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Shear-density coupling for a compressible single-component yield-stress fluid

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 condition 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.

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Publication details

The article was received on 09 Mar 2018, accepted on 01 May 2018 and first published on 07 May 2018


Article type: Paper
DOI: 10.1039/C8SM00495A
Citation: Soft Matter, 2018, Accepted Manuscript
  • Open access: Creative Commons BY license
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    Shear-density coupling for a compressible single-component yield-stress fluid

    M. Gross and F. Varnik, Soft Matter, 2018, Accepted Manuscript , DOI: 10.1039/C8SM00495A

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