Shaping suspensions: Stabilizing anisotropy in viscoelastic media using oscillations.

The rheological properties and curing kinetics of a general‐purpose polyester resin have been determined during isothermal cure. Both steady and oscillatory shearing flow properties were determined using a cone‐and‐plate rheometer, and the curing kinetics were determined using a differential scanning calorimeter (DSC). It was found that, as cure progresses, the steady shear viscosity increases very rapidly with cure time at all shear rates investigated, and normal forces show negative values at low shear rates and positive values at high shear rates. The observed negative normal forces are believed to result from material shrinkage during cure, and positive normal forces from the deformation of large molecules, formed by crosslinking reactions during cure. Note that, in a cone‐and‐plate rheometer, the shrinkage force acts in the direction opposite to that of normal forces. It is, therefore, concluded that extreme caution is needed in the interpretation of normal force measurements with thermosetting resins, subjected to steady shearing flow. Dynamic measurements seem to offer some insight on the onset of gel formation. More specifically, we have found that, when the unsaturated polyester resin was cured at a fast rate, the time at which a maximum in the loss modulus G” occurs coincides reasonably well with the time tη∞ at which the steady shear viscosity η approaches infinity. However, at a slow rate of cure, the time at which tan δ equals unity agrees fairly well with tη∞. DSC measurement has permitted us to determine the degree of cure as a function of cure time and the kinetic parameters in an empirical expression for the curing kinetics advanced by Kamal and co‐workers. By combining the rheological and DSC measurements, we have constructed plots describing how the viscosity increases with the degree of cure, at various values of isothermal curing temperature.

Measurements are made of the viscoelastic properties of a wormlike micellar solution undergoing steady shearing. The wormlike micellar solution has a clearly defined Maxwell response in oscillation. The features (for example, the plateau of the elastic modulus, G′, and the peak of the viscous modulus, G″) are extremely well defined, allowing the differences in elastic properties brought about by steady-shearing to be easily discerned. An important feature of the solution studied is that it displays a plateau-like region with almost constant shear stress over a range of steady shear rates. We find that as the steady shear rate is increased: (i) G′ becomes negative at low frequencies; (ii) the plateau value of G′ decreases; (iii) the frequency at which the plateau value of G′ is reached shifts to higher frequencies; (iv) the width of the G″ peak decreases; (v) the position of the G″ peak shifts to higher frequencies; and (vi) the height of the G″ peak increases then decreases. The constitutive equations of Bautista et al. [J. Non-Newtonian Fluid Mech. 80, 93–113 (1999)] and Boek et al. [J. Non-Newtonian Fluid Mech. 126, 39–46 (2005)] were used to fit and predict bulk rheology measurements. Neither model predicts the observed rise in normal stress, despite fitting the plateau region in the shear-stress versus shear-rate curve. It proved difficult to predict transient shear stress data when both increases and decreases in the shear rate were considered. The features found in combined steady and oscillatory flow are predicted qualitatively but not quantitatively. In particular, the reduction of the plateau of G′ is predicted to occur only at much higher shear rates than found experimentally. We also note that the commercial software controlling the rheometer does not interpret the raw data correctly in the regime where G′ is negative.

Computation and experiment in non- colloidal suspension rheology

Measurements in which a steady shear flow is superimposed on a small amplitude oscillatory shear flow were performed by means of aWeissenberg Rheogoniometer. Solutions of polystyrene and poly-(ethylene oxide) in Acroclor-1248 and also ethylcellulose in a solvent mixture were investigated. By means of special electronical devices we were able to measure accurately at low frequencies when high rates of shear were superimposed. In this range of frequencies and rates of shear, the following effects were noticed for all the investigated solutions: the dynamic viscosity, as a function of the frequency, shows a minimum, the phase shift between the oscillatory stress and strain increases with the increase of the rates of shear even to values larger than 90°, therefore the real part of the dynamic modulus (G′) becomes negative.

Rheological behavior of flexible elongated micelles: temperature effect in an isotropic phase

Association under shear flow in aqueous solutions of pectin

Modelling the rheological behaviour of fibre suspensions in viscoelastic media

The dynamics of fluid vesicles in oscillatory shear flow was studied using differential equations of two variables: the Taylor deformation parameter and inclination angle $\theta$. In a steady shear flow with a low viscosity $\eta_{\rm {in}}$ of internal fluid, the vesicles exhibit steady tank-treading motion with a constant inclination angle $\theta_0$. In the oscillatory flow with a low shear frequency, $\theta$ oscillates between $\pm \theta_0$ or around $\theta_0$ for zero or finite mean shear rate $\dot\gamma_{\rm m}$, respectively. As shear frequency $f_{\gamma}$ increases, the vesicle oscillation becomes delayed with respect to the shear oscillation, and the oscillation amplitude decreases. At high $f_{\gamma}$ with $\dot\gamma_{\rm m}=0$, another limit-cycle oscillation between $\theta_0-\pi$ and $-\theta_0$ is found to appear. In the steady flow, $\theta$ periodically rotates (tumbling) at high $\eta_{\rm {in}}$, and $\theta$ and the vesicle shape oscillate (swinging) at middle $\eta_{\rm {in}}$ and high shear rate. In the oscillatory flow, the coexistence of two or more limit-cycle oscillations can occur for low $f_{\gamma}$ in these phases. For the vesicle with a fixed shape, the angle $\theta$ rotates back to the original position after an oscillation period. However, it is found that a preferred angle can be induced by small thermal fluctuations.

We report studies of the orientation state of multiwalled carbon nanotubes (MWNTs) dispersions in steady and transient shear flows. Uncured epoxy was used as a viscous Newtonian suspending medium and samples were prepared from "aligned" MWNTs using methods previously reported [S. S. Rahatekar et al., J. Rheol. 50, 599 (2006)]. Orientation measurements were performed in both the flow-gradient (1-2) and flow-vorticity (1-3) plane of simple shear flow using in situ x-ray scattering techniques. Steady state measurements in the 1-2 plane indicate that the MWNT orientation is shear rate dependent, with the MWNTs orienting closer to the flow direction at higher shear rates. During steady shear, anisotropy was measured to be higher in the 1-2 plane than in the 1-3 plane, demonstrating that the nanotube orientation state is not unaxially symmetric in shear. It is hypothesized that the steady state MWNT orientation is governed primarily by a rate-dependent state of nanotube aggregation/disaggregation, which was separately characterized by optical microscopy of the same samples under shear. High flux synchrotron radiation allowed for time-resolved structural studies in transient flows. A partial relaxation of flow-induced anisotropy was observed following flow cessation, despite the very small rotational diffusivity estimated for these nanotubes. Long transients are observed in step-down experiments, as the orientation state changes in response to the slow tube aggregation process.

One good way to explore fluid microstructure, experimentally, is to suddenly subject the fluid to a large steady shearing deformation and to then observe the evolving stress response. If the steady shear rate is high enough, the shear stress and also the normal stress differences can overshoot, and then they can even undershoot. We call such responses nonlinear and this experiment shear stress growth. This paper is devoted to providing exact analytical solutions for interpreting measured nonlinear shear stress growth responses. Specifically, we arrive at the exact solutions for the Oldroyd 8-constant constitutive framework. We test our exact solution against the measured behaviors of two wormlike micellar solutions. At high shear rates, these solutions overshoot in stress growth without subsequent undershoot. The micellar solutions present linear behavior at low shear rates; otherwise, their behavior is nonlinear. Our framework provides slightly early underpredictions of the overshoots at high shear rates. The effect of salt concentration on the nonlinear parameters is explored.

The rheological properties of hydraulic fracturing fluids, commonly used in low permeability reservoirs, has been discussed extensively in recent years because of their importance in stimulation treatment design. Rheology of these systems is primarily determined in a coaxial cylinder viscometer and reported as apparent viscosity. However, many problems have been encountered in obtaining accurate measurements of crosslinked gels due to the fluid slipping at the solid boundaries of the bob and cup. This slip creates an unknown velocity profile across the flow field; in other words, the fluid experiences an unknown shear. Since viscosity, as well as job design parameters n' and K' are the direct result of shear rate and shear stress, determination of the actual shear rate experienced by the fluid is critical. Many instances have been observed where the steady shear measurements indicate that the fluid has little or no viscosity. Yet, accounting for slip at the walls, the fluid is still a viscous crosslinked gel. Only by determining the existence and extent of wall slip of fracturing systems and how to correct for it, can the steady shear data that are utilized in treatment design models be meaningful. This paper presents the application of a theory to determine 1). wall slip velocities in a coaxial cylinder viscometer 2). corrected shear rate not based on power law parameters and 3). true viscosity of crosslinked fracturing fluids. Data have been taken over a wide shear rate range to distinquish if wall slip is more prevalent at low or high shear rates. Data also show, that for certain mixing conditions of the polymer and crosslinking reagent, wall slip is very significant and the shear experienced by the fluid is less than expected, resulting in higher viscosity values. Methods of gel testing and preparation have been examined and those methods that minimize wall slip will be discussed. In addition, oscillatory shear measurements, which describe gel structure, are shown to further explain rheological behavior in steady shear. Viscosity values corrected for slip will be compared with viscosity values obtained on a closed loop pipe viscometer.

Viscoelastic properties of hydroxypropyl guar (HPG) crosslinked by borate ions were studied using steady shear and dynamic oscillatory shear experiments. Chemical equilibria involving boric acid, borate ions, and borate ions associated with cis-diol sites on the polysaccharide chains determine the number of crosslinks. These equilibria are functions of temperature and pH, and thus the rheology of the borate gels depend on temperature and pH. Dynamic oscillatory measurements on polymer solutions crosslinked by borax were performed over the temperature range from 10°C to 65°C, and the pH range from 6.35 to 9.5. The storage and loss moduli obey time-temperature superposition so that master curves can be constructed over 6 decades in frequency. Leibler, et al. have recently proposed a theory for the rheology of associating polymer systems. Following this theory, we have subtracted the solution moduli from the gel moduli and the resulting reduced moduli data follow a single time constant Maxwell model. Steady shear experiments were performed in capillary tubes at two different diameters to determine wall slip. The shear rates studied were such that the chains do not have sufficient time to relax completely. By analysing the data from the two tubes, the gel was found to slip at the wall. Three different regions were seen in the stress – shear rate behavior of these gels. At low rates, the stress increases rapidly with shear rate. At intermediate shear rates, the stress remains constant and at high shear rates, the stress increases slowly with rate and the gel is found to slip in this region. The actual stress – shear rate behavior after accounting for slip and slip velocities were determined.

The rheology of the all-aromatic copolyester thermotropic liquid crystal 73/27 HBA-HNA has been studied over a large interval of shear rates. At small shear rates the transient behavior has been analyzed with a cone and plate rheometer. The shear stress and the first normal stress difference have been found to scale with the strain. Steady values for both viscosity and first normal stress difference have been obtained. The steady shear viscosities have been correlated to capillary data at higher shear rates. Three zones can be found in the steady viscosity vs shear rate curve: a shear thinning region at small shear rates, an almost newtonian region, and a second power-law region at higher shear rates. In the shear rate interval studied with the cone and plate rheometer the steady first normal stress difference remains positive.

The effect of heparin on thrombogenesis induced by the subendothelium of rabbit aorta was investigated in 24 healthy volunteers after intravenous injection of different doses (0, 1000, 2500, and 5000 IU). By using an ex vivo perfusion chamber system, the interaction between flowing blood and exposed subendothelium was measured at low (50 s-1), intermediate (650 s-1), and high (2600 s-1) wall shear rates. The low shear rate simulated blood flow in venous, the intermediate shear rate in arterial, and the high shear rate in small or stenosed arterial vessels. Deposition of fibrin, platelets, and platelet thrombi on vascular subendothelium (SE) was quantified by morphometrical and immunological techniques. Fibrin deposition prevailed at low shear rates and was only minimal at high shear rates (30 +/- 1% vs. 1 +/- 0.4% coverage of SE with fibrin, means +/- SEM, p less than 0.001). In contrast, the interaction of platelets with SE was more intense at high compared to low shear rates, as indicated by higher platelet adhesion (54 +/- 5% vs. 4 +/- 1% coverage of SE with platelets, p less than 0.001) and platelet thrombus volumes (4.8 +/- 1.3 vs. 0.5 +/- 0.1 microns 3/microns 2, p less than 0.001). Fibrin deposition on SE was inhibited by heparin in a dose-dependent manner and was abolished after high doses. In addition, high doses of heparin reduced the height and volume of platelet thrombi at low and intermediate wall shear rates, but no effect was found at the high shear rate. Our data show that heparin inhibits the formation of both fibrin and platelet thrombi on vascular subendothelium. The lack of effect of heparin on platelet thrombus formation at high shear rates indicates that thrombin modulates the growth rate and/or stability of platelet thrombi at low and intermediate shear rates, whereas additional factors may control platelet thrombus growth and stability at high shear conditions.

Investigation of shear thinning behavior and microstructures of MWCNT/epoxy and CNF/epoxy suspensions under steady shear conditions