Numerical simulation of acoustic streaming generated by finite-amplitude resonant oscillations in an enclosure

Abstract

Acoustic streaming motion in a compressible gas filled two-dimensional rectangular enclosure is simulated and the effects of the sound field intensity on the formation process of streaming structures are investigated numerically. The oscillatory flow field in the enclosure is created by the vibration of the left wall of the enclosure. The frequency of the wall vibration is chosen such that the lowest acoustic mode propagates along the enclosure. The fully compressible form of the Navier–Stokes equations is considered and an explicit time-marching algorithm is used to track the acoustic waves. The formation of the wave field in the enclosure is computed and fully described and the acoustic boundary layer development is predicted. The interaction of the wave field with viscous effects and the formation of streaming structures are revealed by time-averaging the solutions over a given period. The strength of the pressure waves associated with the acoustic effect and the resulting streaming flow pattern is found to be strongly correlated to the maximum displacement of the wall during a vibration cycle. The wave form determines the shape of the steady streaming structures in the oscillatory flow field.

Modal Rayleigh-like streaming in layered acoustofluidic devices

“…In practical acoustofluidic particle manipulation devices working in the MHz region this approximation is usually valid, and since the fluid channel dimensions are typically several orders larger than the acoustic boundary layer thicknesses only the acoustic streaming field in the bulk of the fluid is usually of interest. While Rayleigh streaming has been recently extensively studied within the field of acoustic particle trapping and manipulation, [23][24][25][26][27][28][29][30] there are acoustic streaming patterns observed experimentally in acoustofluidic particle manipulation devices that cannot be explained by Rayleigh's classical theory. 3,31-34 Recently, we have explained the mechanism behind the four-quadrant transducer-plane streaming, which has a vortex pattern parallel to the transducer face and is driven by the limiting velocity on the walls perpendicular to the axis of main acoustic propagation.…”

Acoustic streaming in the transducer plane in ultrasonic particle manipulation devices

“…In planar manipulation devices the gradients of the velocity in the z-direction are much greater than in the lateral directions due to the planar geometry 36 , hence the left side of equation (19) can be approximated as Meanwhile, using standard relations between density and pressure in linear acoustics 31 and then exploiting the harmonic nature of the excitation, the right hand side of equation (19) becomes Thus, equation (19) can be written Using this, the product ⁄ can be approximated as where the complex intensity, C x , is given by: 37 Thus the x component of the limiting velocity can be written According to Fahy 37 , the complex intensity (a harmonic representation of the real, instantaneous intensity, which is a function of time) can be decomposed into two parts: (i) the real part, called the active intensity, which gives the time average energy flow; and (ii) the imaginary part (the reactive intensity) which corresponds to local, oscillatory energy flows with zero time average. We see from equation 25 that the limiting velocity is proportional to the active intensity.…”

Ultrasound-induced acoustophoretic motion of microparticles in three dimensions

“…Also, in most theoretical work either the radiation force or the streaming effects have been studied separately, but not combined with wall effects to obtain a complete description of microparticle * bruus@fysik.dtu.dk acoustophoresis. Recently, a number of numerical studies of acoustic streaming [19][20][21] and acoustophoresis [22,23] have appeared in the literature. In this work, we present a theoretical analysis of acoustic streaming, taking the effect of the vertical sidewalls into account, and apply it to a theoretical study of microparticle acoustophoresis in rectangular microchannels.…”