Jet formation during the gas penetration through a thin liquid layer

Abstract

A free bubble reaching the liquid surface usually bursts and then forms a liquid jet with drops ejected. While bubble-mediated jetting is a topic widely studied, few investigations deal with the jet produced by a growing bubble. Here, we report and characterize a novel phenomenon, named periodic bubbling-bursting, that can develop when a continuous stream of gas penetrates through a thin liquid layer. This behavior is complex with a characteristic frequency and can be divided into three stages from bubbling to cavity collapse and jetting. We show that increasing the liquid layer thickness and gas velocity leads to a larger bubble. However, the effect is strongly coupled with the orifice diameter and a scaling law of the bubble rupture radius is derived. Subsequently, we demonstrate that the collapsing cavities exhibit shape similarity and deduce the dependence of pinch-off height and opening angle of the conical cavity on the bubble rupture radius and liquid layer thickness. This enables us to disentangle three different neck-pinching mechanisms at play in pinch-off. Accordingly, gravity shapes the cavity and participates in the capillary wave selection that strongly modulates the jet formation. With increasing layer thickness, the jet first becomes fat and small and then ends up thinner and higher, detaching more and smaller droplets. We present a simple scaling law for the jet velocity which involves the liquid layer thickness to the power 1/2. Finally, a phase diagram for jet breakup and no breakup is built with respect to the initial Weber and Bond numbers.