Comparing methods for the modelling of boundary-driven streaming in acoustofluidic devices

Numerical simulations of acoustic streaming flows can be used not only to explain the complex phenomena observed in acoustofluidic manipulation devices, but also to predict and optimise their performances. In this paper, two numerical methods based on perturbation theory are compared in order to demonstrate their viability and applicability for modelling boundary-driven streaming flows in acoustofluidic systems. It was found that the Reynolds stress method, which predicts the streaming fields from their driving terms, can effectively resolve both the inner and outer streaming fields and can be used to demonstrate the driving mechanisms of a broad range of boundary-driven streaming flows. However, computational efficiency typically limits its useful application to two-dimensional models. We highlight the close relationship between the classical boundary-driven streaming vortices and the rotationality of the Reynolds stress force field. The limiting velocity method, which ignores the acoustic boundary layer and solves the outer streaming fields by applying the ‘limiting velocities’ as boundary conditions, is more computationally efficient and can be used for predicting three-dimensional outer streaming fields and provide insight into their origins, provided that the radius of curvature of the channel surfaces is much greater than the acoustic boundary layer thickness (δv\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta_{v}$$\end{document}). We also show that for the limiting velocity method to be valid the channel scales must exceed a value of approximately 100 δv\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta_{v}$$\end{document} (for an error of ~5% on the streaming velocity magnitudes) for the case presented in this paper. Comparisons of these two numerical methods can provide effective guidance for researchers in the field of acoustofluidics on choosing appropriate methods to predict boundary-driven streaming fields in the design of acoustofluidic particle manipulation devices.