Constitutive Model for Time-Dependent Flows of Shear-Thickening Suspensions

J. J. J. Gillissen, C. Ness, J. D. Peterson, H. J. Wilson, and M. E. Cates

Phys. Rev. Lett. 123, 214504 – Published 20 November 2019

Abstract

We develop a tensorial constitutive model for dense, shear-thickening particle suspensions subjected to time-dependent flow. Our model combines a recently proposed evolution equation for the suspension microstructure in rate-independent materials with ideas developed previously to explain the steady flow of shear-thickening ones, whereby friction proliferates among compressive contacts at large particle stresses. We apply our model to shear reversal, and find good qualitative agreement with particle-level, discrete-element simulations whose results we also present.

Received 5 August 2019

DOI:https://doi.org/10.1103/PhysRevLett.123.214504

Physics Subject Headings (PhySH)

Non-Newtonian fluids

Wet granular materials

Shear thickening

Fluid Dynamics

Authors & Affiliations

J. J. J. Gillissen ¹, C. Ness ², J. D. Peterson³, H. J. Wilson ¹, and M. E. Cates ³

¹Department of Mathematics, University College London, Gower Street, London WC1E 6BT, United Kingdom
²Department of Chemical Engineering and Biotechnology, University of Cambridge, Cambridge CB3 0AS, United Kingdom
³DAMTP, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, United Kingdom