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Micro-Macro Modelling of an Array of Spheres Interacting Through Lubrication Forces

Authors
  • Lefebvre-Lepot, Aline
  • Maury, Bertrand
  • Lefebvre, Aline
Type
Preprint
Publication Date
Sep 05, 2012
Submission Date
Feb 19, 2008
Source
arXiv
License
Yellow
External links

Abstract

We consider here a discrete system of spheres interacting through a lubrication force. This force is dissipative, and singular near contact: it behaves like the reciprocal of interparticle distance. We propose a macroscopic constitutive equation which is built as the natural continuous counterpart of this microscopic lubrication model. This model, which is of the newtonian type, relies on an elongational viscosity, which is proportional to the reciprocal of the local fluid fraction. We then establish the convergence in a weak sense of solutions to the discrete problem towards the solution to the partial differential equation which we identified as the macroscopic constitutive equation.

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