measuring anisotropy were used to evaluate the spread, the values resulting from the calculations would give the impression that the two were in fact the same. For this reason the cos anisotropy is used because, as discussed earlier, the equation evaluates the 71

80 liquid spread at every angle and thus, the values obtained for the following spreads would reflect the differences in the shape of the boundaries. Figure Boundary of two separate liquid spreads The cos anisotropy describes the general shape of the liquid spread at any given moment in time. As stated in the experimental methodology section the closer the value is to -1 the more the liquid spread is aligned in the machine direction and the closer the value is to +1 the more the liquid is aligned in the cross direction. A value of zero indicates complete randomness and thus, in the case of liquid distribution, a circular front. Graphing the cos anisotropy at given points locally in time over a set time period produces the trend for the change in the liquid spread front as a function of time. Graphs of the %spread versus orientation angle with respect to time and graphs of the cos anisotropy are pictured in Figure 4.1-7, Figure 4.1-8, and Figure The graph of the %spread versus orientation angle with respect to time display the fact that the shape of the liquid distribution does not change greatly over time. In other words the fluid front is always growing fastest in the machine direction. To determine if the shape is increasing in the machine direction or decreasing in the machine direction the cos anisotropy were graphed. The symbols that are graphed represent the values for the anisotropy and the line running through these circles are linear regression lines. These lines were plotted to determine the slope of the best-fit line. The slopes for all three graphs are only slightly negative. Therefore, it is 7

81 determined that there is no significant change in the shape of the graph in the machine direction. 15 Spread (%) Orientation Angle Time (sec) Machine Direction Cos Anisotropy Linear Regression Line.5 Cos Anisotropy f p = (cos Θ) Time (sec) Figure Woodpulp/Polyester 1.5 top) %spread vs. orientation angle w/ respect to time bottom) cos anisotropy vs. time 73

82 15 Spread (%) Orientation Angle Time (sec) Machine Direction Cos Anisotropy Linear Regression Line.5 Cos Anisotropy f p = (cos Θ) Time (sec) Figure Woodpulp/Polyester 1.6 top) %spread vs. orientation angle w/ respect to time bottom) cos anisotropy vs. time 74

83 15 Spread (%) Orientation Angle Time (sec) Machine Direction Cos Anisotropy Linear Regression Line.5 Cos Anisotropy f p = (cos Θ) Time (sec) Figure Woodpulp/Polyester 1.94 top) %spread vs. orientation angle w/ respect to time bottom) cos anisotropy vs. time 75

84 4.1.4 The Effect of Basis Weight on In-Plane Liquid Distribution The three subsets for sample set A have been shown to have the same ODF. Their liquid spreads have also been shown to follow the trend of the ODF for that particular fabric. The difference in the rate of change in the liquid spread, however, has not been revealed. All the blends are 5/5 Woodpulp/Polyester blends and therefore, as the basis weight increases the level of woodpulp also increases. The woodpulp is the driving mechanism for liquid uptake in this fabric. We wanted to determine if more woodpulp would cause the rate of the liquid spread to change within the fabric. Figure shows the rate of the liquid spread for all three subsets of sample set A Area (sq.cm) Time (sec) Figure Comparison of the effect of basis weight on the liquid distribution rate The graphs show there is little or no difference in the rate of the liquid spread for each of the basis weights. Either the difference in basis weight may not have been substantial enough to change the rate of the liquid spread considerably or the increase of the 76

85 polyester along with the increase of woodpulp canceled out any effects on the rate that the woodpulp may have had Sample Stage Contour of Liquid Spread There is no significant difference in the liquid spread properties of the subsets in sample set A. Their ODFs are the same, the liquid spreads follow the trend of the ODFs, and the rate of the liquid spread is even the same. Therefore, when trying to determine the effect of sample stage on the properties of the liquid spread, only Woodpulp/Polyester with the 1.5 basis weight was tested. Either of the other two materials would have worked just as well. Figure shows polar plots of the liquid spreads when tested on each of the sample stages. The three stages were described in the last chapter and are the hoop plate, the bottom plate, and the bottom plate with the top plate. Note that the sample stage does not appear to affect the shape of the liquid spread. This may be due to the way in which the pulp, the driving mechanism for the liquid, is distributed within the material. We do not know how well the pulp is distributed within the material, but is assumed that it is evenly distributed throughout the material for, if it were not, we would see local variations of the spreading. These local variations are more prominent in the second sample set and will be shown to have an effect on the liquid distribution according to the method in which the testing is carried out. 77

86 8 sec 4 sec sec 6 sec 1 sec 1 sec Dynamic Liquid Distribution Angle Hoop. sec 1. sec.5 sec 1.5 sec.5 sec 3. sec sec 1. sec.5 sec 1.5 sec.5 sec 3. sec Dynamic Liquid Distribution Angle Dynamic Liquid Distribution Angle Bottom plate 7 Bottom with top plate Figure Plot of actual liquid spread on each of the three plates Rate of Liquid Spread The shape of the liquid spread for sample set A is not affected by the sample stage chosen, however, the rate of liquid spread changes significantly. As discussed earlier in the experimental methods and procedures an extra capillary is added when the bottom plate stage is used and two extra capillaries are added when the bottom plus the top plate is used. Figure shows the actual liquid spread for each stage. 78

87 Single front Hoop Plate Two fronts Bottom Plate Two fronts Bottom with Top Plate Figure Actual liquid spread as seen during testing. Note the two fronts in the bottom two pictures 79

88 Note the two fronts for the bottom plate and the bottom with top plate. These are the extra capillaries formed between the plate and the fabric surface. The hoop plate has a small dark middle where the sample is in contact with the delivery hole, but this extends no further than the boundary of the middle delivery cylinder. The test for the hoop, bottom plate, and bottom with top plate needed an average of 4 seconds, seconds and eight seconds to complete respectively. Figure shows the change in area with respect to time for all three stages. 8 7 Hoop w/ bottom plate w/ bottom and top plate Spread Area (sq.cm) Time (sec) Figure Area vs. Time for hoop, bottom, and bottom w/ top plate The graph emphasizes the difference when the traditional stages are used as compared to when the new hoop plate is used. Therefore, it is felt that the traditional stages cannot be utilized to measure the true intrinsic wicking rate of the material because the capillaries cause the liquid to move through the material at a much faster pace. The hoop method, however, does measure the true intrinsic wicking rate of the material because no additional capillaries are added to the system. 8

89 4.1.6 NCRC Horizontal Test Another test method used to measure wicking is the NCRC directional wicking test where a strip of fabric is cut at a particular angle and the liquid absorption is measured. This test was described in an earlier chapter and was basically introduced as a form of testing to eliminate the gravity affects that occur when testing using the vertical wicking test. From sample set A, subset one was tested using the NCRC horizontal wicking test so that a comparison could be made between the tests using a strip of material with that of a test using a circular piece of material. Pictures of the liquid spread for the horizontal wicking test are shown in Figure Figure Actual spread of liquid during the NCRC directional wicking test. Top) shape of spread at the start of test Bottom) shape of spread at end of test The image on the left was cut in the cross direction and the image on the right was cut at a 6 ο angle. This is clear when looking at the spread of the liquid in the pictures at the top of the figure. However, when looking at the spread of the liquid in the pictures at the bottom of the figure it is not so obvious. This discrepancy between the shape at the beginning and the shape at the end is due to edge effects. 81