Scale-partitioned differential modeling of large-amplitude acoustic streaming

Abstract

Classical techniques for modeling acoustic streaming rely on expansion of the flow about the relative slowness of the streaming velocity in comparison to the particle velocity. Rayleigh pioneered this approach nearly a century and a half ago for deducing streaming equations from the Navier-Stokes governing equations. Modern acoustofluidics applications do not generally admit the order of magnitude separation between flow components that is required in classical “slow streaming” approaches. We outline a theoretical technique that provides greater generality by using drastic spatiotemporal scale disparities to decompose the field equations. We achieve this with scale-partitioned differential operations. The framework is useful in general for modeling continuous nonlinear systems. We first provide brief examples of applying the framework to various media before exploring its use in the area of acoustofluidics specifically. We analyze large-amplitude (“fast”) bulk acoustic streaming in a one-dimensional setting. The resulting model explains empirically observed characteristic nonlinear streaming phenomena. From the model, we deduce a variety of bulk streaming properties, including a simple, algebraic upper bound on the maximum achievable streaming velocity in relation to the acoustic forcing. A comparative analysis is undertaken using experimental data from the recent literature.