A theoretical study on the acoustically driven oscillating flow around small spherical particles

In order to study the oscillating flow induced by a high intensity acoustic field, a computer code which employs the two-dimensional, unsteady mass and momentum conservation equations for laminar flow in spherical coordinates has been developed. The displacement amplitude of the incident sound wave is large compared to the characteristic length of particles, and the acoustic Reynolds number based on the particle diameter and the velocity amplitude of the oscillating flow is less than about 100. Numerical solutions of these equations give the velocity field, axial pressure gradient, shear stress and flow separation angle around the particle for acoustically oscillating flow as a function of acoustic Reynolds number and Strouhal number. The axial pressure gradient, shear stress and separation angle are proportional to the magnitude of oscillating flow at low frequency (～50Hz) and can be approximated by the quasi-steady analysis. The effects of flow oscillation increase with increasing frequency (～2000Hz) due to combined effects of curvature and flow acceleration, giving different values of axial pressure gradient, shear stress and separation angle for different frequencies of 500, 1000 and 2000 Hz.