Asymptotic analysis of a thin fluid layer flow between two moving surfaces

TL;DR

This paper investigates the flow of an incompressible viscous fluid between two moving surfaces, using asymptotic expansions to derive lubrication and shallow water models, and discusses their applicability conditions.

Contribution

It formally justifies two asymptotic models for thin fluid layers and clarifies the conditions under which each model is applicable.

Findings

Derivation of lubrication and shallow water models from asymptotic analysis

Conditions for the applicability of each model

Formal justification of the models

Abstract

In this paper we study the behavior of an incompressible viscous fluid moving between two very close surfaces also in motion. Using the asymptotic expansion method we formally justify two models, a lubrication model and a shallow water model, depending on the boundary conditions imposed. Finally, we discuss under what conditions each of the models would be applicable.