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

Modeling of Non-Equilibrium Effects in Particulate Flow Through Porous Media

“…When small fluid drop or particle flows in a viscous fluid at a small Reynolds number not only influenced by Stokes drag but also another drag force called memoryintegral drag, also known as Boussinesq-Basset drag (the last term in Eq. 2.2), particles can experience an oscillatory motion under the effect of external forces (Hassan et al, 2017). In this case, the resonance curve including shape, amplitude, and quality of oscillator become important.…”

Dynamics of entrapped microbubbles with multiple openings

“…The formulation involves an analytical approximation for the natural frequencies and associated vibration modes. Notable examples are models of gas bubbles in inviscid fluids 17,19,20 , viscous fluids 21,22 , yield-stress fluids 23 , viscoelastic fluids 24 , liquid confined in elastic solids 25 , bubbles encapsulated by a viscoelastic shell 26 and lipid coated bubbles 27 . In addition, Maksimova studied the effects of boundaries on the bubble's oscillations 28 .…”