Acoustofluidics 15: streaming with sound waves interacting with solid particles

In Part 15 of the tutorial series "Acoustofluidics-exploiting ultrasonic standing waves forces and acoustic streaming in microfluidic systems for cell and particle manipulation," we examine the interaction of acoustic fields with solid particles. The main focus here is the interaction of standing waves with spherical particles leading to streaming, together with some discussion on one non-spherical case. We begin with the classical problem of a particle at the velocity antinode of a standing wave, and then treat the problem of a sphere at the velocity node, followed by the intermediate situation of a particle between nodes. Finally, we discuss the effect of deviation from sphericity which brings about interesting fluid mechanics. The entire Focus article is devoted to the analysis of the nonlinear fluid mechanics by singular perturbation methods, and the study of the streaming phenomenon that ensues from the nonlinear interaction. With the intention of being instructive material, this tutorial cannot by any means be considered 'complete and comprehensive' owing to the complexity of the class of problems being covered herein.