Inertial forces on an expanding bubble in motion in a fluid

An analysis is presented of inertial forces acting on a bubble with an unsteady radius placed in a nonuniform or unsteady flow. A velocity field is defined for a nonviscous, incompressible fluid, and the energy imparted to the flow by the movements of a sphere are formulated. The Bernoulli theorem is employed to determine the pressure distribution of the liquid on the surface of the bubble, and thus the inertial forces. Account is also taken of the evolution of the radius of the bubble in a time-dependent form. Extension of the model to the case of a bubbly mixture is considered.