Cavity flow with surface tension past a flat plate

Abstract

The effect of surface tension forces on the cavity flow parameters is considered for steady flow past a rounded-edge plate perpendicular to the incident flow. The fluid is assumed to be ideal, weightless, and incompressible. The problem is solved in a parameter region by finding analytical expressions for the flow potential and the function that conformally maps the parameter region into the flow region in the physical plane. The dynamic boundary condition includes the surface tension force, which is proportional to the free boundary curvature, and allows one to obtain an integral equation in the velocity magnitude on the free boundary. The integral equation is solved numerically by the method of successive approximations. The results of calculations of the effect of the Weber number and the plate edge radius on the geometry of the cavity and the drag coefficient of the plate are presented.