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Publication# Effect of friction on dense suspension flows of hard particles

Abstract

We use numerical simulations to study the effect of particle friction on suspension flows of non-Brownian hard particles. By systematically varying the microscopic friction coefficient mu(p) and the viscous number J, we build a phase diagram that identifies three regimes of flow: frictionless, frictional sliding, and rolling. Using energy balance in flow, we predict relations between kinetic observables, confirmed by numerical simulations. For realistic friction coefficients and small viscous numbers (below J similar to 10(-3)), we show that the dominating dissipative mechanism is sliding of frictional contacts, and we characterize asymptotic behaviors as jamming is approached. Outside this regime, our observations support the idea that flow belongs to the universality class of frictionless particles. We discuss recent experiments in the context of our phase diagram.

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Friction

Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction:
*Dry friction is a force

Phase diagram

A phase diagram in physical chemistry, engineering, mineralogy, and materials science is a type of chart used to show conditions (pressure, temperature, volume, etc.) at which thermodynamically disti

Direct numerical simulation

A direct numerical simulation (DNS) is a simulation in computational fluid dynamics (CFD) in which the Navier–Stokes equations are numerically solved without any turbulence model. This means that the

Carolina Brito Carvalho dos Santos, Matthieu Wyart

Amorphous packings of nonspherical particles such as ellipsoids and spherocylinders are known to be hypostatic: The number of mechanical contacts between particles is smaller than the number of degrees of freedom, thus violating Maxwell's mechanical stability criterion. In this work, we propose a general theory of hypostatic amorphous packings and the associated jamming transition. First, we show that many systems fall into a same universality class. As an example, we explicitly map ellipsoids into a system of "breathing" particles. We show by using a marginal stability argument that in both cases jammed packings are hypostatic and that the critical exponents related to the contact number and the vibrational density of states are the same. Furthermore, we introduce a generalized perceptron model which can be solved analytically by the replica method. The analytical solution predicts critical exponents in the same hypostatic jamming universality class. Our analysis further reveals that the force and gap distributions of hypostatic jamming do not show power-law behavior, in marked contrast to the isostatic jamming of spherical particles. Finally, we confirm our theoretical predictions by numerical simulations.

Flows of hard granular materials depend strongly on the interparticle friction coefficient mu(p) and on the inertial number I, which characterizes proximity to the jamming transition where flow stops. Guided by numerical simulations, we derive the phase diagram of dense inertial flow of spherical particles, finding three regimes for 10(-4) less than or similar to I less than or similar to 10(-1): frictionless, frictional sliding, and rolling. These are distinguished by the dominant means of energy dissipation, changing from collisional to sliding friction, and back to collisional, as mu(p) increases from zero at constant I. The three regimes differ in their kinetics and rheology; in particular, the velocity fluctuations and the stress ratio both display nonmonotonic behavior with mu(p), corresponding to transitions between the three regimes of flow. We rationalize the phase boundaries between these regimes, show that energy balance yields scaling relations between microscopic properties in each of them, and derive the strain scale atwhich particles lose memory of their velocity. For the frictional sliding regime most relevant experimentally, we find for I >= 10(-2.5) that the growth of the macroscopic friction mu(I) with I is induced by an increase of collisional dissipation. This implies in that range that mu(I) - mu(0) similar to I1-2b, where b approximate to 0.2 is an exponent that characterizes both the dimensionless velocity fluctuations L similar to I-b and the density of sliding contacts chi similar to I-b.

2016The research work reported in the present dissertation is aimed at the analysis of complex physical phenomena involving instabilities and nonlinearities occurring in fluids through state-of-the-art numerical modeling. Solutions of intricate fluid physics problems are devised in two particularly arduous situations: fluid domains with moving boundaries and the high-Reynolds-number regime dominated by nonlinear convective effects. Shear-driven flows of incompressible Newtonian fluids enclosed in cavities of varying geometries are thoroughly investigated in the two following frameworks: transition with a free surface and confined turbulence. The physical system we consider is made of an incompressible Newtonian fluid filling a bounded, or partially bounded cavity. A series of shear-driven flows are easily generated by setting in motion some part of the container boundary. These driven-cavity flows are not only technologically important, they are of great scientific interest because they display almost all physical fluid phenomena that can possibly occur in incompressible flows, and this in the simplest geometrical settings. Thus corner eddies, secondary flows, longitudinal vortices, complex three-dimensional patterns, chaotic particle motions, nonuniqueness, transition, and turbulence all occur naturally and can be studied in the same geometry. This facilitates the comparison of results from experiments, analysis, and computation over the whole range of Reynolds numbers. The flows under consideration are part of a larger class of confined flows driven by linear or angular momentum gradients. This dissertation reports a detailed study of a novel numerical method developed for the simulation of an unsteady free-surface flow in three-space-dimensions. This method relies on a moving-grid technique to solve the Navier-Stokes equations expressed in the arbitrary Lagrangian-Eulerian (ALE) kinematics and discretized by the spectral element method. A comprehensive analysis of the continuous and discretized formulations of the general problem in the ALE frame, with nonlinear, non-homogeneous and unsteady boundary conditions is presented. In this dissertation, we first consider in the internal turbulent flow of a fluid enclosed in a bounded cubical cavity driven by the constant translation of its lid. The solution of this flow relied on large-eddy simulations, which served to improve our physical understanding of this complex flow dynamics. Subsequently, a novel subgrid model based on approximate deconvolution methods coupled with a dynamic mixed scale model was devised. The large-eddy simulation of the lid-driven cubical cavity flow based on this novel subgrid model has shown improvements over traditional subgrid-viscosity type of models. Finally a new interpretation of approximate deconvolution models when used with implicit filtering as a way to approximate the projective grid filter was given. This led to the introduction of the grid filter models. Through the use of a newly-developed method of numerical simulation, in this dissertation we solve unsteady flows with a flat and moving free-surface in the transitional regime. These flows are the incompressible flow of a viscous fluid enclosed in a cylindrical container with an open top surface and driven by the steady rotation of the bottom wall. New flow states are investigated based on the fully three-dimensional solution of the Navier-Stokes equations for these free-surface cylindrical swirling flows, without resorting to any symmetry properties unlike all other results available in the literature. To our knowledge, this study delivers the most general available results for this free-surface problem due to its original mathematical treatment. This second part of the dissertation is a basic research task directed at increasing our understanding of the influence of the presence of a free surface on the intricate transitional flow dynamics of shear-driven flows.