Acoustic microstreaming due to a pulsating free or coated bubble near a wall: velocity, vorticity shear stress and closed streamlines*

Acoustic microstreaming due to an oscillating microbubble, either coated or free, is analytically investigated. We use the classical 1958 perturbative analysis of Nyborg clarifying its underlying assumptions. The detailed flow field is obtained and the closed streamlines due to the ring vortex are plotted in both Eulerian and Lagrangian descriptions. Analytical expressions are found for the ring vortex showing that its length depends only on the separation of the microbubble from the wall and the dependence is linear. The circulation as a scalar measure of the vortex is computed quantitatively identifying its spatial location using a d2 method of vortex identification. The functional dependence of circulation on bubble separation and coating parameters was shown to be similar to that of the shear stress. The dependence of shear stress on coating parameters are explained using the underlying bubble dynamics such as its resonance.