63071-1Applied Rheology Volume 21 · Issue 6 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 evapora- tion of water. Rheology of gypsum slurries is an uncharted area and is tremendously important for gypsum processing. Generally speaking, gyp- sum 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 gyp- sum obtained by the desulfurization of flue gas- es at coal fired power plants. The term stucco used below is understood as a shorter term applied to this form of gypsum, namely, CaSO4∑(1/2)H2O. Rehydration of stucco in water proceeds according to the following reaction [11] (1) in which b-hemihydrate transforms into dihy- drate [CaSO4∑2H2O] by binding more water, whereas its molecular weight increases from 145.15 Da to 172.17 Da. The reaction is exothermic with the heat release Q = 111.9 - 173.3 J/g. The Reac- tion (1) is not only chemical but also structural. In Abstract: Concentrated gypsum slurries used for wallboard production are studied using shear and elongational rheome- ters. 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 scher- und dehnrheologischer Messungen untersucht. Es wird gezeigt, dass die rheologischen Eigenschaften für ver- schiedene Schlammzusammensetzungen ausreichend genau mit Hilfe des Ostwald-Waele Potenzgesetzes beschrieben werden können, das sowohl die experimentellen Daten in Scherung als auch in Dehnung mit aus- reichend hoher Präzision für den Konsistenz- und den Fließverhaltensindex für alle Schlammzusammenset- zungen 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 Wae- le 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 Shear and Elongational Rheology of Gypsum Slurries Suman Sinha-Ray1, Raman Srikar1, C.C. Lee2, A. Li2, Alexander L. Yarin1,3 1 Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, 842 West Taylor Street, Chicago, IL 60607-7022, 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, 64287 Darmstadt, Germany *Corresponding author: ayarin@uic.edu Fax: x1.312.413.0447 Received: 24.4.2011, Final version: 29.7.2011 © Appl. Rheol. 21 (2011) 63071 DOI: 10.3933/ApplRheol-21-63071 License: CC BY-NC-ND 4.0 International - Creative Commons, Attribution, NonCommercial, NoDerivs mailto:ayarin@uic.edu https://creativecommons.org/licenses/by-nc-nd/4.0/ elon gational experiments are de scribed in the sub- section “Surface Tension Measurements for Slur- ries”, and the method and results of the elonga- tional measurements and their comparison with the shear data are given in the sub-section “Elon- gational 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. Stuc- co with additives was allowed soaking in water for 15 s. After that, the suspensions were mixed vigorously for additional 15 s using a rotary mix- er. Deionized water was used for slurry prepara- tion. The water-to-stucco ratio WSR ranged from 70 to 90 (for example, the notation 75WSR rep- resents 75 parts of water to 100 parts of stucco by weight). The slurry was then poured into the shear rheometer and measurements were car- ried out. The shear rate and time scale of the mea- surements were set up corresponding to the experiment requirements. The slurry density for different compositions was measured. The den- sity 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 particu- lar, in air content (added with foam) responsible for density variation at a fixed WSR. In the present work all the shear experi- ments 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 Ten- siometer Model BP2. A diluted stucco slurry (con- centration 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 diam- eter 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 63071-2 Applied Rheology Volume 21 · Issue 6 particular, mixing of stucco with water for 60 s can result in com- plete disintegration of stucco particles, which is accompanied by reduction of the median particle size from 24 to 1.4 mm [11]. Moreover, the Reac- tion (1) is accompa- nied 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 solid- ification should be already felt. The present work deals with such short time intervals which corre- spond to real industrial slurry processing before aging and solidification become important. Slur- ry 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 rheome- try of gypsum slurries is studied. The article is orga- nized as follows. Materials and methods used for preparing slurries are described in section “Materi- als and Methods”. The next section is “Results and Discussions”. There the rheological behavior of gypsum slurries is outlined in the sub-section “Pre- liminary Observations and Theoretical Frame - work”. The detailed results of the shear measurements are dis- cussed in the sub-sec- tion “Rheological Char- acteristics of Slurries Found in Shear Flows”, the surface tension measurements needed to process the experi- mental data of the Figure 1 (above): SEM image of stucco parti- cles as received. Figure 2: Schematic of the elonga- tional rheometer used in the present study. Table 1: Slurry density. motion was controlled by a solenoid. Elonga- tional 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 addi- tional 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 evap- oration and hydration reactions in the slurry (ultimately leading to solidification) on the rhe- ological 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 mix- ing to the end of thread self-stretching experi- ment 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 devi- ator 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 (3) where mshear is equal to mshear = txy/g· , with txy 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 fad- ed. 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 momen- tum balance equation for shear flow of slurry under the assumption that the power-law mod- el (Equation 2) is applicable is given by (4) where u(y) is the velocity profile, and y is the coor- dinate 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 vis- cosity mshear = txy/g· is given by (6) Equation 4 and 5 were solved numerically by the method of finite differences. Namely, all the the- oretical 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 63071-3Applied Rheology Volume 21 · Issue 6 found at any time moment as g· = ∂u/∂y and the effective shear viscosity mshear is found using Equation 6. The results were compared to the ex - perimental data for various water-stucco ratios in gypsum slur- ries 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 experi- ments are compared to the theoretical flow curves as shown in Figure 3. The experi- mental data is plotted by symbols and the theoretical curves are depicted by lines. It is emphasized that Fig- ure 3 does not repre- sent themselves con- ventional flow curves, since they correspond to the experiments and computations for the sim- ple 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 ini- tially 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 predic- tions, the flow becomes fully developed beyond the shear rate of 10 – 100 s-1. In that range fitting of the theory to the measured data is possible and produces meaningful values of the rheolog- ical parameters K and n. Their values corre- sponding to all the compositions studied are giv- en in Table 2. The successful comparison in the range above 10 – 100 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/s2, 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 hydra- tion and solidification being felt, which deter- mined 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 parame- ters 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 cor- responding average errors for four compositions are shown in Figure 4. An additional benchmark for comparison of the theory with the experi- mental data is provided by the case of viscous Newtonian test fluids with independently veri- fied viscosity values. The comparison of the mea- surements and the theory for one such fluid, a standard solution S600 was done. Fitting the theory to the experimental data revealed the vis- cosity value of 18.6 Poise, whereas the standard independently measured value is reported as 20.45 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- 63071-4 Applied Rheology Volume 21 · Issue 6 Figure 3: The effective shear viscosity (flow curve) for: 80 WSR sys- tem-composition 5, 75 WSR system-composition 1, 80 WSR system-composition 2, 85 WSR system-composition 3, 90 WSR system-composi- tion 4, 80 WSR system-com- position 6, 80 WSR system- composition 7, 75 WSR system-composition 8, 75 WSR system-composition 9. Table 2: Rheological parameters of gypsum slurries. 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 stuc- co. However, even at 90 WSR, slurry still does not approach Newtonian behavior, and stays signif- icantly pseudoplastic (with n = 0.56). The value of the consistency index K increases with the decrease in water content in the slurry. There- fore, 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 experimen- tal 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 consis- tency 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 = (- 5.54·WSR) + 512.9. A sim- ilar fit for the exponent value yields n = (0.012·WSR) - 0.52. 3.3 SURFACE TENSION MEASUREMENTS FOR SLURRIES The values of surface tension coefficient mea- sured in this sub-section will be used in the pro- cessing of the results of elongational experi- ments described in the following section. The data for the stucco slurry is presented in Table 3. The average value of surface tension for the slur- ry was found to be 110.81 mN/m which is signifi- cantly 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 ten- sion of the slurry was implemented employing contact angle measurements using NRL Contact Angle Goniometer Model 100-00. The instrument incorporated a camera which allows for accu- rate measurements of contact angles. A slur- ry drop was placed gently onto a horizon- tal 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 43.5°. The error in both cases was less than 10 %. According to Young’s equation, gSG = gSL + gLGcosqc, where gSG represents the surface tension between glass (solid) and air (gas), gSL represents the surface tension between glass (solid) and liq- uid, gLG represents the surface tension between liquid and air (gas), and qc represents the contact angle. For pure water droplet, correspondingly, gSG = gSL + gWcosqcW , where gW and qcW are the sur- face tension and contact angle of water, respec- tively. It is emphasized that we assume gSG and gSL to be the same for both water and slurries on glass. Also, it is known that gW = 72.1 mN/m and qcW =18°. Therefore, gLG = gWcosqcW/cosqc which yields the surface tension of 75 WSR (composi- tion 11) slurry as gLG75 = 122.02 mN/m, and the sur- face tension of 85 WSR (composition 12) slurry as gLG85 = 94.53 mN/m. Both values are relatively close to the average value of the surface tension of the diluted slurry in Table 3, 110.81 mN/m, which corroborates the latter. We can conclude that the effective surface tension of slurries is sig- nificantly higher than that of water. 63071-5Applied Rheology Volume 21 · Issue 6 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-composi- tion 8. The error bar repre- sents the average error = ± 16.25 % maximum. (b) Consistency index for 75 WSR system-composition 11. The error bar represents the average error = ± 6.978 % maximum; consistency index for 75 WSR-composi- tion 9. The error bar repre- sents the average error = ± 4.225 %. 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). 3.4 ELONGATIONAL RHEOLOGY OF GYPSUM SLURRIES Shear rheology alone is incapable to fully uncov- er true rheological behavior of complex non- Newtonian fluids [13]. The shear mode measure- ments typically are insufficient to shed light on the rheological behavior of the same non-New- tonian 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 flu- id, 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 power- law constitutive equation (2) to describe both shear and elongational behavior of gypsum slur- ries 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 dynam- ics of liquid jets and threads [18] and in the case of the power-law Equation 2 reduces to the fol- lowing equation for the evolution of the thread diameter as a function of time (7) where d is the diameter of the pinching thread, d0 is the initial diameter of the thread, ts is the time of pinching, t is time, b1 is a theoretically established constant (0.175) required to account for the thread non-uniformity [13, 19, 20], and k = K/gLG, where gLG is the surface tension. The value of gLG used in this work was measured in the pre- vious section (110.81 mN/m). Equation 7 can be written as (8) where (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 solidi- fication of gypsum slurries not every experiment was considered to be successful. For the 1st elon- gational experiment with any droplet the fol- lowing two criteria were established for segre- gation 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 densi- ty function), data from 34 successful experi- ments were used for the evaluation of the rheo- logical parameters K and n corresponding to the 1st elongational experiment. Of these 34 experi- ments, only 14 led to successful 2nd stretching experiments with the same droplet. A more relaxed segregation criterion was formulated for the 2nd experiment. Still, the successful 2nd stretch- ing experiment is the one, which provided at least 12 data points. The relaxation in the criteri- on for the 2nd stretching experiment was dictat- ed by rapid evaporation of water from the sur- face of small slurry droplets employed in the elongation experiments, which accelerated slur- ry setting. Accordingly, no successful experi- 63071-6 Applied Rheology Volume 21 · Issue 6 Figure 6 (left): Self-pinching cylindrical liq- uid thread. Figure 7: Thread diameter versus time in the 1st stretching experiment (slurry 75 WSR- composition 11). The inserted images show the slurry thread at different moments during its capil- lary 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 corre- sponding values of the con- sistency index K and power n are also shown. ments were found for the 3rd 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 corre- sponding values of the rheological parameters are shown in Figure 8. Using the measured value of the surface tension of slurry (110.81 mN/m), the value of the consistency index K is found out to be 48.07 g/cms2-n, while n = 0.57. 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 ± 0.064 and K = 32.42 ± 16.18 g/cms2-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 vari- ation in size of the initial droplets used in the elon- gational tests. In Figure 8a the red point corre- sponds to the value of K, to which corresponds the encircled value of n in 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 52 – 55 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 con- sistency index K and decreasing the value of n- both trends in the direction of a more pronounced pseudoplasticity. When the values of the rheolog- ical parameters n and K presented in Figure 8 (n = 0.6 ± 0.064 and K = 32.42 ± 16.18 g/cms2-n for elon- gation of 75 WSR-composition 11) are compared to the values obtained in shear experiments (Table 2: n = 0.55 and K = 51.61 g/cms2-n for shear of 75 WSR-composition 11), it can be seen that the val- ues of n are rather close, whereas there is a differ- ence in the values of K. This might be due to an inaccuracy in the value of the surface tension coef- ficient used to process the data of the elongational experiments. The rheological parameter values evaluated from the 14 successful 2nd 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 2nd 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 evapo- ration 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) con- stitutive equation. The other known examples of materials which follow the tensorial power law constitutive equation in both shear and elonga- tion with roughly the same values of the rheo- logical parameters (the consistency index K and flow behavior index n) also include suspensions of needle-like g-Fe2O3 particles in oil and gelled propellant simulants [13, 18]. However, the fami- 63071-7Applied Rheology Volume 21 · Issue 6 Figure 8 (left): (a) Values of K, and (b) val- ues of n found for all 34 suc- cessful experiments on the 1st stretching (slurry 75 WSR- composition 11). The solid lines correspond to the aver- aged values, the dotted lines to the standard deviations. Figure 9: (a) Values of K and (b) val- ues of n found in the 14 suc- cessful 2nd stretching experi- ments with the same droplet (the data for the 1st stretching is also shown for comparison, 75 WSR-compo- sition 11). Except one case (the encircled data points) the value of n decreased and the value of K increased in the 2nd stretching com- pared to the first one. ly of such materials is not wide. Indeed, the pow- er law model is frequently used to fit the shear data but very rarely efforts are directed to simul- taneous elongational testing, which in many cas- es would disprove applicability of the tensorial model, as for example, in the case of polymer solutions and melts. In the present work the ten- sorial power-law rheological behavior was estab- lished for gypsum slurries with different water content and compositions. In particular, the val- ues 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 ± 0.064 and K = 32.42 ±16.18 g/cm s2-n, whereas for shear of the same slurry it was found that n = 0.55 and K = 51.61 g/cms2-n, which is sufficiently close. ACKNOWLEDGMENTS This work was supported by The US Gypsum Cor- poration (USG). The authors thank Drs. K. Nate- saiyer, 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 nan- otube suspensions-fluids with yield stress, Rhe- ol. Acta 48 (2009) 597-609. [3] Chalencon F, Orgeas L, Dumont PJJ, Foray G, Cavaille JY, Maire E, Rolland du Roscot S: Lubri- cated compression and X-ray microtomography to analyse the rheology of a fibre-reinforced mor- tar, Rheol. Acta 49 (2010) 221-235. [4] Ferraris CF: Measurement of the rheological properties of high performance concrete: state of the art report, J Res NIST 104 (1999) 461-478. 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