Shape curvature effects in viscous streaming

Abstract

Viscous streaming flows generated by objects of constant curvature (circular cylinders, infinite plates) have been well understood. Yet, characterization and understanding of such flows when multiple body length-scales are involved has not been looked into, in rigorous detail. We propose a simplified setting to understand and explore the effect of multiple body curvatures on streaming flows, analysing the system through the lens of bifurcation theory. Our setup consists of periodic, regular lattices of cylinders characterized by two distinct radii, so as to inject discrete curvatures into the system, which in turn affect the streaming field generated due to an oscillatory background flow. We demonstrate that our understanding based on this system can be then generalised to a variety of individual convex shapes presenting a spectrum of curvatures, explaining prior experimental and computational observations. Thus, this study illustrates a route towards the rational manipulation of viscous streaming flow topology, through regulated variation of object geometry.