A volume-averaged model for acoustic streaming induced by focused ultrasound in soft porous media

Equations describing acoustic streaming in soft, porous media driven by focused ultrasound are derived based on the assumption that acoustic waves pass through the porous material as if it were homogeneous. From these equations, a model that predicts the time-averaged flow on the macroscopic scale, as well as the advective transport of the trace components, is created. The model is used to perform simulations for different shapes of the focused ultrasound beam. For a given shape, and using the paraxial approximation for the ultrasound, the acoustic streaming is found to be linearly proportional to the applied ultrasound intensity, to the permeability of the porous material and to the attenuation coefficient, and inversely proportional to the liquid viscosity. Results from simulations are compared to a simplified expression stating that the dimensionless volumetric liquid flux is equal to the dimensionless acoustic radiation force. This approximation for the acoustic streaming is found to be reasonable near the beam axis for focused ultrasound beam shapes that are long in the axial direction, compared to their width. Finally, a comparison is made between the model and experimental results on acoustic streaming in a gel, and good agreement is found.