Three-dimensional geometry and topology effects in viscous streaming

TL;DR

This paper explores how three-dimensional body geometry influences viscous streaming flows, revealing complex flow regimes and topological changes through numerical simulations and bifurcation analysis.

Contribution

It introduces a three-dimensional analysis of viscous streaming flows, extending previous two-dimensional studies to include complex geometries like tori.

Findings

Flow regimes depend on body shape and topology.

Bifurcation theory explains flow reorganization.

Complex flow patterns emerge in 3D geometries.

Abstract

Recent studies on viscous streaming flows in two dimensions have elucidated the impact of body curvature variations on resulting flow topology and dynamics, with opportunities for microfluidic applications. Following that, we present here a three-dimensional characterization of streaming flows as function of changes in body geometry and topology, starting from the well-known case of a sphere to progressively arrive at toroidal shapes. We leverage direct numerical simulations and dynamical systems theory to systematically analyze the reorganization of streaming flows into a dynamically rich set of regimes, the origins of which are explained using bifurcation theory.