Revisiting Shikhmurzaev's approach to the contact line problem

TL;DR

This paper critically revisits and extends Shikhmurzaev's contact line model, deriving new lubrication approximations for thin film flows and meniscus formation, clarifying assumptions and exploring different slip length regimes.

Contribution

It rederives Shikhmurzaev's model, analyzes assumptions for the isothermal limit, and develops several lubrication approximation models for various contact line scenarios.

Findings

Derived new lubrication models for thin film flows.

Clarified assumptions for the isothermal limit.

Extended model applicability to meniscus formation.

Abstract

In this paper, we revisit a model for the contact line problem which has been proposed by Shikhmurzaev (1993). In the first part, in addition to rederiving the model, we study in detail the assumptions required to obtain the isothermal limit of the model. We also derive in this paper several lubrication approximation models, based on Shikhmurzaev's approach. The first two lubrication models describe thin film flow of incompressible fluids on solid substrates, based on different orders of magnitude of the slip length parameter. The third lubrication model describes a meniscus formation where a wedge-shaped solid immerses in a thin film of fluid.