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We analyze acoustic streaming flows using an ALE perspective. The formulationstems from an explicit separation of time-scales resulting in two subproblems:a first-order problem, formulated in terms of the fluid displacement at thefast scale, and a second-order problem formulated in terms of the Lagrangianflow velocity at the slow time scale. Following a rigorous time-averagingprocedure, the second-order problem is shown to be intrinsically steady, andwith exact boundary conditions at the oscillating walls. Also, as thesecond-order problem is solved directly for the Lagrangian velocity, theformulation does not need to employ the notion of Stokes drift, or anyassociated post-processing, thus facilitating a direct comparison withexperiments. Because the first-order problem is formulated in terms of thedisplacement field, our formulation is directly applicable to more complexfluid-structure interaction problems in microacosutofluidic devices. After theformulation's exposition, we present numerical results that illustrate theadvantages of the formulation with respect to current approaches.

Acoustic Streaming: An Arbitrary Lagrangian-Eulerian Perspective