Numerical investigation of acoustic radiation force and microstreaming in a viscoelastic fluid

We present a numerical model to study time-averaged acoustic radiation force and microstreaming around an elastic sphere immersed within an acoustically actuated viscoelastic fluid. We employ a perturbation approach to systematically identify limiting regimes where the viscoelastic fluid can be approximated as a purely viscous fluid at the acoustic and mean time scales. Unlike existing numerical models, we account for microstreaming and fluid elasticity contributions to the radiation force. We elucidate the inherent assumptions within reduced expressions considered in prior numerical models and highlight the divergence between the acoustic radiation force obtained from the reduced and general expressions. We also discuss numerical considerations to ensure the invariance of the acoustic radiation force with the choice of integration surface by recasting the time-averaged mass balance equation in terms of Stokes drift. Our results reveal that the acoustic radiation force exhibits a peak value for an optimal relaxation time, and both the peak acoustic radiation force and the optimal relaxation time increase with increasing polymer viscosity. The results also highlight the significant contribution of fluid elasticity to the radiation force and invalidate the previously employed reduced acoustic radiation force expressions for general viscoelastic regime.