Acoustic Streaming: An Arbitrary Lagrangian-Eulerian Perspective

TL;DR

This paper introduces an ALE-based framework for analyzing acoustic streaming, separating fast and slow time scales, enabling direct comparison with experiments and applicability to complex microfluidic devices.

Contribution

The paper presents a novel ALE formulation for acoustic streaming that explicitly separates time scales and directly computes Lagrangian velocities, avoiding Stokes drift post-processing.

Findings

The formulation provides a steady second-order problem with exact boundary conditions.

Numerical results demonstrate advantages over existing methods.

Applicable to complex fluid-structure interaction problems in microfluidics.

Abstract

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