In-Plane Liquid Distribution In Nonwoven Fabrics: Part 2 Simulation

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1 ORIGINAL PAPER/PEER-REVIEWED In-Plane Liquid Distribution In Nonwoven Fabrics: Part 2 Simulation By H. S. Kim, Department of Textile Engineering, Pusan National University, Pusan , South Korea; B. Pourdeyhimi, Nonwovens Cooperative Research Center, North Carolina State University, Raleigh, NC, In a recent paper, we reported on a new absorbency testing system that measures in-plane fluid flow, absorbency and pore volume distribution [8]. The importance of fiber orientation characteristic in nonwovens, as it directly influences the in-plane fluid flow in nonwovens was explored. In this paper, we present a framework for the prediction of in-plane wicking in nonwovens. This paper describes the underlying foundation for the simulation of in-plane wicking and reports on preliminary comparisons between simulation and experimental data. Key Words: Nonwovens, ODF, Liquid Spreading, Simulation, In-Plane Wicking INTRODUCTION Over the last few years, much focus has been placed on research aimed at establishing links between structure and desired macroscopic properties of nonwoven materials. One key feature that remains essentially unsolved is the prediction of moisture transport as a function of structure at the macro scale [3, 4, 8]. In a related paper, we reported on a new instrument for measuring fluid flow though nonwovens [8]. The role of fiber orientation distribution (ODF) on in-plane flow was demonstrated and was reported that the in-plane liquid distribution was driven dominantly by the fiber orientation distribution of nonwovens. In this paper, we explore the applicability of a simulation method for the prediction of in-plane fluid wicking and reports on comparisons between experimental and simulation data. We further demonstrate the link between ODF and inplane fluid flow for structures differing in fiber orientation distribution. THEORETICAL BACKGROUND (SPREADING LENGTH) The framework below was developed by Russel, et.al [3,4]. For completeness, we present a summary below, and demonstrate how it may be extended to determine spreading. The drag force per unit length acting on a single fiber surrounded by similar fibers, all oriented along the direction of flow can be deduced [1]: where and ø is the volume fraction of solid materials, n is the internal viscosity of the fluid and q is the superficial flow velocity of the fluid stream. The drag force per unit length acting on a single fiber oriented perpendicular to the fluid flow is given by: (2) where The drag force acting on the fiber in the direction θ can be obtained by considering the contribution of each of the components of the drag force and flow velocity on the equation (1) and (2): (1) (3) 29 INJ Summer 2003

2 where n is aligned angle of a fiber of a particular unit length, α is the fluid flow direction over the fiber. The total drag force on the material is equal to the sum of the individual drag forces acting on each fiber [1]. Hence, for a flow in a particular direction, say θ, the drag force acting on all the fibers, where the unit volume of the fabric consists of n fibers, will be, where n is the number of fibers of unit length per unit volume and Ω(α) is fiber orientation function. The ODF Ω is a function of the angle θ. The integral of the function Ω from an angle θ 1 to θ 2 is equal to the probability that a fiber will have an orientation between the angles θ 1 to θ 2. The function Ω must satisfy the following conditions: (4) given by Laplace equation given below: (10) Where Rc is the capillary radious, σ is the surface tension and µ is the contact angle. According to equation 9, the capillary pressure in the direction θ in the fabric will be (11) Substituting k(θ)and p(θ) into one dimensional D Arcy s Law, the rate of absorption in the direction θ [3, 4]: (5) (12) The pressure gradient in the flow direction due to the drag force in unit volume of the fabric is equal to the pressure drop per unit length of flow resulting from the drag force in this direction. Thus, (6) From the rate of absorption, we can derive equation 13 below for predicting the spreading length: The established theory of laminar fluid flow through homogenous porous materials is based on D Arcy s Law [2] described as: Thus, by substituting from Equation (3) into D Arcy s law the directional permeability is given by [3, 4]: The hydraulic radius theory treats the flow through a porous medium as a conduit flow. The equivalent hydraulic capillary diameter, D H, in the direction θ in the nonwoven fabrics will be: The magnitude of the capillary pressure, p, is commonly (7) (8) (9) (13) IMAGE CAPTURE AND ORIENTATION DISTRIBUTION FUNCTION The material used for (see Figure 1) is a hydroentangled 50/50 woodpulp/polyester blend. The specimen was illuminated by a directional light source described previously [5]. A CCD camera equipped with a macro zoom lens was used to capture images large enough for further analysis. The ODF was determined using our FFT procedure and is shown in Figure 2. This is an essential input for the in-plan liquid wicking simulation scheme. A full description of the Fourier transform for nonwoven web was given previously [6]. IN-PLAN LIQUID SPREADING For comparison purposes, in-plan liquid spreading was determined by using our absorbency device previously described [8]. This instrument is set up with a liquid reservoir that is placed on top of a balance (or a compression load cell) and is connected to the bottom of a plate using a plastic tube. In addition to this configuration, a camera is mounted above 30 INJ Summer 2003

3 the plate and is used to record the spreading of the liquid. The new instrument uses an A/D interface card and appropriate software for fast and accurate data collection. The software automatically maintains the platform height at the same level as the reservoir, thereby maintaining a constant pressure head during testing. 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, and the image stays in focus. A full description of the device was given previously [8]. Figure 1 IMAGE OF NONWOVEN SAMPLE USED IN THIS STUDY Figure 2 ORIENTATION DISTRIBUTION FUNCTION FOR IMAGE SHOWN IN FIGURE 1 RESULTS AND DISCUSSION The results from experimental and simulation are shown together in Figure 3. A reasonable agreement is seen between the two. The experimental data indicate that the spreading rate is faster than the one predicted by simulation. This may be in part due to any surface finish that may be present on the surface of the fibers. Additionally, this difference may be partly because of the slight differences between the simulation and the actual experimental set up. The opening in the instrument plate connected to the tube is about 1cm in diameter in comparison with that of the simulation which is assumed to be a point. Regardless however, the anisotropy of the flow is predicted correctly. A simulation scheme such as the one described here, can help eliminate much of the elaborate experimentation that is currently required in the development of new products or the improvement of current products and processes. We demonstrate the role of structure by examining a case where the structures fiber orientation distributions are different. The extreme cases chosen for this purpose are shown in Figure 4. Images with such an ODF are simulated and shown Figure 5. It will be expected that a uniform random distribution will result in a perfectly circular liquid spreading and that the degree of ellipticity of the distribution will increase with increasing ODF anisotropy. This is indeed the case as may be seen in the simulated results shown in Figure 6 and confirms our previously reported experimental data [8]. Figure 6. Predicted in-plane wicking for images shown in Figure 5. Figure 3 IN-PLANE WICKING RESULTS; EXPERIMENTAL (LEFT) AND SIMULATION (RIGHT) CONCLUSIONS We have presented a simple simulation scheme for predicting in-plane liquid spreading in nonwovens. We note the role of structure on spreading and conclude that the in-plane liquid spreading is driven by structure anisotropy. We believe that the method reported here has important implications for the accurate simulation of wicking and has considerable promise in eliminating much of the elaborate experimentation that is currently required in the understanding the wicking behavior of nonwoven fabrics. 31 INJ Summer 2003

4 Figure 4 FIBER ORIENTATION DISTRIBUTIONS SELECTED FOR SIMULATION Figure 6 IMAGES WITH FIBER ORIENTATION DISTRIBUTIONS SHOWN IN FIGURE 4 32 INJ Summer 2003

5 REFERENCE 1. Happel, J., Viscous Flow Relative to Arrays of Cylinders. Amer. Inst. Chem. Engrs J, 5, (1959) 2. D Arcy, H., Les Fontaines Publiques de la Ville de Dijon, Dalmont, Paris, France (1856) 3. Mao, M. and S. J. Russell, Directional Permeability in homogeneous Nonwoven Structures: Part I: The Relationship between Directional Permeability and Fiber Orientation, J. Text. Inst., 1(2), (2000) 4. Mao, M. and S. J. Russell, Directional Permeability in homogeneous Nonwoven Structures: Part II: Permeability in Idealised Structures, J. Text. Inst., 1(2), (2000) 5. Pourdeyhimi, B., Dent, R., Jerbi, A., Tanaka, S. and Deshpande, A., Measuring Fiber Orientation in Nonwovens, Part V: Real Webs, Textile Res. J. 67, (1997). 6. Pourdeyhimi, B., R. Dent and H. Davis, Measuring Fiber Orientation in Nonwovens, Part III: Fourier Transform, Textile Res. J., 67(2), (1997). 7. Durran, J. H., Statistics and probability, London, Cambridge U.P. (1970). 8. Konopka, A., B. Pourdeyhimi and H. S. Kim, In-Plane Liquid Distribution of Nonwoven Fabrics: Part I, Experimental Observations, INJ, Winter Vol 11, No. 4 (2002). ACKNOWLEDGEMENTS This work was supported in part by Nonwovens Cooperative Research Center. Their generous support of this project is gratefully acknowledged. INJ 33 INJ Summer 2003