Volume 58, Issue 6, November 2014
Index of content:

Rheological studies of thermotropic phase transitions in cationic vesicle suspensions: Instantaneous “jamming” and aging behavior
View Description Hide DescriptionCationic doubletailed surfactants exhibit a rich thermotropic phase behavior. Here, we examine the effect of thermal gradients and processing history on the rheology and microstructure of concentrated multilamellar vesicle (MLV) suspensions made from a doubletailed cationic surfactant (diC18:0 DEEDMAC), whose bilayers are in the crystalline (solid) state at room temperature. The rheological properties of the MLV suspensions are found to be strongly dependent on the thermal behavior of the constituent bilayer with the viscoelastic moduli exhibiting a nonmonotonic variation with temperature, initially increasing by 1–2 orders of magnitude at an intermediate temperature, before rapidly decreasing at higher temperatures. Furthermore, when subject to a contraction flow through an extruder, above the main phase transition temperature of the bilayers, the suspensions instantaneously transform into a “jammed,” glassystate at the extruder outlet. The glassy dispersions behave like stiff gellike materials, having viscoelastic moduli that are several orders of magnitude higher than their unextruded counterparts. We probe mechanisms leading to the formation and subsequent aging of the jammed suspensions and show that the microstructural evolution of the extruded “gels” on aging is qualitatively different from that of the unextruded suspensions.

On the appearance of vorticity and gradient shear bands in wormlike micellar solutions of different CPCl/salt systems
View Description Hide DescriptionWormlike micellar salt/surfactant solutions (Xsalicylate, cetylpyridinium chloride) are studied with respect to the applied shear stress, concentration, temperature, and composition of the counterions (X = lithium, sodium, potassium, magnesium, and calcium) of the salicylate salt solute to determine vorticity and gradient shear bands. A combination of rheological measurements, laser technique, video analysis, and rheosmallangle neutron scattering allow for a detailed exploration of number and types of shear bands. Typical flow curves of the solutions show Newtonian, shearthinning, and shearthickening flow behavior. In the shearthickening regime, the solutions show vorticity and gradient shear bands simultaneously, in which vorticity shear bands dominate the visual effect, while gradient shear bands always coexist and predominate the rheological response. It is shown that gradient shear bands change their phases (turbid, clear) with the same frequency as the shear rate oscillates, whereas vorticity shear bands change their phases with half the frequency of the shear rate. Furthermore, we show that with increasing molecular mass of the counterions the number of gradient shear bands increases, while the number of vorticity shear bands remains constant. The variation of temperature, shear stress, concentration, and counterions results in a predictable change in the rheological behavior and therefore allows adjustment of the number of vorticity shear bands in the shear band regime.

On the theory of magnetoviscous effect in magnetorheological suspensions
View Description Hide DescriptionA theoretical model of magnetoviscous effect in a suspension of nonBrownian linearly magnetizable particles is suggested. A simple shear flow in the presence of an external magnetic field aligned with the velocity gradient is considered. Under the action of the applied field, the particles are supposed to form dense highly elongated droplike aggregates. Two different scenarios of the aggregates' destruction under shearing forces are considered, namely, a “bulk” destruction of aggregates into pieces and an “erosive” destruction connected to the rupture of individual particles from the aggregate surface. Both models are based on a balance of forces acting either on the whole aggregate or on individual particles. The two approaches lead to qualitatively different Mason number (Ma) behaviors of the magnetic suspensions: The suspension viscosity scales as either Ma ^{−2/3} for the bulk destruction of aggregates or Ma ^{−4/5} for the erosive destruction. In any case, we do not recover Bingham behavior (Ma ^{−1}) often predicted by chain models of the magneto or electrorheology. Our theoretical results are discussed in view of comparison with existing theories and experimental results in the wide range of Mason numbers.

Shear thickening, frictionless and frictional rheologies in nonBrownian suspensions
View Description Hide DescriptionParticles suspended in a Newtonian fluid raise the viscosity and also generally give rise to a shearrate dependent rheology. In particular, pronounced shear thickening may be observed at large solid volume fractions. In a recent article [R. Seto et al., Phys. Rev. Lett. 111, 218301 (2013)], we have considered the minimum set of components to reproduce the experimentally observed shear thickening behavior, including discontinuous shear thickening. We have found frictional contact forces to be essential and were able to reproduce the experimental behavior by a simulation including this physical ingredient along with viscous lubrication. In the present article, we thoroughly investigate the effect of friction and express it in the framework of the jamming transition. The viscosity divergence at the jamming transition has been a well known phenomenon in suspension rheology, as reflected in many empirical laws for the viscosity. Friction can affect this divergence, and in particular the jamming packing fraction is reduced if particles are frictional. Within the physical description proposed here, shear thickening is a direct consequence of this effect: As the shear rate increases, friction is increasingly incorporated as more contacts form, leading to a transition from a mostly frictionless to a mostly frictional rheology. This result is significant because it shifts the emphasis from lubrication hydrodynamics and detailed microscopic interactions to geometry and steric constraints close to the jamming transition.

Creep and recovery of magnetorheological fluids: Experiments and simulations
View Description Hide DescriptionA direct comparative study on the creeprecovery behavior of conventional magnetorheological (MR) fluids is carried out using magnetorheometry and particlelevel simulations. Two particle concentrations are investigated ( and ) at two different magnetic field strengths (53 and 173 kA·m^{−1}) in order to match the yield stresses developed in both systems for easier comparison. Simulations are mostly started with random initial structures with some additional tests of using preassembled single chains in the low concentration case. Experimental and simulation data are in good qualitative agreement. The results demonstrate three regions in the creep curves: (i) In the initial viscoelastic region, the chainlike (at ) or percolated threedimensional network (at structures fill up the gap and the average cluster size remains constant; (ii) Above a critical strain of 0.1 (10%), in the retardation region, these structures begin to break and rearrange under shear. At large enough imposed stress values, they transform into thin sheetlike or thick lamellar structures, depending on the particle concentration; (iii) Finally in the case of larger strain values either the viscosity diverges (at low stress values) or reaches a constant low value (at high stress values), showing a clear bifurcation behavior. For stresses below the bifurcation point, the MR fluid is capable to recover the strain by a certain fraction. However, no recovery is observed for large stress values.

A fractional KBKZ constitutive formulation for describing the nonlinear rheology of multiscale complex fluids
View Description Hide DescriptionThe relaxation processes of a wide variety of soft materials frequently contain one or more broad regions of powerlaw like or stretched exponential relaxation in time and frequency. Fractional constitutive equations have been shown to be excellent models for capturing the linear viscoelastic behavior of such materials, and their relaxation modulus can be quantitatively described very generally in terms of a Mittag–Leffler function. However, these fractional constitutive models cannot describe the nonlinear behavior of such powerlaw materials. We use the example of Xanthan gum to show how predictions of nonlinear viscometric properties, such as shearthinning in the viscosity and in the first normal stress coefficient, can be quantitatively described in terms a nonlinear fractional constitutive model. We adopt an integral KBKZ framework and suitably modify it for powerlaw materials exhibiting Mittag–Leffler type relaxation dynamics at small strains. Only one additional parameter is needed to predict nonlinear rheology, which is introduced through an experimentally measured damping function. Empirical rules such as the Cox–Merz rule and Gleissle mirror relations are frequently used to estimate the nonlinear response of complex fluids from linear rheological data. We use the fractional model framework to assess the performance of such heuristic rules and quantify the systematic offsets, or shift factors, that can be observed between experimental data and the predicted nonlinear response. We also demonstrate how an appropriate choice of fractional constitutive model and damping function results in a nonlinear viscoelastic constitutive model that predicts a flow curve identical to the elastic HerschelBulkley model. This new constitutive equation satisfies the RutgersDelaware rule, which is appropriate for yielding materials. This KBKZ framework can be used to generate canonical threeelement mechanical models that provide nonlinear viscoelastic generalizations of other empirical inelastic models such as the Cross model. In addition to describing nonlinear viscometric responses, we are also able to provide accurate expressions for the linear viscoelastic behavior of complex materials that exhibit strongly shearthinning Crosstype or Carreautype flow curves. The findings in this work provide a coherent and quantitative way of translating between the linear and nonlinear rheology of multiscale materials, using a constitutive modeling approach that involves only a few material parameters.

Mechanisms of shear thickening in transient guar network
View Description Hide DescriptionThe shearthickening behavior of reversibly crosslinked guar network is studied using rheological and particle imaging velocity measurements. New evidence suggests that both shearinduced increase in crosslink density and nonGaussian chain stretching are possible mechanisms for shear thickening. Which mechanism plays a predominant role depends on the applied shear rate and shear time. At not too much larger than , where is the network relaxation time, shear thickening is mainly caused by the increase in crosslink density. At higher shear rates, shear thickening is initiated by the increase in chain density at short times, and nonGaussian chain stretching occurs at longer times. It is demonstrated that the linear elastic modulus measured for the shearthickening state and its relaxation time can be used to discriminate between nonGaussian chain stretching and shearinduced crosslinking mechanisms. The detection of a linear step strain regime where the measured modulus does not change with the strain amplitude indicates the absence of nonGaussian chain stretch. When chains are stretched into the nonGaussian regime, the relaxation time becomes smaller whereas relaxation time remains unchanged if only crosslink density increases. At high shear rates, flow may become unstable with bulk fracture, shear banding, and continuous flow occurring randomly as revealed by the velocity profile across the flow cell gap.

Bubble migration in twodimensional foam sheared in a widegap Couette device: Effects of nonNewtonian rheology
View Description Hide DescriptionWe report experiments on the migration of a large bubble in an otherwise monodisperse twodimensional (2D) foam sheared in a widegap Couette device. The bubble migrates away from the walls toward an equilibrium position between the center of the gap and the inner cylinder. This differs from the situation in a narrowgap Couette device, where the equilibrium position is at the center of the gap [Mohammadigoushki and Feng, Phys. Rev. Lett. 109, 084502 (2012)]. The shift in equilibrium position is attributed to the nonNewtonian rheology of the foam, which is brought out by the nonhomogeneous shearing in a widegap geometry. Two aspects of the rheology, shearthinning and the first normal stress difference, are examined separately by comparing with bubble migration in a xanthan gum solution and a Boger fluid. Shearthinning shifts the equilibrium position inward while the normal stress does the opposite. Bubble migration in the 2D foam is the outcome of the competition between the two effects.

Magnetorheological effect in the magnetic field oriented along the vorticity
View Description Hide DescriptionIn this work, we have studied the magnetorheological (MR) fluid rheology in the magnetic field parallel to the fluid vorticity. Experimentally, the MR fluid flow was realized in the Couette coaxial cylinder geometry with the magnetic field parallel to the symmetry axis. The rheological measurements were compared to those obtained in the coneplate geometry with the magnetic field perpendicular to the lower rheometer plate. Experiments revealed a quasiBingham behavior in both geometries with the stress level being just a few dozens of percent smaller in the Couette cylindrical geometry at the same internal magnetic field. The unexpectedly high MR response in the magnetic field parallel to the fluid vorticity is explained by stochastic fluctuations of positions and orientations of the particle aggregates. These fluctuations are induced by magnetic interactions between them. Once misaligned from the vorticity direction, the aggregates generate a high stress independent of the shear rate, and thus assimilated to the suspension apparent (dynamic) yield stress. Quantitatively, the fluctuations of the aggregate orientation are modeled as a rotary diffusion process with a diffusion constant proportional to the mean square interaction torque. The model gives a satisfactory agreement with the experimental field dependency of the apparent yield stress and confirms the nearly quadratic concentration dependency , revealed in experiments. The practical interest of this study lies in the development of MR smart devices with the magnetic field nonperpendicular to the channel walls.

Pompomlike constitutive equations for comb polymers
View Description Hide DescriptionIn analogy with the pompom model, we introduce a simple model for comb polymers with multiple sidearms attached to a linear backbone by considering a set of coupled equations describing the stretch in the individual interbranch backbone segments. The stretch equations predict a sudden onset of backbone stretch as the flow rate is increased. Dragstrain coupling smooths this transition to some extent. For a series of well characterized polyisoprene and polystyrene combs, we find good agreement with the experimentally determined transient stress growth coefficients in uniaxial extension.

Resttime effects in repeated shearstartup runs of branched SBR polymers
View Description Hide DescriptionNew data of shear startup on branched styrenebutadiene random (SBR) copolymers are reported, where the novelty consists in repeating the startup run after different rest times at zero stress. Here, the aim is one of exploring the “damage” introduced by the first run, as well as the subsequent recovery, if any, upon waiting increasingly long times. Differently from a linear sample, our branched melts show multiple peaks during the first run, as previously reported by Bacchelli [Kautschuk Gummi Kunststoffe 61, 188–191 (2008)] for similar SBR samples, and, more recently, by Snijkers et al. [ACS Macro Lett. 2, 601–604 (2013)] for a wellcharacterized comblike polystyrene melt. The repeated runs show an intriguing novel feature with respect to the case of linear polymers, namely, the first peak goes up initially, instead of down. The second peak goes down and seemingly recovers only after an extremely long time, longer than the largest relaxation time practically accessible to linear viscoelasticity, the latter not reaching the terminal behavior. All such features of nonlinear viscoelasticity of highly branched polymers are interpreted by using a simple theory inspired by the wellknown pompom model.

Large amplitude oscillatory shear of immiscible polymer blends and comparison to anisotropy and droplet models
View Description Hide DescriptionLarge amplitude oscillatory shear (LAOS) experiments were carried out for a model immiscible blend composed of two Newtonian components at different viscosity ratio and volume fraction values. Data for the first, third, and fifth harmonics of the sinusoidal stress response were recorded and compared to the constrained volume (CV) model and to the Maffettone and Minale model. Moreover, various constitutive equations were investigated: The Batchelor constitutive equation with the viscous part of the interfacial contribution to stress neglected, Peters et al. [J. Rheol. 45, 659–689 (2001)] constitutive equation, the Lee and Park [J. Rheol. 38, 1405–1425 (1994)] constitutive equation, and the Yu and Bousmina [J. Rheol. 47, 1011–1039 (2003)] constitutive equation. It was found that a modification of the Peters et al constitutive equation, when combined with the CV model predictions, results in good description of the first harmonic data, as well as reasonable description for the third and fifth harmonic data. Experimental LAOS results at large viscosity ratio agreed well with the scaling law developed by Reinheimer et al. [J. Colloid Interface Sci. 360, 818–825 (2011)].

Origin of shear thickening in semidilute wormlike micellar solutions and evidence of elastic turbulence^{a)}
View Description Hide DescriptionThe origin of shear thickening in an equimolar semidilute wormlike micellar solution of cetylpyridinium chloride and sodium salicylate was investigated in this work by using Couette rheometry, flow visualization, and capillary Rheoparticle image velocimetry. The use of the combined methods allowed the discovery of gradient shear banding flow occurring from a critical shear stress and consisting of two main bands, one isotropic (transparent) of high viscosity and one structured (turbid) of low viscosity. Mechanical rheometry indicated macroscopic shear thinning behavior in the shear banding regime. However, local velocimetry showed that the turbid band increased its viscosity along with the shear stress, even though barely reached the value of the viscosity of the isotropic phase. This shear band is the precursor of shear induced structures that subsequently give rise to the average increase in viscosity or apparent shear thickening of the solution. Further increase in the shear stress promoted the growing of the turbid band across the flow region and led to destabilization of the shear banding flow independently of the type of rheometer used, as well as to vorticity banding in Couette flow. At last, vorticity banding disappeared and the flow developed elastic turbulence with chaotic dynamics.

Rheology of compatibilized immiscible blends with dropletmatrix and cocontinuous morphologies during coarsening
View Description Hide DescriptionIt is well known that addition of block copolymers to immiscible polymer blends may result in finer and more stable microstructures by reducing the driving force for coarsening, namely, the interfacial tension. This compatibilization is also reflected in the rheological behavior of the blends. We present an experimental study on the morphology and rheology of model blends composed of fluorescently labeled polystyrene and styreneranacrylonitrile copolymer compatibilized with a polystyrenebpolymethyl methacrylate diblock copolymer (BC). Three different weight ratios (wt/wt) are studied: 20/80, 35/65, and 50/50, with the following morphologies: Droplet/matrix, metastable cocontinuous, and abiding cocontinuous, respectively. It is found that regardless the type of initial morphology, the addition of BC reduces the characteristic size and increases the elastic modulus in the terminal regime, where the relaxation of the interface is probed. The relaxation spectra in the terminal zone are greatly affected by the presence of BC, which reflects the strong dependence of the viscoelastic behavior on the local microstructure (shape and area) of the interface. Furthermore, the addition of BC reduces the rate of coarsening, which is characterized by the time evolution of both the elastic modulus and the specific interfacial area. These effects are more pronounced when the molecular weight or concentration of the BC is higher. Finally, two regimes of coarsening in the symmetric (50/50) blends were identified and characterized by two different power laws.

The effects of geometrical confinement and viscosity ratio on the coalescence of droplet pairs in shear flow
View Description Hide DescriptionThe effects of geometrical confinement and viscosity ratio on droplet coalescence in shear flow are experimentally investigated by means of a counter rotating parallel plate device, equipped with a microscope. The ratio of droplet diameter to gap spacing is varied between 0.03 and 0.33 to study both bulk and confined conditions. Three grades of a Newtonian droplet material are combined with a Newtonian matrix, resulting in three different viscosity ratios, namely, 0.1, 1.1, and 2.6. The effects of confinement are qualitatively similar for all three viscosity ratios. For each system, confinement decreases the coalescence angle and renders coalescence possible up to higher capillary numbers and initial offsets. Moreover, for all three viscosity ratios, confinement induces a lower initial offset boundary below which the approaching droplets reverse flow direction without coalescence. However, there are quantitative differences between the systems. With increasing viscosity ratio, the critical capillary number and critical upper and lower offset boundaries decrease. Since the decrease of the upper offset boundary is more predominant, the coalescence efficiency decreases with viscosity ratio. The droplet trajectories of interacting droplets are affected by both the viscosity ratio and geometrical confinement, which clearly has implications on the coalescence behavior.

Stress relaxation in the nonequilibrium state of a polymer melt
View Description Hide DescriptionThe influence of entanglement density on the constraint renewal time is studied experimentally in transitory nonequilibrium polymer melts. The entanglement density, as quantified by the rubber elasticity, increases as the linear polymer melt transforms into the equilibrium state. The relaxation modulus obtained from linear stepstrain deformations, performed at different points during the equilibration, shows an increase in constraint renewal time as the entanglement density increases. The normalized relaxation modulus curves collapse onto a single curve by rescaling the time axis with a factor (where is the normalized instantaneous modulus). These findings suggest that, though the relaxation time increases with the increasing number of entanglements, the mechanism responsible for stress relaxation, after application of stepstrain, is similar to that in a fully entangled melt.

Scaling laws for the flow of generalized Newtonian suspensions
View Description Hide DescriptionIt has been observed that flow curves (viscosity vs shear rate) of spherical solid inclusions suspended in a generalized Newtonian fluid medium can be rescaled so as to collapse onto the flow curve of the fluid medium. This result is surprising given the range of values and the spatial heterogeneity of local shear rates and viscosity in such systems. We consider such scaling for the cases of shear thinning, Newtonian, and shearthickening fluid media. Results from experiment and computational modeling are presented that examine the microscopic origins of this scaling behavior. Over a wide range of volume fractions (5–50%), it is shown that the distribution of local shear rates can be collapsed onto a single universal curve. The parameters for rescaling the shear rate distributions can be analytically related to the macroscopic rescaling parameters for the viscosity. As a result of this rescaling capability, one may measure the properties of the fluid medium and predict the macroscopic behavior of the suspension.

Elongational deformation of wormlike micellar solutions
View Description Hide DescriptionWe have investigated the uniaxial elongation behavior of six different wormlike micelle systems covering a broad range of surfactant concentrations and salt/surfactant ratios R using the capillary breakup elongational rheometry (CaBER). In the fastbreaking limit (high and R), filament lifetime is controlled by the equilibrium shear modulus G0 and the breakage time obtained from small oscillatory shear according to and relaxation time ratios are found. When reptation dominates (high , low R) is observed similar as for solutions of covalently bound polymers. In this concentration regime, the micellar structure seems not to be affected by the strong elongational flow. In contrast, high filament lifetimes up to 1000 s and values up to 10 are observed at low irrespective of R. This indicates the formation of elongationinduced structures (EISs). A minimum viscosity and a minimum initial diameter are required for creating EIS. Additional filament stretching experiments indicate that a critical total deformation has to be exceeded for structure buildup. Finally, our experiments reveal a distinct difference regarding the dependence between solutions of linear and branched micelles of filament lifetime on viscosity suggesting that CaBER is a versatile means to distinguish between these structures.