Convergence to the Reynolds approximation with a double effect of roughness

Catherine Choquet (1) , Laurent Chupin (2) , Marguerite Gisclon (3)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités
2 ICJ - Institut Camille Jordan
3 LAMA - Laboratoire de Mathématiques

We prove that the lubrication approximation is perturbed by a non-regular roughness of the boundary. We show how the flow may be accelerated using adequate rugosity profiles on the bottom. We explicit the possible effects of some abrupt changes in the profile. The limit system is mathematically justified through a variant of the notion of two-scale convergence. Finally, we present some numerical results, illustrating the limit system in the three-dimensional case.

Mots clés: Boundary conditions; upscaling; two-scale convergence; micro-fluidic; Reynolds and Stokes equations; rough boundaries; thin films

Domaines: Equations aux dérivées partielles [math.AP]

Catherine Choquet, Laurent Chupin, Marguerite Gisclon. Convergence to the Reynolds approximation with a double effect of roughness. 2010. ⟨hal-00457146⟩