Nonlinear dynamics of a solid particle in an acoustically excited viscoelastic fluid. I. Acoustic streaming

An analytical theory is developed for acoustic streaming induced by an axisymmetric acoustic wave field around an isotropic solid spherical particle in a compressible viscoelastic fluid. The particle is assumed to undergo pulsation, translation, and shape deformations of all orders. The fluid motion is described by the compressible Oldroyd-B model. No restrictions are imposed on the particle size with respect to the acoustic wavelength and the viscous penetration depth. The obtained analytical solutions are used in numerical simulations. It is shown that in the general case, the streaming velocity magnitude decreases with increasing polymer viscosity. Increasing relaxation time (elasticity) of the polymer solution leads to increasing streaming velocity magnitude as long as the relaxation time remains relatively small. It is also observed that the variation of the polymer viscosity and the relaxation time can change the pattern of streamlines.