Force transmission and the order parameter of shear thickening

Abstract

The origin of the abrupt shear thickening observed in some dense suspensions has been recently argued to be a transition from frictionless (lubricated) to frictional interactions between immersed particles. The Wyart-Cates rheological model, built on this scenario, introduced the concept of fraction of frictional contacts $f$ as the relevant order parameter for the shear thickening transition. Central to the model is the "equation-of-state" relating $f$ to the applied stress $\sigma$, which is directly linked to the distribution of the normal components of non-hydrodynamics interparticle forces. Here, we develop a model for this force distribution, based on the so-called $q$-model that we borrow from granular physics. This model explains the known $f(\sigma )$ in the simple case of sphere contacts displaying only sliding friction, but also predicts strong deviation from this "usual" form when stronger kinds of constraints are applied on relative motion. We verify these predictions in the case of contacts with rolling friction, in particular a broadening of the stress range over which shear thickening occurs. We finally discuss how a similar approach can be followed to predict $f(\sigma )$ in systems with other variations from the canonical system of monodisperse spheres with sliding friction, in particular the case of large bidispersity.

11 pages, 10 figures

References in corpus (9)

• A constitutive model for simple shear of dense frictional suspensions
• Force Mobilization and Generalized Isostaticity in Jammed Packings of Frictional Grains
• Bidisperse and polydisperse suspension rheology at large solid fraction
• Non-monotonic flow curves of shear thickening suspensions
• A constraint-based approach to granular dispersion rheology
• Flow regime transitions in dense non-Brownian suspensions: rheology, microstructural characterisation and constitutive modelling
• Conching chocolate: A prototypical transition from frictionally jammed solid to flowable suspension with maximal solid content
• Shear jamming and fragility in dense suspensions
• Jamming transition in a two-dimensional open granular pile with rolling resistance

Cited by in corpus (8)

• Shear thickening and jamming of dense suspensions: the "roll" of friction
• The physics of dense suspensions
• Granular packings with sliding, rolling and twisting friction
• Stress-activated Constraints in Dense Suspension Rheology
• Stress fluctuations and shear thickening in dense granular suspensions
• Shear thickening of suspensions of dimeric particles
• Non-monotonic Rheology and Stress Heterogeneity in confined Granular suspensions
• Attraction-enhanced emergence of friction in colloidal matter