Steady streaming induced by a trapped oscillating microbubble

A sessile micro bubble oscillating under the influence of an ultrasound field creates strong steady microstreaming vortices. These induced vortices have been exploited by researchers in particle trapping, micro-pumping, micro-mixing and particle separation. Analytical studies in the past have been conducted assuming the sessile bubble to be semi-cylindrical. However, experiments with applications in micro-mixing and micro-pumping often encounter an oscillating bubble interface which is relatively flat at steady state. Our focus in this study is to obtain an analytical solution to the steady two-dimensional flow field induced by an oscillating trapped interface of a slug in a micro channel. We consider three different boundary layers i.e., two close to the enclosing wall and one close to the oscillating gas-liquid interface separately, as Reynolds stresses are high in these regions. We obtain a composite solution to the flow using matched asymptotics.