The contact angle in inviscid fluid mechanics

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.

Nonlinear model reduction for computational vibration analysis of structures with weak geometrical nonlinearity coupled with linear acoustic liquids in the presence of linear sloshing and capillarity

“…Concerning the linear formulation for the compressible liquid with free surface, the sloshing is taken into account with surface tension (capillarity) effects. We refer the reader to [6,7] for the classical theory on capillarity, to [8,9,10] for developments of the behavior of liquids in microgravity environment, to [11,12] for general analyzes of sloshing problems for incompressible liquids in rigid structures, to [13,14,15,16,17,18] for sloshing problems of incompressible liquids without capillarity effects in elastic structures, to [13,19,20,21] for sloshing problems of incompressible liquids with capillarity effects in rigid structures, to [22,23,24,25,26,27,28,13,29] for the conditions of contact angle between the free surface and the structure, to [30] for sloshing problems of incompressible liquids with capillarity effects in elastic structures, to [31,32,33] for sloshing problems of compressible liquids with capillarity effects in rigid structures, to [1] for linear dissipative acoustic liquids with sloshing and capillarity effects in linear elastic structures. Concerning nonlinear sloshing and capillarity for incompressible liquids in rigid tanks submitted to rigid body motions, see [34,35,36,37,38].…”

Vibration of structures containing compressible liquids with surface tension and sloshing effects. Reduced-order model

“…For computational methods concerning the sloshing problems of incompressible liquids with capillarity effects in rigid structures, see [15,18,19,37,57]. In this framework, the difficult problem concerning the conditions of contact angle, has been discussed in literature [8,9,11,17,29,32,37,45,46,[49][50][51]56,58].…”