Translational motion of spherical gas bubbles in viscoelastic liquids subject to acoustic standing wave fields

Abstract

Translational motion of a single tiny spherical gas bubble subject to a weak acoustic standing wave field is studied both analytically and numerically assuming that the liquid surrounding the bubble is a viscoelastic fluid obeying the second-grade rheological model. Equations of motion are derived in radial and translational directions for this particular fluid model and shown to be coupled through the virtual mass effect. A perturbation analysis is carried out first to show that the natural frequency of a gas bubble is increased the higher the fluid’s elasticity. Fourth-order Runge-Kutta method is used to investigate the effects of a fluid’s elasticity on the bubble dynamics in the translational direction. It is shown that bubbles exhibiting erratic behavior in the translational direction for the case of Newtonian fluids can be stabilized provided that the liquid surrounding the bubble is sufficiently elastic.

Keywords

bubble dynamics / acoustic standing wave field / translational motion / viscoelastic fluid

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