Model For The Dynamics Of A Bubble Undergoing Small Shape Oscillations Between Elastic Layers

A model is presented for a pulsating and translating gas bubble in a channel formed by two soft elastic parallel layers. The bubble is free to undergo small shape deformations. Coupled nonlinear second-order differential equations are obtained for the shape and position of the bubble, and numerical integration of an expression for the liquid velocity at the layer interfaces yields an estimate of their displacement. Simulations reveal behavior consistent with laboratory observations.