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To predict the complex rheology and shear-rate inhomogeneities of lamellar gel networks, we propose a simple thixotropic constitutive model with an elastoplastic stress and a smoothly decreasing modulus near a solid boundary, motivated by the analysis of the effect of confinement and shear flow on lamellae orientation near surfaces. We show that the model qualitatively captures the important features of the lamellar gel shear rheology observed in experiments [Datta et al., J. Rheol. 64(4), 851–862 (2020)]. These include thixotropic shear thinning that is intermediate between constant viscosity and constant stress, a power-law slow creep under small constant shear stress and abrupt transition to fast creep at higher stress, as well as partial recovery of strain upon stress removal. In addition, the model correctly predicts a gap-dependent rheology and roughly predicts the amplitude dependence of storage and loss moduli in oscillatory tests despite having only a single thixotropic time constant. Most importantly, the introduction of the modulus gradient enables the model to predict the unique shear-banding phenomenon of lamellar gel networks wherein a thin, fast-shearing band exists near the boundary that widens only slowly with increased apparent shear rate until a very high rate is reached, while the bulk moves as a plug [Datta et al., J. Rheol. 64(4), 851–862 (2020)]. We discuss the influence of a lower modulus near the boundary and its possible origin in the underlying lamellar structure of the material. [ABSTRACT FROM AUTHOR]

Our recent continuum theory for stress-gradient-induced migration of polymers in confined solutions, including the depletion from the solid boundaries [Hajizadeh, E., and R. G. Larson, Soft Matter, 13, 5942–5949 (2017)], is applied to a two-dimensional rotational shearing flow in the gap between eccentric cylinders. Analytical results for the steady-state distribution of polymer dumbbells in the limit of dilute polymer solution c / c ∗ ≪ 1 (c∗ is the chain overlap concentration) and in the absence of hydrodynamic interactions are obtained. The effects of eccentricity e and of three perturbation variables, namely, Weissenberg number W i , gradient number G d (which defines the level of polymer chain confinement), and Péclet number P e on the polymer concentration pattern, are investigated. The stress-gradient-induced migration results in polymer migration toward the inner cylinder, while wall-depletion-induced migration results in near-zero polymer concentration close to flow boundaries, which couples to a stress-gradient-induced migration effect. In the presence of wall-depletion, we obtain first order concentration variation proportional to W i. However, in the absence of wall-depletion, there is no first order contribution and, therefore, the lowest-order concentration variation is proportional to W i 2. An upper limit of W i = 1.6 exists, beyond which the numerical solution demands an excessive under-relaxation to converge. In addition, for a high degree of polymer chain confinement, i.e., for G d greater than 0.5, the continuum theory fails to be accurate and mesoscopic simulations that track individual polymer molecules are needed. [ABSTRACT FROM AUTHOR]

Brownian dynamics simulations are performed to study the binding kinetics in the dilute-sphere limit by considering interactions of two spheres under shear flow across the entire range of Peclet numbers, spanning both perikinetic (diffusion-controlled) and orthokinetic (flow-controlled) coagulation regimes. The dilute regime is attained by carrying out two-sphere simulations in periodic boxes of different sizes and aspect ratios and extrapolating toward the infinite box limit. Effects of particle type (Janus and isotropic particles), shear rate, hydrodynamic interactions, and inter-particle potential are explored. We find that rectangular boxes with appropriate aspect ratios overcome a particle "shadow effect" that cannot be overcome with cubic boxes unless huge boxes are used. With rectangular boxes, we obtain converged binding kinetics for the whole Peclet number range, while cubic boxes of increasing size allow converged results only in the absence of flow. We consider the effect of binding both in a secondary minimum controlled by a combination of electrostatic repulsion and depletion attraction, as well as in a primary minimum governed by induced-dipole attraction. Results are computed using both realistic interaction potentials and by replacing the potential with a simple cutoff gap distance at which binding is deemed to occur. Results agree with several existing reports including Smoluchowski predictions in the zero- and infinite-shear-rate limits, and high-Pe perturbation results of Feke and Schowalter [J. Fluid Mech. 133, 17-35 (1983)] at Peclet numbers (Pe) above 100. Finally, we compute binding times for anisotropic Janus particles which have both repulsive and attractive faces, for a wide range of Pe number. [ABSTRACT FROM AUTHOR]

The authors report the rheology and shear flow velocity profiles of pseudo-ternary "lamellar gel networks" commonly found in cosmetic emulsions such as creams, lotions, and hair conditioners, consisting of the cationic surfactant behentrimonium methosulfate, a fatty alcohol mixture of cetyl and stearyl alcohol, and water at surfactant/fatty alcohol mole fractions ranging from 0.1 to 0.6 and water mass fractions of 85%–97%. The high shear-thinning viscosity shows hysteresis in up- and down-ramps of the shear rate, with the gel "remembering" its highest shear for around 12 h before it heals and recovers its original viscosity. These materials exhibit rheological signatures characteristic of a soft glassy material (as described by the soft glassy rheology model) such as shear hysteresis, inhomogeneous velocity gradient, a solidlike creep response, power-law stress decay in step strain experiments, and high storage modulus relative to loss modulus over a wide range of frequencies, confirming its nearly elastic response for small deformations. Using particle image velocimetry (PIV) in steady shear experiments, a transition from a linear velocity profile to a pluglike profile was observed at shear rates above around 0.01 s−1. PIV also revealed macroscopic inhomogeneities including the development of fracture planes and shear bands, with rheology becoming gap-dependent and displaying some characteristics of solidlike friction. [ABSTRACT FROM AUTHOR]

To predict the complex transient rheology of thixotropic elasto-viscoplastic (TEVP) fluids, we generalize a previous scalar thixotropic-only "multilambda" (ML) model [Wei et al., J. Rheol. 60(6), 1301-1315 (2016)] and combine it with the isotropic kinematic hardening (IKH) model [C. J. Dimitriou and G. H. Mckinley, Soft Matter 10(35), 6619-6644 (2014)]. This new constitutive equation, which we call ML-IKH model, has the following features: (1) Multiple thixotropic structure parameters that collectively exhibit a stretch-exponential thixotropic relaxation in step tests; (2) nonlinear thixotropic kinetic equations in both the shear rate or stress and the structure parameters; (3) incorporation of the Armstrong-Frederick kinematic hardening rule [C. O. Frederick and P. Armstrong, Mater. High Temp. 24(1), 1-26 (2007)] for the evolution of yield stress; and (4) viscoelasticity. We evaluate this 12-parameter model, discuss its four key features, and compare its predictions with those of the ML, IKH, and modified Delaware thixotropic models [Armstrong et al., J. Rheol. 60(3), 433-450 (2016)] for two sets of experimental data [Wei et al., J. Rheol. 60(6), 1301-1315 (2016); Armstrong et al., J. Rheol. 60(3), 433-450 (2016)] of a TEVP fumed silica suspension. The shear-rate histories include steady state, step shear rate, step stress, intermittent shear, flow reversal, and large amplitude oscillatory shear (LAOS). We show that in step tests the thixotropic and viscoelastic evolutions are dominant, while intermittent shear tests the multiple thixotropic timescales, and flow reversal tests the viscoelastic and plastic evolutions. The rheological responses in LAOS tests are more complex and involve all aspects of TEVP rheology. The four features quantitatively capture different aspects of TEVP rheology. We also provide a tensorial formulation of the ML-IKH model that is frame-invariant, obeys the second law of thermodynamics, and can reproduce the predictions of the scalar version. [ABSTRACT FROM AUTHOR]

We propose a rheological model for ideal thixotropy, defined as a reversible time-dependent shear-thinning viscous response, in both shearrate- controlled (RC Model) and stress-controlled (SC Model) forms. The model introduces a spectrum of structure parameters that collectively relaxes as a stretched exponential. It retains time-invariance symmetry with only a stretching exponent β as an additional model parameter relative to conventional single-structure-parameter models. The kinetic equations are nonlinear in both the structure parameters and the flow parameters of strain rate or stress. We demonstrate that introducing multiple structure parameters can successfully capture the stretched-exponential and nonmonotonic evolution of stress or shear rate in general step tests; and using nonlinear kinetic equations can explain the relaxation time's dependence on both the initial and final values of shear rate or stress in step tests. We present rheological data for a fumed silica dispersion in a number of shear histories including steady state, step shear rate, step stress, shear-rate ramp, and stress ramp. A systematic way to parameterize the models is provided. Both models fit experimental data well although the SC Model provides better agreement with the measurements. The ideal thixotropic models can be combined with existing methods that incorporate viscoelasticity so as to extend their validity into the region of low shear rates. [ABSTRACT FROM AUTHOR]

A detailed study of the effects of hydrodynamic interaction (HI) and excluded volume (EV), on isolated bead-rod chains in shear flows, where the 'rods' are mimicked by stiff Fraenkel springs is presented. It is observed that the deformation behavior at weak and intermediate shear rates is qualitatively similar to that observed for polymer chains in the absence of EV and HI, while that at high-shear rates is sensitive to modeling details and chain resolution. Our simulations with varying degrees of resolution reveal universality in chain behavior in the presence of EV (without HI), while the onset of the transition to a compressed chain in the presence of HI (without EV) shifts to higher shear rates with increasing chain resolution. The results also highlight the success of the bead-spring models in predicting the chain behavior in shear flows in the presence of HI, when the HI parameter is appropriately chosen. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1400-1412, 2014 [ABSTRACT FROM AUTHOR]

The effects of self-entanglements (spring-spring uncrossability) and solvent quality on the static and dynamic properties of a polymer chain in shear and extensional flows are investigated using Brownian dynamics simulations. We model the polymer chain by a sequence of beads connected by finitely extensible non-linear elastic springs, and spring-spring uncrossability is enforced by applying a spring-spring repulsive potential together with an adaptive time-stepping. Our findings suggest that chain uncrossability has an insignificant effect on the dynamics of a polymer chain. Furthermore, we considered four different combinations of intramolecular interactions: (i) no interactions, (ii) repulsive spring-spring and attractive bead-bead interactions, (iii) only repulsive bead-bead interactions, and (iv) only repulsive spring-spring interactions. The first two cases model 'theta' solvents, where the radius-of-gyration of a polymer chain, Rg∼N0.5, where N is the number of beads. For appropriately chosen parameters of interaction potentials, the last two cases model good solvents, where Rg∼N0.59. In the presence of a simple shear flow, the stretching behavior is alike in all the cases except case (ii). In case (ii), the polymer chain forms 'pearl-necklace-like' structures at zero Weissenberg number, Wi. With an increase in Wi, Rg first increases due to stretching of bonds between neighboring 'pearls,' and then decreases when the decrease in the number of pearls becomes limiting. In the presence of an extensional flow, normal stretching behavior is observed even in case (ii); the number of pearls increases with increasing extension rate because larger pearls break into smaller 'pearls.' The results show that even for fixed overall solvent quality for a chain at rest (e.g., a theta solvent), the ability of the chain to stretch in a shear flow is sensitive to the nature of intramolecular interactions. A chain with short-range attraction (between beads) and a long-range repulsion (between springs) tuned to balance each other and so create a theta condition at rest does not stretch much in a shear flow, while a chain for which the theta condition is achieved by applying no interactions at all does stretch in a shear flow. [ABSTRACT FROM AUTHOR]

We develop a coarse-graining procedure,using bead–rod chainswith varying numbers of rods per Kuhn length (Nr,K), to model the conformational dynamics of polymer chainswith bending stiffness and self-attraction. We find the conditionsunder which increased chain resolution leads to converged resultsfor the effect of bending stiffness, attractive interaction strength(ε), and shearing flow on the conformational dynamics. As chainstiffness increases, we find a collapse transition that becomes steeperas attractive strength increases. The collapsed state depends notonly on the net dimensionless attractive strength ε* = εNr,Kbetween each Kuhn step of the chain butalso on the ratio of bead diameter to Kuhn length (σ*). At highε* (>0.8/σ*), collapsed globules are produced at moderatechain diameter σ* = 1/4, while for fat chains with σ*= 1, helices are formed, and for thin ones with σ* = 1/16, tori,folded bundles, and finally globules are formed as ε* increases. [ABSTRACT FROM AUTHOR]

Using Brownian dynamics simulations of polymer chainsover a widerange of resolution, we find universal scaling laws for polymer coildimensions and tumbling time. At high shear rates γ̇,the coil thickness in the gradient direction becomes independent ofchain length, scaling as NK0γ̇–1/4,where NKdenotes the numbers of Kuhn steps,and the tumbling time scales as NKγ̇–3/4, correcting scaling laws presented in prior studies.We find this to be a consequence of the formation of loops whose lengthis limited by the time required to stretch them and derive scalinglaws from a balance of convection and diffusion of monomers. We findthat, in the absence of hydrodynamic interaction (HI) and excludedvolume (EV), for wormlike chains, the shrinkage in chain stretch observedat ultrahigh shear rates is pushed out to arbitrarily high shear ratesif the chain is resolved increasingly finely below the persistencelength. Finally, scaling laws in the presence of excluded volume andhydrodynamic interactions are derived that are expected to be validfor long chains at high shear rates. [ABSTRACT FROM AUTHOR]

To assess the role of particle roughness in the rheological phenomena of concentrated colloidal suspensions, we develop model colloids with varying surface roughness length scales up to 10% of the particle radius. Increasing surface roughness shifts the onset of both shear thickening and dilatancy towards lower volume fractions and critical stresses. Experimental data are supported by computer simulations of spherical colloids with adjustable friction coefficients, demonstrating that a reduction in the onset stress of thickening and a sign change in the first normal stresses occur when friction competes with lubrication. In the quasi-Newtonian flow regime, roughness increases the effective packing fraction of colloids. As the shear stress increases and suspensions of rough colloids approach jamming, the first normal stresses switch signs and the critical force required to generate contacts is drastically reduced. This is likely a signature of the lubrication films giving way to roughness-induced tangential interactions that bring about load-bearing contacts in the compression axis of flow. [ABSTRACT FROM AUTHOR]