Modelling of cavitational erosion in the area of surfaces of smooth contact

A qualitative and numerical analysis of the differential equation, describing pulsation of a symmetrical cavity in the area of the contact of smooth surfaces with different curvatures, forming a slot is presented in this article. This particular model is a slot between a plane and a sphere. Qualitative reasons of high erosion activity of such a toroidal bubble are defined. The boundary values were found when solutions of the equation are either non-harmonic periodic and non-vanishing, or vanishing (i.e., the bubble bursts). The results of this article can be applied to the controlling tasks of ultrasonic cavitation processes.