The volumetric force term (F ) in momentum balance is calculated from the pressure intensity field I, determined from Eq. 9. Assuming plane wave approximation F can be expressed by the following relationship:

F = \(\frac{2\ \alpha}{\ C_{s}}\text{\ I}\) [Eq. 9]

Detail of this derivation can be obtained from (Huang, Holt, Cleveland, & Roy, 2004).

Where F , \(\alpha,\) C_s and I are volumetric force, sound attenuation coefficient, sound speed and intensity, respectively. Solving this with finite element analysis in COMSOL using the specified boundary conditions (Table 2) and input parameters (Supplementary table 2) yields the velocity field at each point of the sonication tube (Fig 7b). Velocity streamline indicates the direction of fluid flow. The area inside the streamlines are marked yellow and quantified with ImageJ. (details in supplementary figure 1-5, table 3- 12)