A numerical study of the effect of viscoelasticity on cavitation and bubble dynamics

In the interests of gaining crucial initial insights, a simplified system of governing equations is first considered. The ambient fluid around the bubble is considered incompressible and the flow irrotational.  Viscoelastic effects are included through the normal stress balance at the bubble surface. The governing equations are then solved using a boundary element method. With regard to spherical bubble collapse, the model captures the behaviour seen in other studies, including the damped oscillation of the bubble radius with time and the existence of an elastic-limit solution. The model is extended in order to investigate multi-bubble dynamics near a rigid wall and a free surface. It is found that viscoelastic effects can present jet formation, produce cusped bubble shapes, and generally prevent the catastrophic collapse that is seen in the inviscid cases. The model is then used to investigate the role of viscoelasticity in the dynamics of rising gas bubbles. The dynamics of bubbles rising in a viscoelastic liquid are characterised by three phenomena: the trailing edge cusp, negative wake, and the rise velocity jump discontinuity. The model predicts the cusp at the trailing end of a rising bubble to a high resolution.  However, the irrotational assumption precludes the prediction of the negative wake. The corresponding absence of the jump discontinuity supports the hypothesis that the negative wake is primarily responsible for the jump discontinuity, as mooted in previous studies. A second model confirms that the findings are a faithful account of bubble dynamics in viscoelastic fluids