Effect of the polymer viscosity and relaxation time on the Worthington jet produced by bubble bursting in weakly viscoelastic liquids

Abstract

We study the influence of bulk viscoelasticity on bubble bursting experimentally. We consider polymers with disparate molecular weights to analyze the effects of the polymer’s extensional relaxation time and viscosity separately. Within the parameter region explored in this study, the polymer relaxation time has a larger influence on whether a droplet is emitted or not, while the polymeric viscosity has the largest effect on the Worthington jet velocity. Viscoelasticity suppresses the droplet emission roughly if the characteristic strain rate of the Worthington jet exceeds the inverse of the polymer relaxation time. The viscosity of the polymer with the highest molecular weight is insufficient to produce noticeable effects on the Worthington jet dynamics for extensional relaxation times that lead to droplet ejection. This polymer transitions from a quasi-Newtonian behavior to droplet emission suppression as the polymer concentration increases. Polymeric viscosities ${\eta }_p\gtrsim 10^{-2}$ mPa s significantly affect the Worthington jet dynamics. In this case, the strain rate arising in certain phases of the bubble bursting considerably increases the jet’s extensional viscosity. As a result, the first-emitted droplet size increases, and the velocity decreases.