Asymptotic analysis of the behavior of a viscous fluid between two very close mobile surfaces

Abstract

The aim of this work is the study of the behavior of an incompressible viscous fluid moving between two closely spaced surfaces, also in motion. To carry out this work we use the asymptotic expansion method that allows us to formally justify two different models starting from the same initial problem: a lubrication model and a shallow water model. The type of model that yields depends on whether the fluid is“pressure dominated” and on the boundary conditions imposed. We discuss in detail under what conditions each of the models would be applicable.