Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, 842 West Taylor Street, Chicago, IL , USA 2

Transcription

1 Shear and Elongational Rheology of Gypsum Slurries Suman Sinha-Ray 1, Raman Srikar 1, C.C. Lee 2, A. Li 2, Alexander L. Yarin 1,3 1 Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, 842 West Taylor Street, Chicago, IL , USA 2 USG Corp., Research & Technology Center, 700 N US Highway 45, Libertyville, IL 60048, USA 3 Center for Smart Interfaces, Technische Universität Darmstadt, Petersenstrasse 32, Darmstadt, Germany *Corresponding author: ayarin@uic.edu Fax: x Received: , Final version: Abstract: Concentrated gypsum slurries used for wallboard production are studied using shear and elongational rheometers. It is shown that the rheological behavior of different slurry compositions can be sufficiently accurately described in the framework of the Ostwald de Waele power law, which reproduces both shear and elongational experimemtal data with sufficiently close values of the consistency and flow behavior indexes for each slurry composition studied. Zusammenfassung: In dieser Arbeit wurden konzentrierte Gipsschlämme für die Produktion von Wandbauplatten mit Hilfe scherund dehnrheologischer Messungen untersucht. Es wird gezeigt, dass die rheologischen Eigenschaften für verschiedene Schlammzusammensetzungen ausreichend genau mit Hilfe des Ostwald-Waele Potenzgesetzes beschrieben werden können, das sowohl die experimentellen Daten in Scherung als auch in Dehnung mit ausreichend hoher Präzision für den Konsistenz- und den Fließverhaltensindex für alle Schlammzusammensetzungen erfassen kann. Résumé: Des boues concentrées de gypse utilisées pour la production de panneaux muraux ont été étudiées à l aide de rhéomètres extensionels et rotationnels. Nous démontrons que le comportement rhéologique des différentes compositions de boue peut être suffisamment et précisément décrit dans le cadre du modèle Ostwald-de Waele à loi de puissance, qui reproduit les données expérimentales avec des valeurs suffisamment proches des index de consistance et de comportement d écoulement pour chaque composition de boue étudiée. Key words: gypsum slurry, shear rheology, elongational rheology, power-law fluid, flow curve, capillary thread thinning 1 INTRODUCTION Gypsum is a naturally occurring mineral, which is also referred to as calcium sulfate dihydrate. Gypsum in the form of stucco, when mixed with water at sufficient concentrations, constitutes concentrated slurries. Such slurries represent themselves a key element of gypsum processing in industry to wet-form gypsum products, e. g. wallboards. In addition, gypsum slurries solidify due to rapid hydration of gypsum and evaporation of water. Rheology of gypsum slurries is an uncharted area and is tremendously important for gypsum processing. Generally speaking, gypsum slurries belong to a wide class which can loosely be termed as muddy materials, materials with a complex internal structure or construction materials. Complicated rheological behavior of such materials is currently in focus [1 10]. In the present work the term gypsum is applied to b-hemihydrate form of synthetic gypsum obtained by the desulfurization of flue gases at coal fired power plants. The term stucco used below is understood as a shorter term applied to this form of gypsum, namely, CaSO 4 (1/2)H 2 O. Rehydration of stucco in water proceeds according to the following reaction [11] in which b-hemihydrate transforms into dihydrate [CaSO 4 2H 2 O] by binding more water, whereas its molecular weight increases from Da to Da. The reaction is exothermic with the heat release Q = J/g. The Reaction (1) is not only chemical but also structural. In (1) Appl. Rheol. 21 (2011) DOI: /ApplRheol

2 Figure 1 (above): SEM image of stucco particles as received. Figure 2: Schematic of the elongational rheometer used in the present study. Table 1: Slurry density. particular, mixing of stucco with water for 60 s can result in complete disintegration of stucco particles, which is accompanied by reduction of the median particle size from 24 to 1.4 mm [11]. Moreover, the Reaction (1) is accompanied by three-stage solidification process: (1) a true crystalline intergrowth where ions are shared within the particles, (ii) a gel-like network formation with crystalline outgrowth through water-filled spaces between the particles, and (iii) hydrogen bonding of touching crystals. Rheology of stucco slurries can be treated as time-independent for sufficiently short time intervals (of the order of minutes from the moment of preparation). Longer than that, the effect of Reaction (1) and the accompanying solidification should be already felt. The present work deals with such short time intervals which correspond to real industrial slurry processing before aging and solidification become important. Slurry rheology is significantly affected by a number of additional parameters: for example, water/ stucco ratio, mixing conditions, additives, etc. In this work, shear and elongational rheometry of gypsum slurries is studied. The article is organized as follows. Materials and methods used for preparing slurries are described in section Materials and Methods. The next section is Results and Discussions. There the rheological behavior of gypsum slurries is outlined in the sub-section Preliminary Observations and Theoretical Frame - work. The detailed results of the shear measurements are discussed in the sub-section Rheological Characteristics of Slurries Found in Shear Flows, the surface tension measurements needed to process the experimental data of the elon gational experiments are de scribed in the subsection Surface Tension Measurements for Slurries, and the method and results of the elongational measurements and their comparison with the shear data are given in the sub-section Elongational Rheology of Gypsum Slurries. After that, conclusions are drawn. 2 MATERIALS AND METHODS Stucco-b-hemihydrate form of synthetic gypsum (Figure 1) - and all the additives were supplied by US Gypsum Corporation, IL. Deionized water was used for preparing slurries in all the cases. Stucco with additives was allowed soaking in water for 15 s. After that, the suspensions were mixed vigorously for additional 15 s using a rotary mixer. Deionized water was used for slurry preparation. The water-to-stucco ratio WSR ranged from 70 to 90 (for example, the notation 75WSR represents 75 parts of water to 100 parts of stucco by weight). The slurry was then poured into the shear rheometer and measurements were carried out. The shear rate and time scale of the measurements were set up corresponding to the experiment requirements. The slurry density for different compositions was measured. The density is given in Table 1. The compositions listed in Table 1 varied not only in water content but also in the other property-control agents, in particular, in air content (added with foam) responsible for density variation at a fixed WSR. In the present work all the shear experiments for the rheological characterization of gypsum slurries were carried out using the shear viscometer, TA Instruments AR 2000ex. Surface tension measurements for stucco slurries were carried out using the Krüss Bubble Pressure Tensiometer Model BP2. A diluted stucco slurry (concentration of water in slurry > 75WSR-water to stucco ratio) was prepared and investigated using the tensiometer. The measurements were carried out several times to ensure repeatability. Prior to these measurements, the capillary diameter used for measuring the bubble pressure was found using water as a standard whose physical parameters was known. The elongational rheometer was similar to that of [2]. The schematic of the experimental setup is shown in Figure 2. The elongational rheometer consisted of a stationary lower plate and a movable spindle-like upper contact, whose

3 motion was controlled by a solenoid. Elongational rheometry of 75 WSR (composition 11 in Table 1) is done only. Stucco with additives was allowed soaking in water for 15 s. After that, the suspensions were mixed vigorously for additional 15 s. Then, a single droplet of the prepared slurry was rapidly (in 5 10 s) transferred to the elongational rheometer. Droplets were used in the elongational experiments. They were stretched by the spindle-like contact, and then experienced capillary self-thinning, the later being the observation stage. The experiments were repeated with the same droplet for 2 3 times to elucidate the effect of the water evaporation and hydration reactions in the slurry (ultimately leading to solidification) on the rheological parameters. The evolution of diameter of pinching threads was recorded using a high speed digital camera (Redlake-Motion Pro) equipped with a 185 mm macro lens at the frame rate of 500 fps. The images thus obtained were analyzed using the image analysis software developed on the platform of MATLAB R-2007A. The complete process starting from slurry mixing to the end of thread self-stretching experiment was recorded using a digital camcorder to quantify the timing involved in every single operation. 3 RESULTS AND DISCUSSION 3.1 PRELIMINARY OBSERVATIONS AND THEORETICAL FRAMEWORK The measured effective shear viscosity versus shear rate reveals that the rheological properties of gypsum slurries are strongly affected by their composition. For example, the effective shear viscosity decreased with the increase of the water-to-stucco ratio, WSR. The preliminary ex - peri ments suggested that gypsum slurries are non-newtonian fluids and the first rheological constitutive equation to be applied to them should be the Ostwald de Waele power law [12] (2) where s is the stress tensor, t is the stress deviator tensor, p is pressure, D is the rate of-strain tensor, I is unit tensor, K is the consistency index and n is the exponent (the flow behavior index). In simple shear flows Equation 2 reduces to where m shear is equal to m shear = t xy /g, with t xy being the shear stress, and g the shear rate. Simple shear flows in rheometry are typically employed at a constant shear rate g (which values can be chosen different). Then, measurements of shear viscosity are conducted after transients have faded. In the present experiments this shear rheo - meter was operated with a gradually increasing shear rate. Therefore, the value of g was not set in the present experiments but was linearly increasing in time. The interpretation of such experimental data requires a fully transient de - scription which is provided below. The momentum balance equation for shear flow of slurry under the assumption that the power-law model (Equation 2) is applicable is given by (3) (4) where u(y) is the velocity profile, and y is the coordinate normal to the wall, r is the density and t is time. The initial and boundary conditions imposed are as follows (5) where h is the gap and A is the acceleration. According to Equation 2, the effective shear viscosity m shear = t xy /g is given by (6) Equation 4 and 5 were solved numerically by the method of finite differences. Namely, all the theoretical curves for shear flows arise from the numerical solutions of Equation 4 subjected to the initial and boundary conditions (Equation 5). Using the numerical results, the shear rate is

4 Figure 3: The effective shear viscosity (flow curve) for: 80 WSR system-composition 5, 75 WSR system-composition 1, 80 WSR system-composition 2, 85 WSR system-composition 3, 90 WSR system-composition 4, 80 WSR system-composition 6, 80 WSR systemcomposition 7, 75 WSR system-composition 8, 75 WSR system-composition 9. Table 2: Rheological parameters of gypsum slurries. found at any time moment as g = u/ y and the effective shear viscosity m shear is found using Equation 6. The results were compared to the ex - perimental data for various water-stucco ratios in gypsum slurries to determine the corresponding values of K and n. 3.2 RHEOLOGICAL CHARACTERISTICS OF SLURRIES FOUND IN SHEAR FLOWS The results of some of our shear experiments are compared to the theoretical flow curves as shown in Figure 3. The experimental data is plotted by symbols and the theoretical curves are depicted by lines. It is emphasized that Figure 3 does not represent themselves conventional flow curves, since they correspond to the experiments and computations for the simple shear flow with variable in time, rather then constant shear rate. This means that both the effective viscosity and shear rate depend on time, rather represent themselves time-independent values as in the case of the conventional flow curves. The data and curves in Figure 3 are not straight lines in the log-log framework, since initially the flow is not fully developed. Indeed, the model predicts that during the initial shear rates, the flow is underdeveloped, the velocity profile is not triangular, as is assumed by the rheometer software, and hence no meaningful agreement with the rheometer-processed data can be achieved. According to the theoretical predictions, the flow becomes fully developed beyond the shear rate of s -1. In that range fitting of the theory to the measured data is possible and produces meaningful values of the rheological parameters K and n. Their values corresponding to all the compositions studied are given in Table 2. The successful comparison in the range above s -1 shows that the effects of water evaporation and slurry solidification due to the chemical Reaction (1) are still negligible in the present experiments. In the experiments the acceleration was of the order of A ª 10 cm/s 2, the effective gap filled with slurry of the order of 0.1 cm, and the duration of shear tests similar to those in Figure 3 was about 20 s. Each experiment started about 45 s after slurry preparation has begun, which made the total time to the end of each shear test of about 65 s. An additional delay of about 40 s was already sufficient for the hydration and solidification being felt, which determined the need in the transient rather than steady-state shear experiments in the present work. Similar comparisons of the measurements and the theoretical predictions were done for a range of slurry compositions. Table 2 lists the results for the values of the rheological parameters K and n found in all the cases. In order to ensure repeatability, all the experiments were carried out more than once. The values of the consistency index and the corresponding average errors for four compositions are shown in Figure 4. An additional benchmark for comparison of the theory with the experimental data is provided by the case of viscous Newtonian test fluids with independently verified viscosity values. The comparison of the measurements and the theory for one such fluid, a standard solution S600 was done. Fitting the theory to the experimental data revealed the viscosity value of 18.6 Poise, whereas the standard independently measured value is reported as Poise. This is quite close given the fact that the data were obtained using the rheometer with a cross-like rotor (as is required for testing gyp

5 sum slurries for their easy pouring and removal) and thus, pronounced three-dimensional effects. The results in Table 2 show the following general trends for the consistency index and power law exponent with variations in system composition. The value of n increases with the increase in water content relative to that of stucco. However, even at 90 WSR, slurry still does not approach Newtonian behavior, and stays significantly pseudoplastic (with n = 0.56). The value of the consistency index K increases with the decrease in water content in the slurry. Therefore, lower water content results in a higher effective viscosity of slurries. Also, lower water content enables faster solidification of slurries, which manifests itself in a dramatic increase in K. This dramatic increase in K is expressed by the data in Table 2, which shows that the increase in K value is almost 100 % when the system changes from 75 WSR to 70 WSR. An analytical correlation of the experimental data on shear rheology of stucco slurries is desirable to be able to extrapolate the results towards compositions for which measurements are extremely difficult due to the rapid setting time. The experimental results for the consistency index K of compositions 1 4 from Table 1 are plotted versus the water-to-stucco ratio (WSR) in Figure 5. The data can be fitted using the linear correlation K = ( WSR) A similar fit for the exponent value yields n = (0.012 WSR) SURFACE TENSION MEASUREMENTS FOR SLURRIES The values of surface tension coefficient measured in this sub-section will be used in the processing of the results of elongational experiments described in the following section. The data for the stucco slurry is presented in Table 3. The average value of surface tension for the slurry was found to be mn/m which is significantly higher than that of water. The increase in the effective surface tension is a manifestation of surface solidification processes proceeding in an accelerated manner at the free surface due to water evaporation. Another step towards measuring surface tension of the slurry was implemented employing contact angle measurements using NRL Contact Angle Goniometer Model The instrument incorporated a camera which allows for accurate measurements of contact angles. A slurry drop was placed gently onto a horizontal surface ( glass) aligned to the camera and the contact angle measurements were then conducted. It was found that for 75 WSR (composition 11) slurry the average contact angle was approximately 55.81, and for 85 WSR (composition 12) slurry the average contact angle was The error in both cases was less than 10 %. According to Young s equation, g SG = g SL + g LG cosq c, where g SG represents the surface tension between glass (solid) and air (gas), g SL represents the surface tension between glass (solid) and liquid, g LG represents the surface tension between liquid and air (gas), and q c represents the contact angle. For pure water droplet, correspondingly, g SG = g SL + g W cosq cw, where g W and q cw are the surface tension and contact angle of water, respectively. It is emphasized that we assume g SG and g SL to be the same for both water and slurries on glass. Also, it is known that g W = 72.1 mn/m and q cw =18. Therefore, g LG = g W cosq cw /cosq c which yields the surface tension of 75 WSR (composition 11) slurry as g LG75 = mn/m, and the surface tension of 85 WSR (composition 12) slurry as g LG8 5 = mn/m. Both values are relatively close to the average value of the surface tension of the diluted slurry in Table 3, mn/m, which corroborates the latter. We can conclude that the effective surface tension of slurries is significantly higher than that of water. Figure 4 (above): (a) Consistency index for 70 WSR system-composition 10. The error bars represent the average error = ± 6.13 % maximum; consistency index for 75 WSR-composition 8. The error bar represents the average error = ± % maximum. (b) Consistency index for 75 WSR system-composition 11. The error bar represents the average error = ± % maximum; consistency index for 75 WSR-composition 9. The error bar represents the average error = ± %. Figure 5: The consistency index and flow behavior index versus WSR. The symbols represent the experimental data and the solid line the linear fit. The data correspond to compositions 1 4 from Table 1, which differ only in their WSR values but have the same amount of air and other additives. Table 3: Surface tension of diluted stucco slurry (concentration of water in slurry > 75WSR)

6 Figure 6 (left): Self-pinching cylindrical liquid thread. Figure 7: Thread diameter versus time in the 1st stretching experiment (slurry 75 WSRcomposition 11). The inserted images show the slurry thread at different moments during its capillary self-pinching. The scale bar in the images is 1 mm. The experimental data is shown by symbols, the curve was plotted according to Equation 8, the corresponding values of the consistency index K and power n are also shown. of g LG used in this work was measured in the previous section ( mn/m). Equation 7 can be written as 3.4 ELONGATIONAL RHEOLOGY OF GYPSUM SLURRIES Shear rheology alone is incapable to fully uncover true rheological behavior of complex non- Newtonian fluids [13]. The shear mode measurements typically are insufficient to shed light on the rheological behavior of the same non-newtonian fluid in elongational flow. In the present work, an elongational rheometer developed in our previous works [2, 13 17] is applied to study the rheological behavior of gypsum slurries. In order to ascertain rheological description of a fluid, the constitutive equation in question should consistently fit both the elongational and shear measurements with the same set of parameters. The elucidation of the capability of the powerlaw constitutive equation (2) to describe both shear and elongational behavior of gypsum slurries in both shear and elongational flows is aimed in the present section. The elongational rheometry is based on the observation of flow in a self-thinning liquid thread driven by capillary forces (self-pinching; Figure 6). It is described in the framework of the quasi-one dimensional equations of the dynamics of liquid jets and threads [18] and in the case of the power-law Equation 2 reduces to the following equation for the evolution of the thread diameter as a function of time (7) where d is the diameter of the pinching thread, d 0 is the initial diameter of the thread, t s is the time of pinching, t is time, b 1 is a theoretically established constant (0.175) required to account for the thread non-uniformity [13, 19, 20], and k = K/g LG, where g LG is the surface tension. The value where (8) (9) The results of the elongational experiments for d(t) were processed by fitting Equation 8 using the least square method which allows for the evaluation of the values of K and n. It is emphasized that due to the fast solidification of gypsum slurries not every experiment was considered to be successful. For the 1st elongational experiment with any droplet the following two criteria were established for segregation of successful experiments: (i) the initial diameter of the thread at the centre should be at least 1.2 mm, and (b) there should be at least 12 data points recorded before complete thread pinching. To achieve statistically sound results (with respect to the Gaussian probability density function), data from 34 successful experiments were used for the evaluation of the rheological parameters K and n corresponding to the 1st elongational experiment. Of these 34 experiments, only 14 led to successful 2 nd stretching experiments with the same droplet. A more relaxed segregation criterion was formulated for the 2 nd experiment. Still, the successful 2 nd stretching experiment is the one, which provided at least 12 data points. The relaxation in the criterion for the 2 nd stretching experiment was dictated by rapid evaporation of water from the surface of small slurry droplets employed in the elongation experiments, which accelerated slurry setting. Accordingly, no successful experi

7 Figure 8 (left): (a) Values of K, and (b) values of n found for all 34 successful experiments on the 1 st stretching (slurry 75 WSRcomposition 11). The solid lines correspond to the averaged values, the dotted lines to the standard deviations. Figure 9: (a) Values of K and (b) values of n found in the 14 successful 2 nd stretching experiments with the same droplet (the data for the 1st stretching is also shown for comparison, 75 WSR-composition 11). Except one case (the encircled data points) the value of n decreased and the value of K increased in the 2 nd stretching compared to the first one. ments were found for the 3 rd stretching of the same droplet. One of the 34 successful experiments on the 1st stretching is shown in Figure 7. The theory, Equation 8 was fitted to the experimental data using the least square method and the corresponding values of the rheological parameters are shown in Figure 8. Using the measured value of the surface tension of slurry ( mn/m), the value of the consistency index K is found out to be g/cms 2-n, while n = Values of K and n for the other successful experiments of this series are combined in Figure 8. The average values of n and K are n = 0.6 ± and K = ± g/cms 2-n. The large standard deviation in the value of K can be attributed to variability in slurry mixing and non-uniformity of slurries, which are ultimately related to irregular shapes and sizes of the stucco particles (Figure 1), as well as some inevitable variation in size of the initial droplets used in the elongational tests. In Figure 8a the red point corresponds to the value of K, to which corresponds the encircled value of nin Figure 8b. For this data point, the 1st stretching of slurry droplet was done in 60 s. after the moment when water was added to stucco at the stage of slurry preparation, whereas for all the other data points-only in s. This was done on purpose, to evaluate the effect of slurry setting on the results. The comparison of the red data point with the other data points shows that slurry setting results in increasing the consistency index K and decreasing the value of n- both trends in the direction of a more pronounced pseudoplasticity. When the values of the rheological parameters n and K presented in Figure 8 (n = 0.6 ± and K = ± g/cms 2-n for elongation of 75 WSR-composition 11) are compared to the values obtained in shear experiments (Table 2: n = 0.55 and K = g/cms 2-n for shear of 75 WSR-composition 11), it can be seen that the values of n are rather close, whereas there is a difference in the values of K. This might be due to an inaccuracy in the value of the surface tension coefficient used to process the data of the elongational experiments. The rheological parameter values evaluated from the 14 successful 2 nd stretching experiments are plotted in Figure 9. The data in Figure 9 show a clear tendency of the value of n to decrease and the value of K to increase for the 2 nd stretching of the same droplet compared to the 1st one. This shows a clear tendency toward the enhancement of pseudoplasticity of slurry due to water evaporation and hydration chemical reactions, similarly to the finding related to different delay times in the 1st stretching experiment discussed before. 4 CONCLUSIONS Using the shear and elongational viscometry, it is shown that concentrated gypsum slurries can be roughly characterized as materials following the tensorial Ostwald de Waele (power law) constitutive equation. The other known examples of materials which follow the tensorial power law constitutive equation in both shear and elongation with roughly the same values of the rheological parameters (the consistency index K and flow behavior index n) also include suspensions of needle-like g-fe 2 O 3 particles in oil and gelled propellant simulants [13, 18]. However, the fami

8 ly of such materials is not wide. Indeed, the power law model is frequently used to fit the shear data but very rarely efforts are directed to simultaneous elongational testing, which in many cases would disprove applicability of the tensorial model, as for example, in the case of polymer solutions and melts. In the present work the tensorial power-law rheological behavior was established for gypsum slurries with different water content and compositions. In particular, the values of the rheological parameters n and K found in elongation of slurry with water-to-stucco ratio of 75 (composition 11) were: n = 0.6 ± and K = ±16.18 g/cm s 2-n, whereas for shear of the same slurry it was found that n = 0.55 and K = g/cms 2-n, which is sufficiently close. ACKNOWLEDGMENTS This work was supported by The US Gypsum Corporation (USG). The authors thank Drs. K. Natesaiyer, D. Song, S. Veeramasuneni, as well as W. White and D. Dannessa (USG) and Dr. C.M. Megaridis (UIC) for useful discussions. REFERENCES [1] Barnes HA: Thixotropy, rheopexy, yield stress, in Springer Handbook of Experimental Fluid Me - chanics, Springer-Verlag, Berlin, Heidelberg (2007). [2] Tiwari MK, Bazilevsky AV, Yarin AL, Megaridis CM: Elongational and shear rheology of carbon nanotube suspensions-fluids with yield stress, Rheol. Acta 48 (2009) [3] Chalencon F, Orgeas L, Dumont PJJ, Foray G, Cavaille JY, Maire E, Rolland du Roscot S: Lubricated compression and X-ray microtomography to analyse the rheology of a fibre-reinforced mortar, Rheol. Acta 49 (2010) [4] Ferraris CF: Measurement of the rheological properties of high performance concrete: state of the art report, J Res NIST 104 (1999) [5] Banfill PFG: The rheology of fresh cement and concrete-a review, Proc. 11 th Int. Cement Chem. Congress, Durban (2003). [6] Shenoy SS, Wagner NJ: Influence of medium viscosity and adsorbed polymer on the reversible shear thickening transition in concentrated colloidal dispersions, Rheol. Acta 44 (2005) [7] Egres RG, Nettesheim F, Wagner NJ: Rheo-SANS investigation of acicular- precipitated calcium carbonate colloidal suspensions through the shear thickening transition, J. Rheol. 50 (2006) [8] Egres RG, Wagner NJ : The rheology and micro - structure of acicular precipitated calcium carbonate colloidal suspensions through the shear thickening transition, J. Rheol. 49 (2005) [9] Ruiz-Agudo E, Rodriguez-Navarro C: Microstructure and rheology of lime putty, Langmuir 26 (2009) [10] Alexandrou AN, Bazilevskii AV, Entov VM, Rozh - kov AN, Sharaf A: Breakup of a capillary bridge of suspensions, Fluid Dyn. 45 (2010) [11] Kuntze RA: Gypsum. Connecting Science and Technology. ASTM International, West Consho - hocken (2009). [12] Astarita G, Marruci G: Principles of Non-Newtonian Fluid Mechanics, McGraw- Hill, London (1974). [13] Yarin AL, Zussman E, Theron A, Rahimi S, Sobe Z, Hasan D: Elongational behavior of gelled propellant stimulants, J. Rheol. 48 (2004) [14] Stelter M, Wunderlich T, Rath SK, Brenn G, Yarin AL, Singh RP, Durst F: Shear and extensional investigations in solutions of grafted/ungrafted amylopectin and polyacrylamide, J. Appl. Polym. Sci. 74 (1999) [15] Stelter M, Brenn G, Yarin AL, Singh RP, Durst F: Validation and application of a novel elongational device for polymer solutions, J. Rheol. 44 (2000) [16] Stelter M, Brenn G, Yarin AL, Singh RP, Durst F: Investigation of the elongational behavior of polymer solutions by means of an elongational rheometer, J. Rheol. 46 (2002) [17] Brenn G, Yarin AL, Stelter M, Durst F: Capillary thinning of filaments of polymer solutions with surfactants, Colloid Surf A-Physicochem Eng Asp (2006) [18] Yarin AL: Free Liquid Jets and Films: Hydrodynamics and Rheology, Longman, Harlow, and Wiley, New York (1993). [19] McKinley GH: A decade of filament stretching rheology, XIII th International Congress on Rheology, Cambridge, UK (2000). [20] McKinley GH, Tripathy A: How to extract the Newtonian viscosity from capillary breakup measurements, J. Rheol. 44 (2000)