Theory of sphere motions in viscous fluids including elasticity and compressibility

We study the motions of an elastic sphere and a compressible fluid sphere suspended in a compressible fluid. To this end, we use a scheme of a vector representation for the velocity in hydrodynamics and for the displacement in elasticity. First, we calculate the steady-state elastic displacement of a solid sphere under a gravity and a surface-tension gradient. Second, we examine the finite-size effects in a spherical container and find bulk acoustic resonance induced by an oscillating solid sphere. Third, applying periodic forces, we calculate the displacement, the velocity field, and the frequency-dependent friction constant for an elastic sphere and a compressible fluid sphere. We find complex acoustic effects sensitively depending on the frequency.