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

TL;DR

This paper investigates how memory-integral drag forces affect the resonance behavior of small particles and bubbles oscillating in viscous fluids at low Reynolds numbers, providing exact solutions and comparing with traditional models.

Contribution

It introduces exact solutions for oscillations considering both Stokes and memory-integral drag forces, clarifying their impact on resonance characteristics.

Findings

Memory-integral drag significantly alters resonance curves.

Resonance amplitude and phase dependences differ from traditional models.

Exact solutions enable better understanding of oscillation dynamics at low Reynolds numbers.

Abstract

We consider small oscillations of micro-particles and gaseous bubbles in 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 (amplitude versus frequency of external force), as well as 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.