Abstract

The displacement of a liquid by an air finger is a generic two-phase flow that underpins applications as diverse as microfluidics, thin-film coating, enhanced oil recovery, and biomechanics of the lungs. I will present two intriguing examples of such flows where, firstly, multiple states of bubble propagation are generated by a simple change in tube geometry, and secondly, flexible vessel boundaries suppress viscous fingering instability.

1) Microscale process engineering requires precise control of bubbles and droplets. We investigate geometry-induced control and find that a centred constriction in the cross section of rectangular tubes can lead to new families of steadily propagating bubbles, which localize in the least-constricted regions of the cross section. Tuning the constriction geometry can cause a switchlike transition from centered to localized bubbles at a critical value of the flow rate: a mechanism for flow-rate-driven bubble control. The accompanying large change in bubble volume could be significant for liquid recovery applications.

2) We investigate the radial displacement of a viscous liquid by an air bubble in an elastic Hele-Shaw cell, i.e. an elastic membrane separated from a glass plate by a thin liquid film. We find that the presence of the elastic membrane suppresses the viscous fingering instability that always arises in the rigid configuration. The interface now becomes unstable beyond a critical flow rate that decreases as K^{-1/4} (K is the bending stiffness of the membrane), and we propose a physical mechanism for damping that agrees with our experimental findings.