Resonance properties of forced oscillations of particles and gaseous bubbles in a viscous fluid at small Reynolds numbers

We consider small oscillations of micro-particles and gaseous bubbles in a viscous fluid around equilibrium states under the action of a sinusoidal external force. Exact solutions to the governing integro-differential equations containing both Stokes and memory-integral drag forces are obtained. The main aim of this study is to clarify the influence of the memory-integral drag force on the resonance characteristics of oscillating particles or gaseous bubbles in a viscous fluid at small Reynolds numbers. The resonant curves (the amplitude versus the frequency of an external force) and phase-frequency dependences are obtained for both these objects and compared with the corresponding dependences of the traditional oscillator with the Stokes drag force only.