Shape curvature effects in viscous streaming

TL;DR

This paper investigates how multiple object curvatures influence viscous streaming flows, using bifurcation theory and lattice models to generalize findings to various convex shapes, enabling flow control through geometry.

Contribution

It introduces a simplified lattice-based model to analyze the effects of multiple curvatures on viscous streaming, extending understanding beyond single-curvature cases.

Findings

Multiple curvatures significantly alter streaming flow topology.

The bifurcation analysis explains experimental and computational observations.

Geometry regulation can manipulate flow patterns effectively.

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, analyzing 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 generalized 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.