An analytical solution of the potential velocity field induced by a growing bubble from a plate orifice

An analytical solution is derived with the mirror image method of the velocity field of an inviscid liquid induced by a growing bubble from a plate orifice. The flow is assumed potential, and the bubble shape is idealised as spherical. In deriving the motion equation, the spherical image of a point source, which is a combination of a point source and a line source, is proved approximate to a double source. This approximation enables continuation of the effectiveness of mirror image method to the case studied in this paper. The derived velocity potential equation is verified for the boundary conditions on the bubble surface and the orifice plate. The streamlines of the velocity field are presented and compared with experimental results in the literature.