Model problem of instantaneous motion of a three-phase contact line

Hydrodynamic problems of fluid flow with three-phase contact lines (for example, solid body-liquid-gas or solid body and two nonmixing liquids) are of special interest. Much attention has been paid lately to steady and quasisteady flows. Significantly unsteady problems of this kind have almost escaped consideration. In the present paper, we study a model problem of a significantly unsteady motion of a finite volume of an incompressible fluid with a three-phase contact line. The static contact angle is assumed to be right and the initial free surface of the liquid is assumed to be cylindrical. One of the planes instantaneously begins to move toward the other with a constant finite velocity. Flows with high Reynolds numbers and small capillary numbers are considered. Mass forces are ignored in the problem. The basic result is the construction of a formal asymptotic of the solution at small times.