# Bulk-driven acoustic streaming at resonance in closed microcavities

## TL;DR

This paper investigates how bulk-driven acoustic streaming, especially in double-mode resonances within closed microcavities, can generate rotating flow patterns, challenging the traditional boundary-driven streaming dominance in acoustofluidic devices.

## Contribution

It derives analytical solutions for double modes in rectangular cavities, revealing how rotating bulk-driven streaming can be excited by non-rotating actuation and identifying optimal geometries for such effects.

## Key findings

- Rotating bulk-driven streaming can be excited without rotating actuation.
- High-frequency patterns are dominated by bulk-driven streaming.
- Optimal cavity geometries maximize the excitation of rotating streaming patterns.

## Abstract

Bulk-driven acoustic (Eckart) streaming is the steady flow resulting from the time-averaged acoustic energy flux density in the bulk of a viscous fluid. In simple cases, like the one-dimensional single standing-wave resonance, this energy flux is negligible, and therefore the bulk-driven streaming is often ignored relative to the boundary-driven (Rayleigh) streaming in the analysis of resonating acoustofluidic devices with length scales comparable to the acoustic wavelength. However, in closed acoustic microcavities with viscous dissipation, two overlapping resonances may be excited at the same frequency as a double mode. In contrast to single modes, the double modes can support a steady rotating acoustic energy flux density and thus a corresponding rotating bulk-driven acoustic streaming. We derive analytical solutions for the double modes in a rectangular box-shaped cavity including the viscous boundary layers, and use them to map out possible rotating patterns of bulk-driven acoustic streaming. Remarkably, the rotating bulk-driven streaming may be excited by a non-rotating actuation, and we determine the optimal geometry that maximizes this excitation. In the optimal geometry, we finally simulate a horizontal 2-by-2, 4-by-4, and 6-by-6 streaming-roll pattern in a shallow square cavity. We find that the high-frequency 6-by-6 streaming-roll pattern is dominated by the bulk-driven streaming as opposed to the low-frequency 2-by-2 streaming pattern, which is dominated by the boundary-driven streaming.