Bursting bubble in an elasto-viscoplastic medium

TL;DR

This paper uses simulations to explore how elasto-viscoplastic properties of a medium influence the complex dynamics of bursting bubbles, revealing non-monotonic effects of elasticity and yield stress on jet formation and droplet ejection.

Contribution

It introduces a detailed analysis of bursting bubble dynamics in elasto-viscoplastic media, highlighting the roles of elasticity and plasticity through parameter space exploration.

Findings

Elastic stress relaxation non-monotonically affects jet development.

Plasticity influences jet evolution mainly at low Deborah numbers.

Polymer viscosity impacts jet thickness and maximum height.

Abstract

A gas bubble sitting at a liquid-gas interface can burst following the rupture of the thin liquid film separating it from the ambient, owing to the large surface energy of the resultant cavity. This bursting bubble forms capillary waves, a Worthington jet, and subsequent droplets for a Newtonian liquid medium. However, rheological properties of the liquid medium like elasto-viscoplasticity can greatly affect these dynamics. Using direct numerical simulations, this study exemplifies how the complex interplay between elasticity (in terms of elastic stress relaxation) and yield stress influences the transient interfacial phenomena of bursting bubbles. We investigate how bursting dynamics depends on capillary, elastic, and yield stresses by exploring the parameter space of the Deborah number $De$ (dimensionless relaxation time of elastic stresses) and the plastocapillary number $\mathcal{J}$ (dimensionless yield-stress of the medium), delineating four distinct characteristic behaviours. Overall, we observe a non-monotonic effect of elastic stress relaxation on the jet development while plasticity of the elasto-viscoplastic medium is shown to affect primarily the jet evolution only at faster relaxation times (low $De$). The role of elastic stresses on jet development is elucidated with the support of energy budgets identifying different modes of energy transfer within the elasto-viscoplastic medium. The effects of elasticity on the initial progression of capillary waves and droplet formation are also studied. In passing, we study the effects of solvent-polymer-viscosity ratio on bursting dynamics and show that polymer viscosity can increase the jet thickness apart from reducing the maximum height of the jet.