Micro-Macro Modelling of an Array of Spheres Interacting Through Lubrication Forces - Archive ouverte HAL Access content directly
Journal Articles Advances in Mathematical Sciences and Applications Year : 2011

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

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.
Fichier principal
Vignette du fichier
LefebvreMaury_MicroMacro2012.pdf (217.29 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-00257250 , version 1 (18-02-2008)
hal-00257250 , version 2 (05-09-2012)

Identifiers

Cite

Aline Lefebvre-Lepot, Bertrand Maury, Aline Lefebvre. Micro-Macro Modelling of an Array of Spheres Interacting Through Lubrication Forces. Advances in Mathematical Sciences and Applications, 2011, 21 (2), pp.535-557. ⟨hal-00257250v2⟩
357 View
207 Download

Altmetric

Share

Gmail Facebook X LinkedIn More