Eur. Phys. J. E (2009) 30: 291-301
https://doi.org/10.1140/epje/i2009-10528-1

Regular Article

Soft Dynamics simulation. 2. Elastic spheres undergoing a T₁ process in a viscous fluid

Centre de Recherche Paul Pascal, CNRS UPR 8641 - Av. Dr. Schweitzer, Pessac, France and Matière et Systèmes Complexes, Université Paris-Diderot - CNRS UMR 7057, Paris, France

^* e-mail: cyprien.gay@univ-paris-diderot.fr

Received: 1 January 2009
Revised: 15 July 2009
Accepted: 30 September 2009
Published online: 22 October 2009

Abstract

Robust empirical constitutive laws for granular materials in air or in a viscous fluid have been expressed in terms of timescales based on the dynamics of a single particle. However, some behaviours such as viscosity bifurcation or shear localization, observed also in foams, emulsions, and block copolymer cubic phases, seem to involve other micro-timescales which may be related to the dynamics of local particle reorganizations. In the present work, we consider a T₁ process as an example of a rearrangement. Using the Soft Dynamics simulation method introduced in the first paper of this series, we describe theoretically and numerically the motion of four elastic spheres in a viscous fluid. Hydrodynamic interactions are described at the level of lubrication (Poiseuille squeezing and Couette shear flow) and the elastic deflection of the particle surface is modeled as Hertzian. The duration of the simulated T₁ process can vary substantially as a consequence of minute changes in the initial separations, consistently with predictions. For the first time, a collective behaviour is thus found to depend on a parameter other than the typical volume fraction of particles.