A gluey particle model

B. Maury¹

¹ Laboratoire de Mathématiques, Université Paris Sud, 91405 Orsay cedex.

ESAIM. Proceedings, Tome 18 (2007), pp. 133-142.

Résumé

We present here a new framework to handle the short-range interaction between rigid bodies in a viscous, incompressible fluid. This framework is built as the vanishing viscosity limit of a lubrication model. We restrict ourselves here to the case of a single particle and a rigid wall. Our approach is based on a standard first-order approximation for the lubrication force between two rigid bodies, where a small parameter ε plays the role of the underlying fluid viscosity. We establish convergence when ε goes to 0 of a subsequence of trajectories towards a solution to a problem of the hybrid type: it relies on two distincts states, unglued and glued, the latter being described by a new variable γ which expresses in a way the asymptotic smallness of the distance, and which plays the role of an adhesion potential. The limit problem has a surprising property: although it is well-posed in many situations, uniqueness does not generally hold as soon as left-hand clusters of contact times are allowed. Some prospective extensions of this model (other types of singularities, roughness of surfaces, macroscopic version) are proposed.

Détail

DOI : 10.1051/proc:071811