Index of content:
Volume 52, Issue 2, March 2008
Large amplitude oscillatory shear behavior of entangled polymer solutions: Particle tracking velocimetric investigation52(2008); http://dx.doi.org/10.1122/1.2833453View Description Hide Description
Large amplitude oscillatory shear (LAOS) has been employed widely to probe the nonlinear behavior of complex fluids. Typically, the system undergoing LAOS has been assumed to experience homogeneous shear in each cycle so that material functions can be introduced to analyze the nonlinear dependence of these functions on the amplitude and frequency. Using particle-tracking velocimetric technique, we have carried a more systematic investigation on four different entangled polybutadiene (PBD) solutions with the number of entanglements per chain , 27, 64 and 119, extending well beyond the initial observations of shear banding in entangled PBD solutions under LAOS [Tapadia et al., Phys. Rev. Lett.96, 196001–4 (2006a)]. At strain amplitudes and frequencies higher than the overall chain relaxation rate, we observed, for the three samples with 27 or more entanglements per chain, the development of a thin “liquid” layer where severe chain disentanglement may have taken place. The thin liquid layer takes most of the imposed deformation, while a significant portion of the sample stays hardly deformed and remains presumably well entangled. When the applied was between 100% and 250%, this “liquid” layer developed only after some oscillation cycles. For , the disentangled layer formed in the first cycle, a phenomenon analogous to failure of solids under external deformation. The solution with the least entanglements of 13 per chain did not show visible inhomogeneous deformation under LAOS.
Linear viscoelasticity of entangled wormlike micelles bridged by telechelic polymers: An experimental model for a double transient network52(2008); http://dx.doi.org/10.1122/1.2828645View Description Hide Description
We survey the linear viscoelasticity of a new type of transient network: bridged wormlike micelles, whose structure has been characterized recently by Ramos and Ligoure [Macromolecules40, 1248–1251 (2007)]. This composite material is obtained by adding telechelic copolymers (water-soluble chains with hydrophobic stickers at each extremity) to a solution of entangled wormlike micelles (WM). For comparison, naked WM and WM decorated by amphiphilic copolymers are also investigated. While these latter systems exhibit almost a same single ideal Maxwell behavior, solutions of bridged WM can be described as two Maxwell fluids component blends, characterized by two markedly different characteristic times, and , and two elastic moduli, and , with . We show that the slow mode is related to the viscoelasticity of the transient network of entangled WM, and the fast mode to the network of telechelic active chains (i.e., chains that do not form loops but bridge two micelles). The dependence of the viscoelasticity with the surfactant concentration, , and the sticker-to-surfactant molar ratio, , is discussed. In particular, we show that is proportional to the number of active chains in the material, . Simple theoretical expectations then allow evaluation of the bridges/loops ratio for the telechelic polymers.
52(2008); http://dx.doi.org/10.1122/1.2836937View Description Hide Description
We have studied the concentration dependence of velocity profiles for a micellar system consisting of cetylpyridium chloride and sodium salicylate and demonstrated a shear thinning to shear banding transition. By constructing the local flow curve from local stress and shear rate obtained from the velocity profiles, we show that the slope of the stress plateau decreases with increasing surfactant concentration and becomes zero at a critical concentration of 4.9%. Above this concentration, the local flow curve becomes discontinuous, suggesting a non-monotonic constitutive relation and a transition from shear thinning to shear banding behavior. Steady state shear banding occurs only in systems with a non-monotonic constitutive relation, even though temporary banding and highly inhomogeneous shear rate profiles are observed for systems with a monotonic constitutive relation.
Cross-slot extensional flow birefringence observations of polymer melts using a multi-pass rheometer52(2008); http://dx.doi.org/10.1122/1.2836671View Description Hide Description
This paper reports initial experimental flowbirefringence studies of cross-slot flow for a range of molten polyethylenes using a multipass rheometer (MPR). An MPR was modified to accommodate a cross-slot center section insert thereby enabling small quantities of molten polymer to be evaluated in a near two-dimensional pure shear extensional flow. The results show that it was possible to obtain precise processing data for cross-slot flow using quantities of polymer. Experimental observations on different polyethylenes showed that in all cases the flow commenced from a Newtonian situation where the optical birefringent fringes around the central stagnation point were essentially symmetric. As the flow developed, the fringe pattern became progressively more asymmetric about the exit symmetry plane and the extent of the viscoelasticity of the polymer could be quantified by the observed level of anisotropy between the birefringence fringes on the entry and exit symmetry planes of the flow. The progressive development of anisotropy and stress with increasing extensional flow rate and type of polymer is presented for a number of flow conditions and it was found that increasing viscoelasticity of the polymer resulted in a progressive increase in viscoelastic center-line extensional stresses. The data provide benchmark large strain extensional flow experiments for certain polymer melts that can in the future be used to compare with numerical simulation.
52(2008); http://dx.doi.org/10.1122/1.2828018View Description Hide Description
Many complex fluids exhibit power-law responses in their relaxationmodulus; examples include foods, soft solids, fractal gels, and other polydisperse systems. In the present study we investigate the rheological characteristics of such materials beyond the linear regime using a gluten-water gel as a prototypical system. The material functions of gluten dough under finite strains can be described by combining the linear viscoelastic response of a critical gel [Chambon, and Winter, J. Rheol.31, 683–697 (1987)] with a Lodge rubberlike network to develop a frame invariant constitutive equation [Winter and Mours, Adv. Polym. Sci.134, 165–233 (1997)]. This generalized gel equation is a simple but accurate description of the material functions in the linear regime and also at large strains, using only two parameters. We compare the model predictions with experimental measurements in transient shear and elongational flows of gluten gels over a wide range of deformation rates. An essential feature of both the experimental data and the generalized gel model is a strain∕rate separability in the system response. Further modifications to the generalized gel equation can be made by incorporating a damping function to include nonlinear strain softening effects seen in more complex gels such as wheat-flour doughs. From the rheological data, we find compelling evidence that indicates gluten to be a polymeric network consisting of flexible or semiflexible chains between junction points with a typical mesh size of approximately .
Effect of magnetic field on molecular orientation of nematic liquid crystalline polymers under simple shear flow52(2008); http://dx.doi.org/10.1122/1.2837113View Description Hide Description
The effect of magnetic fields on molecular configuration of liquid crystalline polymers(LCPs) under shear flows is numerically analyzed using the Doi theory. The evolution equation for the probability density function of the liquid crystalline polymer (LCP) molecules is directly solved without any closure approximations. Two cases of the magnetic fields are considered: (1) the magnetic field parallel to the flow direction, and (2) the magnetic field parallel to the velocity gradient direction. For both cases, the magnetic fields strongly affect the transition among flow-orientation modes, such as tumbling, wagging, and aligning modes. When the magnetic field is imposed on the LCP shear flow, a new aligning flow-orientation mode emerges at low shear rate, which is macroscopically the same, but microscopically quite different from the ordinary aligning mode. For the magnetic field parallel to the flow direction, the field affects the scalar order parameter rather than the major orientation direction. On the other hand, for the magnetic field parallel to the velocity gradient direction, the effect of the field on the major orientation direction is more remarkable than the effect on the scalar order parameter.
52(2008); http://dx.doi.org/10.1122/1.2837525View Description Hide Description
This paper reports finite-element simulations of dropdeformation in converging flows in an axisymmetric conical geometry. The moving interface is captured using a diffuse-interface model and accurate interfacial resolution is ensured by adaptive refinement of the grid. We have explored the effects of viscoelasticity on dropdeformation when either the drop or the matrix is a Giesekus fluid. Contrary to the popular belief that viscoelasticity in the drop hinders deformation and that in the matrix enhances deformation, we predict a more complex picture in which viscoelasticity in either component may suppress or promote dropdeformation depending on the capillary number and the drop-to-matrix viscosity ratio . Smaller and are conducive to the behavior mentioned above, while large and may produce the opposite effect. Both trends are explained by the reaction of the polymer stress to the inhomogeneous and transient deformation in the converging flow field. Finally, this understanding reconciles contradictory results in the literature as opposite limits in the parameter space.
Homogenization approach to the behavior of suspensions of noncolloidal particles in yield stress fluids52(2008); http://dx.doi.org/10.1122/1.2838254View Description Hide Description
The behavior of suspensions of rigid particles in a non-Newtonian fluid is studied in the framework of a nonlinear homogenization method. Estimates for the overall properties of the composite material are obtained. In the case of a Herschel–Bulkley suspending fluid, it is shown that the properties of a suspension with overall isotropy can be satisfactorily modeled as that of a Herschel–Bulkley fluid with an exponent equal to that of the suspending fluid. Estimates for the yield stress and the consistency at large strain rate levels are proposed. These estimates compare well to both experimental data obtained by Mahaut et al. [J. Rheol.52(1), 287–313 (2008)] and to experimental data found in the literature.
Unsteady circular tube flow of compressible polymeric liquids subject to pressure-dependent wall slip52(2008); http://dx.doi.org/10.1122/1.2837104View Description Hide Description
A mathematical model is developed for the time-dependent circular tube flow of compressible polymeric liquids subject to pressure-dependent slip at the wall and applied to a poly (dimethyl siloxane) (PDMS). The parameters of pressure-dependent wall slip velocity and shear viscosity of the PDMS were determined using combinations of small-amplitude oscillatory shear, steady torsional and squeeze flows and were employed in the prediction of the time-dependent circular tube flow behavior of the PDMS. The numerical solutions suggest that a steady tube flow is generated when the flow boundary condition at the wall is stable, that is, either a contiguous stick (or weak slip) or a contiguous strong slip condition along the entire length of the wall. On the other hand, when the flow boundary condition changes from stick (or weak slip) to strong slip at any location along the length of the wall, undamped periodic oscillations in pressure and mean velocity are observed. The experimentally characterized and simulated tube flow curves of PDMS are similar and the simulation findings for flow stability are in general consistent with the experimentally observed flow instability behavior of PDMS.
52(2008); http://dx.doi.org/10.1122/1.2833594View Description Hide Description
The effect of salt concentration on the critical shear rate required for the onset of shear thickening and apparent relaxation time of the shear-thickened phase has been investigated systematically for dilute Cetyl-trimethylammonium bromide/sodium salicylate solutions. Experimental data suggest a self-similar behavior of and as functions of . Specifically, whereas such that an effective Weissenberg number for the shear-thickened phase is only weakly dependent on . A procedure has been developed to collapse the apparent shear viscosity versus shear rate data obtained for various values of into a single master curve. The effect of on the elastic modulus and mesh size of the shear-induced gel phase for different surfactant concentrations is discussed. Experiments performed using different flow cells (Couette and cone-and-plate) show that , and the maximum viscosity attained are geometry independent. The elastic modulus of the gel phase inferred indirectly by employing simplified hydrodynamic instability analysis of a sheared gel-fluid interface is in qualitative agreement with that predicted for an entangled phase of living polymers. A qualitative mechanism that combines the effect of on average micelle length and Debye parameter with shear-induced configurational changes of rod-like micelles is proposed to rationalize the self-similarity of shear induced structure formation.
52(2008); http://dx.doi.org/10.1122/1.2829149View Description Hide Description
In this paper we analyze the crystallization kinetics under steady shear flow conditions of different samples obtained by blending two isotactic poly(1-butene)s with different average molecular weights. It is observed that the addition of a small amount of high molecular weight (MW) polymer to a low MW sample does not produce any appreciable effect upon the crystallization kinetics under both quiescent and shear flow conditions. When more elevated amounts of high MW polymer are added, only mild effects upon the crystallization kinetics, under both quiescent and shear conditions, are observed. This behavior can be attributed to constraint release of high MW chains due to the relaxation of the shorter chains. Such a physical phenomenon can be described by the double reptation theory, which, indeed, allows for good quantitative predictions of the experimental results by using the relaxation times of the two blend components as the only fitting parameters.
52(2008); http://dx.doi.org/10.1122/1.2838250View Description Hide Description
The thermodynamical aspects of polymeric liquids subjected to uniaxial elongational flow are examined using atomistically detailed nonequilibrium Monte Carlo simulations. In particular, attention is paid to the energetic effects, in addition to the entropic ones, which occur under conditions of extreme deformation. Atomistic nonequilibrium Monte Carlo simulations of linear polyethylene systems, ranging in molecular length from to and for temperatures from , demonstrate clear contributions of energetic effects to the elasticity of the system. These are manifested in a conformationally dependent heat capacity, which is significant under large deformations. Violations of the hypothesis of purely entropic elasticity are evident in these simulations, in that the free energy of the system is demonstrated to be composed of significant energetic effects under high degrees of orientation. These arise mainly from favorable intermolecular side-to-side interactions developing in the process of elongation due to chain uncoiling and alignment in the direction of extension.
Modeling the inhomogeneous response and formation of shear bands in steady and transient flows of entangled liquids52(2008); http://dx.doi.org/10.1122/1.2829769View Description Hide Description
We simulate the spatial and temporal evolution of inhomogeneous flow fields in viscometric devices such as cylindrical Couette cells. The computations focus on a class of two species elastic network models which are prototypes for a model which can capture, in a self-consistent manner, the creation and destruction of elastically active network segments as well as diffusive coupling between the microstructural conformations and the local state of stress in regions with large spatial gradients of local deformation. For each of these models, the “flow curve” of stress and apparent shear rate resulting from an assumption of homogeneous deformation is nonmonotonic and linear stability analysis shows that the region of nonmonotonic response is unstable. Steady state calculations of the full inhomogeneous flow field lead to localized shear bands that grow linearly in extent across the gap as the apparent shear rate is incremented. Time-dependent calculations in step strain experiments and in start up of steady shear flow show that the velocity profile in the gap and the total stress measured at the bounding surfaces are coupled and evolve in a complex nonmonotonic manner as the shear bands develop. These spatio-temporal dynamics are consistent with time-resolved particle imaging velocimetry measurements in both concentrated solutions of monodisperse entangled polymers and in wormlike micellar solutions. The computational results have a number of implications for experimental observations of “apparent” or “gap-averaged” quantities in nearly viscometric devices, and lead to plateaus or “yield-like” transitions in the steady flow curve and deviations from the Lodge–Meissner relation in nonideal step shearing deformations.
52(2008); http://dx.doi.org/10.1122/1.2833469View Description Hide Description
Flows of concentrated suspensions at low Reynolds number through an asymmetric T-junction bifurcation composed of rectangular channels are studied experimentally using nuclear magnetic resonance imaging. In contrast to the unequal division of a uniform concentration material, the suspension and the neutrally buoyant, noncolloidal particles are almost equally partitioned between downstream branches, and motion of particles across the dividing stream surface is deduced to occur at the bifurcation. We attribute the rearrangement of particles to enhanced spreading of high concentration (and therefore high local viscosity) regions of the suspension toward the side branch. The partitioning is accompanied by lateral asymmetry in the concentration and velocity profiles of the downstream branches, although the inlet profiles are symmetric. In the spanwise direction, inhomogeneous concentration distributions that develop upstream persist throughout the inlet and downstream channels. Overall, the fractions of the flow rate and cross-sectional area flowing into the side branch vary slightly with bulk particle volume fraction. Also, inertial effects likely cause an observed shift of the dividing streamline toward the side branch as the flow rate increases, while the flow rate and particle flux fractions entering the side branch hardly change. Finally, directional asymmetry is observed between diverging and converging flows.
52(2008); http://dx.doi.org/10.1122/1.2838255View Description Hide Description
We report a number of experiments, mainly rheological measurements, examining the yielding behavior of colloidalglasses with hard-sphere interaction plus a short-range attraction. The system is a suspension of nearly hard-sphere colloidal particles and non-adsorbing linear polymer which induces an adjustable depletion attraction between the particles. The pure hard-sphere glass shows a simple yielding process at a strain corresponding to the maximum distortion of the cage of nearest neighbors—the structural arrest length scale. However, the attraction-dominated glasses show a two-step yielding process at different ranges of strain. We suggest that the first step at low yield strain corresponds to the breaking of attractive bonds between particles. The other at larger strain corresponds to the cage breaking process.