Steady Streaming generated by an acoustically oscillating slug

A sessile micro bubble oscillating under the influence of an ultrasound field creates strong 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 that is comparatively flat at a steady state. Our focus in this study is to obtain a semi–analytical solution to the steady two-dimensional flow field induced by an oscillating trapped interface of a slug in a microchannel using perturbation techniques in cartesian coordinates. We consider three different boundary layers i.e., two close to the enclosing walls 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 zeroth order flow using matched asymptotics. Mixed mode streaming is observed in first order non – oscillatory flow. The simplified first-order problem is solved numerically to obtain the flow field generated by the bubble.