The contact angle in inviscid fluid mechanics

TL;DR

This paper demonstrates that imposing a contact angle condition at the contact line in inviscid fluid flows generally conflicts with classical equations, questioning many existing solutions that assume such conditions.

Contribution

It derives the limited conditions under which a contact angle can be specified in inviscid flows, highlighting the incompatibility with classical boundary conditions.

Findings

Contact angle specification often incompatible with classical equations.

Many existing potential flow solutions with contact angles are 'weak solutions'.

Implications for analyzing free-surface inviscid flows are discussed.

Abstract

We show that in general, the specification of a contact angle condition at the contact line in inviscid fluid motions is incompatible with the classical field equations and boundary conditions generally applicable to them. The limited conditions under which such a specification is permissible are derived; however, these include cases where the static meniscus is not flat. In view of this situation, the status of the many `solutions' in the literature which prescribe a contact angle in potential flows comes into question. We suggest that these solutions which attempt to incorporate a phenomenological, but incompatible, condition are in some, imprecise sense `weak-type solutions'; they satisfy or are likely to satisfy, at least in the limit, the governing equations and boundary conditions everywhere except in the neighbourhood of the contact line. We discuss the implications of the result for the analysis of inviscid flows with free surfaces.