Periodic Rayleigh streaming vortices and Eckart flow arising from traveling-wave-based diffractive acoustic fields

Kirill Kolesnik, Pouya Hashemzadeh, Danli Peng, Melanie E. M. Stamp, Wei Tong, Vijay Rajagopal, Morteza Miansari, and David J. Collins

Phys. Rev. E 104, 045104 – Published 15 October 2021

Abstract

Recent studies have demonstrated that periodic time-averaged acoustic fields can be produced from traveling surface acoustic waves (SAWs) in microfluidic devices. This is caused by diffractive effects arising from a spatially limited transducer. This permits the generation of acoustic patterns evocative of those produced from standing waves, but instead with the application of a traveling wave. While acoustic pressure fields in such systems have been investigated, acoustic streaming from diffractive fields has not. In this work we examine this phenomenon and demonstrate the appearance of geometry-dependent acoustic vortices, and demonstrate that periodic, identically rotating Rayleigh streaming vortices result from the imposition of a traveling SAW. This is also characterized by a channel-spanning flow that bridges between adjacent vortices along the channel top and bottom. We find that the channel dimensions determine the types of streaming that develops; while Eckart streaming has been previously presumed to be a distinguishing feature of traveling-wave actuation, we show that Rayleigh streaming vortices also results. This has implications for microfluidic actuation, where traveling acoustic waves have applications in microscale mixing, separation, and patterning.

Received 31 January 2021
Revised 24 June 2021
Accepted 16 September 2021

DOI:https://doi.org/10.1103/PhysRevE.104.045104

Physics Subject Headings (PhySH)

Acoustic interactions Acoustic modeling Nonlinear acoustics

Microfluidic devices

Surface acoustic wave

Polymers & Soft MatterFluid Dynamics

Authors & Affiliations

Kirill Kolesnik¹, Pouya Hashemzadeh⁵, Danli Peng ^1,2, Melanie E. M. Stamp ^2,3, Wei Tong², Vijay Rajagopal¹, Morteza Miansari^4,5,*, and David J. Collins ^1,†

¹Department of Biomedical Engineering, The University of Melbourne, Melbourne, VIC 3010, Australia
²Department of Physics, The University of Melbourne, Melbourne, VIC 3010, Australia
³Cognitive Interaction Technology Center (CITEC) Research Institute, Bielefeld University, 33619 Bielefeld, Germany
⁴Micro+Nanosystems & Applied Biophysics Laboratory, Department of Mechanical Engineering, Babol Noshirvani University of Technology, P.O. Box 484, Babol, Iran
⁵Department of Cancer Medicine, Cell Science Research Center, Royan Institute for Stem Cell Biology and Technology, ACECR, Isar 11, 47138-18983 Babol, Iran

^*Corresponding author: mmiansari@nit.ac.ir
^†Corresponding author: david.collins@unimelb.edu.au

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Issue

Vol. 104, Iss. 4 — October 2021

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Images

Figure 1
(a) Concept image showing vortices and acoustic radiation forces in a microchannel with the application of a traveling surface acoustic wave (SAW). (b) The simulation modeling domain with a perfectly matched layer (PML) for the top and side walls (used in Fig. 2). (c) The simulation modeling domain, with impedance boundary conditions for polydimethylsiloxane (PDMS) on the top and left walls and water on the rightmost wall (used in Figs. 3 and 4). Both have a traveling-wave velocity boundary condition on the lithium niobate substrate $(LiNb O_{3})$ . The modeling domain length in the $x$ direction is $25 λ_{SAW}$ . The phase velocity of the SAW is in the positive $x$ direction.
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Figure 2
Numerical examination of acoustofluidic effects arising from traveling surface acoustic waves. In all simulations the SAW propagates from left to right along the lower boundary. (a) Pressure field $\tilde{p}$ [Eq. (7)] in a microchannel with a height of $λ_{l}$ . (b) Periodic vortices in a microchannel with a height of $λ_{l}$ . The colored contours indicate the scaled streaming velocity $\tilde{u}$ [Eq. (7)], the black lines the fluid streamlines, and the white arrows the direction of fluid streaming. (c) Eckart streaming in the case of a channel with height $8 λ_{l}$ , showing a primary vortex spanning multiple fluid wavelengths. (d) Highlight showing (top) fluid velocities for the first two streaming velocity maxima in the vicinity of the acoustic transducer, plotted here for the first $10 δ_{v}$ , and (bottom) the rectangular mesh elements used. (e) The magnitude of the acoustic streaming velocity, both maximum ( $v_{2}^{\max})$ and mean $({\bar{v}}_{2})$ values, scale with the square of the applied displacement magnitude boundary condition ( $f =$ 18.75 MHz). (f) Streaming velocity magnitudes near the transducer boundary ( $\tilde{z} < 5 / 3$ , red), and farther away ( $\tilde{z} > 5 / 3$ , black). Black line indicates $v \sim {\tilde{h}}^{2}$ scaling.
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Figure 3
Pressure field and fluid streamlines for different channel heights in a PDMS-bounded microchannel. (a) Rayleigh streaming mode-dominant flow for smaller channel heights, here for $\tilde{h} =$ 0.25, 0.5, 0.75, and 1. (b) Mixed dominance modes wherein Rayleigh streaming periodicity is disrupted and Eckart streaming vortex develops, here for $\tilde{h} =$ 2, 3, and 4. (c) Eckart streaming dominates channel flow for larger channel heights, although Rayleigh streaming is still present near the transducer boundary. Pressure is plotted as $\tilde{p}$ , which is scaled as per Eq. (7), and arrows show streaming directions.
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Figure 4
Vortex and pressure spacing as a function of channel height. (a) Example demonstrating the determinate of vortex locations, illustrating the detection of vortices (top) across the channel domain and (bottom) a closeup of the Rayleigh streaming vortices near the transducer boundary. The white dashed line is plotted across the domain at $\tilde{z} = 5 / 3$ . (b) Vortex spacing examined for across $\tilde{h} =$ 0 to 2. Vortex spacing is scaled by the periodicity from Eq. (8). (c) Vortex spacing in both the Rayleigh streaming dominant region ( $\tilde{z} < 5 / 3,$ black squares) and the Eckart streaming region ( $\tilde{z} > 5 / 3$ , blue circles). (d) Pressure field maxima spacing with channel height, showing asymptotic alignment with Eq. (8) for channel heights $\tilde{h} > 2$ . Both the average (black squares) and median (red circles) spacings are plotted in both (b) and (d); the black dashed line denotes spacing corresponding to Eq. (8).
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