A theoretical study of time-dependent, ultrasound-induced acoustic streaming in microchannels

TL;DR

This study numerically investigates the temporal development of ultrasound-induced acoustic streaming in microchannels, revealing the dynamics of unsteady fields, the dominance of resonance effects, and implications for particle manipulation.

Contribution

It provides a first- and second-order perturbation theory-based numerical model for unsteady acoustic streaming in microchannels, highlighting the impact of resonance quality factor Q.

Findings

Acoustic resonance builds up faster than streaming flow.

Pulsed actuation does not significantly reduce streaming.

Amplitude of oscillating velocity is Q times larger than steady velocity.

Abstract

Based on first- and second-order perturbation theory, we present a numerical study of the temporal build-up and decay of unsteady acoustic fields and acoustic streaming flows actuated by vibrating walls in the transverse cross-sectional plane of a long straight microchannel under adiabatic conditions and assuming temperature-independent material parameters. The unsteady streaming flow is obtained by averaging the time-dependent velocity field over one oscillation period, and as time increases, it is shown to converge towards the well-known steady time-averaged solution calculated in the frequency domain. Scaling analysis reveals that the acoustic resonance builds up much faster than the acoustic streaming, implying that the radiation force may dominate over the drag force from streaming even for small particles. However, our numerical time-dependent analysis indicates that pulsed actuation does not reduce streaming significantly due to its slow decay. Our analysis also shows that for an acoustic resonance with a quality factor Q, the amplitude of the oscillating second-order velocity component is Q times larger than the usual second-order steady time-averaged velocity component. Consequently, the well-known criterion v << c for the validity of the perturbation expansion is replaced by the more restrictive criterion v << c/Q. Our numerical model is available in the supplemental material in the form of Comsol model files and Matlab scripts.