Abstract
An air bubble expanding into a viscous liquid in the small gap between parallel plates deforms into highly branched, continuously evolving interfacial fingering patterns. By separating the plates following a power law in time, it is found that the interface can also form self-similar fingering patterns.
Highlights
An expanding air bubble that displaces a viscous fluid within the narrow gap between two parallel plates is unstable to nonaxisymmetric perturbations beyond a critical value of the capillary number Ca, the ratio of viscous to surface tension forces [1,2,3,4]
We studied the dynamics of an expanding gas bubble that displaces a viscous liquid in a radial Hele-Shaw cell with a time-varying gap width, focusing on the case of a t1/7 power-law for the plate separation
This showed that for unimodal perturbations with a wave number that matches the most unstable wave number from the linear stability analysis, self-similar fingers formed on the interface
Summary
An expanding air bubble that displaces a viscous fluid within the narrow gap between two parallel plates (a Hele-Shaw cell) is unstable to nonaxisymmetric perturbations beyond a critical value of the capillary number Ca, the ratio of viscous to surface tension forces [1,2,3,4] In this radial geometry, the unstable interface typically deforms into a set of growing fingers which evolve continuously in time through a sequence of tip-splitting events followed by competition between the newly formed fingers. Finger competition events reminiscent of the patterns in a radial cell with fixed parallel plates
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