DUMPING OF CAPILLARY-GRAVITY WAVES IN A CHANNEL: THE WEDGE DISSIPATION EFFECT*

This paper presents rst a numerical investigation into a novel class of wave motions in narrow open channels. The distinctive condition on these motions is that: dissipation in vicinity of contact line is described by De Gennes approach; the macroscopic lines of contact between the free surface and the sides of the channel move with velocity proportional to cosine of dynamic contact angle; the eect of the contact angle hysteresis is included; there are no restriction to the equilibrium contact angle to be close to 90 degrees. We obtain the time evolution of the waves. We investigate inuense of the wedge dissipation on the damping rate and frequency of the waves. There is a large body of literature dealing with the wave motion in an unbounded uid. A number of analytical, experimental and numerical studies exist on liquid sloshing in containers, mostly in simple rectangular, cylindrical and spherical geometries and for vertical walls. Usually extreme case when the free surface meets the boundary orthogonally is considered in analytical and in numerical studies. This case is known as free-end edge condition. Benjamin and Scott [1] proposed another extreme boundary condition, known as stick condition at the edge of the free surface, namely that contact line between the free surface and sides of the channel is xed in its equilibrium positions. They argue this condition with phenomenon of contact angle hysteresis. Hocking [2] rstly suggests to apply the universal contact line moving models to obtain the boundary condition for waves in container. He proposed simplest, non-trivial, linear hypothesis for the determination of unsteady contact-line motion when equilibrium contact angle is close to 90. He postulates that eect of viscosity in the boundary layers on the wall leads to relation (referred as the wetting condition)