Shear thickening, frictionless and frictional rheologies in non-Brownian suspensions

Abstract

Particles suspended in a Newtonian fluid raise the viscosity and also generally give rise to a shear-rate dependent rheology. In particular, pronounced shear thickening may be observed at large solid volume fractions. In a recent article (R. Seto, R. Mari, J. F. Morris, and M. M. Denn., Phys. Rev. Lett., 111:218301, 2013) we have considered the minimum set of components to reproduce the experimentally observed shear thickening behavior, including Discontinuous Shear Thickening (DST). We have found frictional contact forces to be essential, and were able to reproduce the experimental behavior by a simulation including this physical ingredient along with viscous lubrication. In the present article, we thoroughly investigate the effect of friction and express it in the framework of the jamming transition. The viscosity divergence at the jamming transition has been a well known phenomenon in suspension rheology, as reflected in many empirical laws for the viscosity. Friction can affect this divergence, and in particular the jamming packing fraction is reduced if particles are frictional. Within the physical description proposed here, shear thickening is a direct consequence of this effect: as the shear rate increases, friction is increasingly incorporated as more contacts form, leading to a transition from a mostly frictionless to a mostly frictional rheology. This result is significant because it shifts the emphasis from lubrication hydrodynamics and detailed microscopic interactions to geometry and steric constraints close to the jamming transition.

Shear-induced rigidity in athermal materials: A unified statistical framework

“…2 (d)). As we discuss below, DST occurs in the φ range corresponding to R R DST , where M is a monotonically decreasing function of X, which explains the monotonic decrease of the stress anisotropy with f iso observed in numerical simulations [7,14]. …”

“…We examine the consequences of the interplay between the driving field and the underlying disorder of the contact network on the development of a robust, force-bearing network. The model focuses solely on the force network: changes in the network of frictional contacts with their associated tangential forces strongly affect the viscosity of suspensions in the DST regime [7,9,14] Mapping to spin 1 Ising variables: grains with more than 2 contacts (green) are assumed to have S = 0 (stress anisotropy below threshold) , and grains with 2 contacts have either S = 1 (red) or S = −1 (blue), depending on whether the contact is aligned along the compressive (yellow broken line in (a)) or dilational direction. (c) Enlargement of a small section of (a) illustrating the grain-spin mapping.…”

“…We envision the SJ and DST processes as ones where the contact network and grain-level stresses reach a force and torque balanced state in the presence of driving [5,7,14]. We model this by the zero-temperature, single-spin flips, energy minimizing dynamics of the energy function ( Fig.…”

“…The nature of this self-organization process has been intensely investigated in recent months, and striking similarities have been observed between the two transitions. This is remarkable since the SJ transition occurs through a quasistatic process and refers to static states of particles interacting via purely repulsive contact interactions [2,4,5], and DST occurs through a dynamical process that creates non-equilibrium steady states (NESS) of particles interacting via hydrodynamic and contact interactions [7,14]. The single most important trigger for these transitions has been identified as the proliferation of frictional contacts [2,7,14,15].…”

“…4(c) [4,15] : universal function of . Increases dramatically at [14] Pressure is assumed to be uniquely determined by , . ⇒ Δ 0 > Δ : The scaling form of X(R, H) implies that the pressure scales as: P (R, H) ∼ f (X(R, H)) ∝ g P (H/H peak (R)), where g P (x) is a scaling function similar to g X defined above.…”