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

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.

14 pages, Revtex, 8 eps figures

References in corpus (1)

• A numerical study of thermoviscous effects in ultrasound-induced acoustic streaming in microchannels

Cited by in corpus (16)

• Acoustic streaming and its suppression in inhomogeneous fluids
• Theory of pressure acoustics with boundary layers and streaming in curved elastic cavities
• Characterization of Acoustic Streaming in Gradients of Density and Compressibility
• Unveiling of the mechanisms of acoustic streaming induced by sharp edges
• Three-dimensional numerical modeling of surface acoustic wave devices: Acoustophoresis of micro- and nanoparticles including streaming
• Suppression of acoustic streaming in shape-optimized channels
• Whole-system ultrasound resonances as the basis for acoustophoresis in all-polymer microfluidic devices
• Three-Dimensional Numerical Modeling of Acoustic Trapping in Glass Capillaries
• Modeling of microdevices for SAW-based acoustophoresis --- a study of boundary conditions
• Performance study of acoustophoretic microfluidic silicon-glass devices by characterization of material- and geometry-dependent frequency spectra
• Orientation-dependent propulsion of cone-shaped nano- and microparticles by a traveling ultrasound wave
• Fabrication, characterization, and simulation of glass devices with AlN-thin-film-transducers for excitation of ultrasound resonances
• Theory and simulation of AC electroosmotic suppression of acoustic streaming
• Analytical solution for an acoustic boundary layer around an oscillating rigid sphere
• Theory of acoustic trapping of microparticles in capillary tubes
• Consistent continuum equations and numerical benchmarks for a perturbation-based, variable-coefficient acoustofluidic solver