Continuous generation of confined bubbles: viscous effect on the gravito-capillary pinch off

Abstract

We investigate continuous generation of bubbles from a bath of air in viscous liquid in a confined geometry. In our original setup, bubbles are spontaneously generated by virtue of buoyancy and a gate placed in the cell: the gate acts like an inverted funnel trapping air beneath it before continuously generating bubbles at the tip. The dynamics is characterized by the bubble-formation period and the bubble size as a function of the amount of air under the gate. By analyzing the data obtained for various parameters, we clearly identified that the dynamics of the bubble formation is governed by dissipation in the viscous fluid beneath the trapped air balanced by a gravitational energy change due to buoyancy, after examining numerous possibilities of dissipation, which demonstrates the potential of scaling analysis even in complex cases. Furthermore, we uncover a novel type of pinch-off condition, which convincingly explains the bubble size: in the present case viscosity plays a vital role, different from the conventional mechanism of Tate, in which gravity competes with capillarity, revealing a general mechanism of pinching-off at low Reynolds number. Accordingly, the present study significantly and fundamentally advances our knowledge of generation and pinch-off of bubbles, with the results relevant for a wide variety of applications in many fields. In particular, the present study demonstrates a promising avenue in microfluidics for understanding physical principles by scaling up the system, without losing the characteristics of the flow at low Reynolds numbers.