Oscillatory bubbles induced by geometric constraint
AbstractCo-authors: Alice Thompson (University of Manchester), Andrew Hazel (University of Manchester)
We show that a simple change in pore geometry can radically alter the behaviour of a fluid-displacing air finger [1,2]. A rich array of propagation modes, including symmetric, asymmetric, localised fingers, is uncovered when air displaces oil from axially uniform tubes that have local variations in flow resistance within their cross-sections. The most surprising propagation mode exhibits spatial oscillations formed by periodic sideways motion of the interface at a fixed distance behind the moving finger tip . This rich behaviour is in contrast to the single, symmetric mode observed in tubes of regular cross-section, e.g. circular, elliptical, rectangular and polygonal.
We derive a two-dimensional depth-averaged model for bubble propagation through wide channels with a smooth occlusion, which is similar to that describing Saffman-Taylor fingering, but with a spatially varying channel height. We solve the resulting system numerically, using the finite-element library oomph-lib (www.oomph-lib.org), and find that numerical solutions to the model exhibit most the qualitative features of the experimental propagation modes, including the oscillatory modes of propagation.
The existence of these novel propagation modes suggests that models based on over-simplification of the pore geometry will suppress fundamental physical behaviour present in practical applications, where pore geometry often contains many regions of local constriction, e.g. connecting or irregularly shaped pores in carbonate oil reservoirs, and airway collapse or mucus buildup in the lungs. Moreover, these modes offer further potential for geometry-induced manipulation of droplets for lab-on-the-chip applications, in which geometric variations have so far been restricted to the axial direction.
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