Athermal analogue of sheared dense Brownian suspensions

Abstract

-The rheology of dense Brownian suspensions of hard spheres is investigated numerically beyond the low shear rate Newtonian regime. We analyze an athermal analogue of these suspensions, with an effective logarithmic repulsive potential representing the vibrational entropic forces. We show that both systems present the same rheology without adjustable parameters. Moreover, all rheological responses display similar Herschel-Bulkley relations once the shear stress and the shear rate are respectively rescaled by a characteristic stress scale and by a microscopic reorganization time-scale, both related to the normal confining pressure. This pressure-controlled approach, originally developed for granular flows, reveals a striking physical analogy between the colloidal glass transition and granular jamming.Amorphous materials [1] such as granular packings [2], colloidal suspensions [3][4][5][6][7] or glassy molecular systems [8-10] display a severe increase in their viscosity before solidifying. With glass-forming liquids, an amorphous solid is obtained by rapidly cooling below the freezing temperature. In the case of systems of hard particles with size dispersion, an emergent solid-like behavior as the packing fraction φ is increased and the amorphous character stems from geometrical disorder. In spite of essential differences in microscopic interactions, the existence of a universal scenario leading to a dynamical slowing down and to the emergence of rigidity [11] remains a vivid issue [10,[12][13][14][15]. Colloids, by the nature of their interparticle interactions and their size, are at the cross-roads between molecular thermal systems and athermal granular materials [16,17,[22][23][24][25][26][27][28][29]. In the dense regime, colloidal suspensions bear all the phenomenological complexity shared by glassforming materials. The strong dynamical slowing down is associated with particle trapping in cages formed by their neighbours [6,30]. Because of this relatively simple picture, colloids are often considered as paradigmatic systems to approach the general issues of dynamical arrest, glass transition and non-Newtonian rheology observed in complex fluids.The overall viscosity of an athermal suspension results from two contributions: the fluid and the particles. (Fig. 1), that there is an increase with particle density in the system's viscosity due to an increase in hydrodynamic interactions. However, this effect does not account for the drastic dynamical slowing-down measured experimentally [22][23][24][25]: even for the state of the art numerical simulations [20,21], the viscosity is strongly underestimated in the dense limit (Fig. 1). As shown in [25], a stress related to collective particle effects and in the complexity of the particle trajectories under geometrical constraints, is actually responsible for the diverging viscosity [26,27].In this letter, we extend this line of thought to dense Brownian suspensions using a model that focusses on collective particle phenomena, the physics at play becoming cl...

Discontinuous shear thickening in Brownian suspensions by dynamic simulation

“…A comparison between our numerical results and experimental data (26) shows that in actual suspensions the repulsive effect of the Brownian force adds to an actual potential repulsive force. This analogy between Brownian force and repulsive force is not restricted to the thickening regime and has been proposed for suspensions at equilibrium (43) and, recently, in the shear thinning regime (44). Our work supports the view that a theoretical modeling of shear thickening should be centered on a framework common to Brownian and non-Brownian systems (45), e.g., a geometric description (46,47) including a stress-induced friction mechanism.…”

Rheology of granular flows across the transition from soft to rigid particles

“…Statistical properties of trajectories are essentially determined by steric effects and are insensitive to the details of dissipative mechanisms. Interestingly, the rheology of Brownian suspensions can also be mapped to that of non-Brownian suspensions of soft elastic spheres, replacing thermal noise by mean field entropic repulsions [35,36]. The analogy between constitutive relations of grains in the overdamped and inertial regimes thus strongly suggests that steric effects control the statistical properties of grain trajectories in dense granular flows, and these results showing the quasiindependence of the law µ(I) with respect to the grain stiffness reinforce this idea.…”

Theory of the jamming transition at finite temperature

“…75,76 It would be interesting to see if the notion of effective potential could be used to extend such considerations to finite temperature, a path recently proposed in Ref. 77. …”