Abstract
Flow behavior of a single-component yield stress fluid is addressed on the hydrodynamic level. A basic ingredient of the model is a coupling between fluctuations of density and velocity gradient via a Herschel-Bulkley-type constitutive model. Focusing on the limit of low shear rates and high densities, the model approximates well-but is not limited to-gently sheared hard sphere colloidal glasses, where solvent effects are negligible. A detailed analysis of the linearized hydrodynamic equations for fluctuations and the resulting cubic dispersion relation reveals the existence of a range of densities and shear rates with growing flow heterogeneity. In this regime, after an initial transient, the velocity and density fields monotonically reach a spatially inhomogeneous stationary profile, where regions of high shear rate and low density coexist with regions of low shear rate and high density. The steady state is thus maintained by a competition between shear-induced enhancement of density inhomogeneities and relaxation via overdamped sound waves. An analysis of the mechanical equilibrium condition provides a criterion for the existence of steady state solutions. The dynamical evolution of the system is discussed in detail for various boundary conditions, imposing either a constant velocity, shear rate, or stress at the walls.
Highlights
Heterogeneous flow and shear banding are ubiquitous phenomena, commonly occurring in a variety of complex fluids such as polymer solutions and worm-like micelles,[1,2,3] colloidal gels,[4] hard sphere colloidal glasses[5,6] and granular media.[7]
We focus on the limit of gently sheared dense singlecomponent fluids, such as colloidal hard sphere glasses, where hydrodynamic interactions are negligible
Instead of a coupling to the concentration field as in the original theory of shear– concentration coupling,[13] in the present case, fluctuations of the velocity field are coupled to fluctuations of the fluid density
Summary
Heterogeneous flow and shear banding are ubiquitous phenomena, commonly occurring in a variety of complex fluids such as polymer solutions and worm-like micelles,[1,2,3] colloidal gels,[4] hard sphere colloidal glasses[5,6] and granular media.[7]. There is a common consensus that the effect of hydrodynamic interactions can be neglected in colloidal hard-sphere systems close to the glass transition in the low shear rate limit, which is of primary interest to the present study.[14,15] Accepting this standpoint, it is tempting to fully neglect the background fluid and investigate the issue of flow heterogeneity within hydrodynamic equations of a single-component non-. The viscosity and the pressure are sensitive to the total density, since this quantity describes the caging and trapping responsible for the dynamic slowing down near the glass transition In view of these arguments on the single-component fluid nature of the problem, it appears more appropriate to analyze the hard-sphere system of ref. Where we defined Pr q(P À syyiyeld)/qr, Pg_ qP/qg_, sr q(syxiyeld + Zg_)/qr, sg_ q(Zg_)/qg_, which are generally functions of r and g_
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