Abstract
Rising motion of an air bubble in viscous liquid, confined strongly by the front and back walls of the cell and weakly by the side walls, is studied to establish clear scaling laws for rising velocity, viscous drag force, and shape, revealing striking analogies with the viscous fingering problem.
Highlights
The dynamics of a bubble rising in a confined space is a classic problem that is replete with interesting physics yet to be explored
Our study presented below is in contrast with studies such as [2] that focused on capillary tubes whose cross-section is characterized by length scales which are all smaller than the capillary length and, neglected the gravity term in the Navier-Stokes equation
Rising dynamics of a bubble confined in a vertical cell with a high aspect ratio rectangular cross-section was discussed, where the bubble is strongly confined in one horizontal direction and is weakly confined or is not confined in the remaining one horizontal direction
Summary
The dynamics of a bubble rising in a confined space is a classic problem that is replete with interesting physics yet to be explored. With the development of microfluidics [31,32], many studies have been performed on the transportation of strongly confined bubbles in a tube with a square or rectangular cross-section with an aspect ratio close to one, both in the inertial [1,33,34,35,36], and viscous [2,3,35,37,38,39] regimes. Reviewing the literature to date, we asked what would happen if a vertically rising bubble was strongly confined in one direction, as in a Hele-Shaw cell, and weakly confined in a second direction, by using a vertical tube with a high aspect ratio rectangular cross-section This question was briefly addressed in the viscous regime by Clanet et al in 2004 [1]. We show that bubble rising behavior in the present study can be mapped to a type of viscous fingering using a velocity transformation, which provides novel insight into the study
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