# Séminaire de Mécanique d'Orsay

## Le Jeudi 22 mars à 14h00 - Salle de conférences du FAST

### Bubble instabilities in rigid and flexible vessels

## Anne Juel

Manchester Centre for Nonlinear Dynamics, University of Manchester

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, oscillations in the shape of propagating bubbles are induced by a simple change in tube geometry, and secondly, flexible vessel boundaries suppress viscous fingering instability. 1) A simple change in pore geometry can radically alter the behaviour of a fluid displacing air finger, indicating that models based on idealized pore geometries fail to capture key features of complex practical flows. In particular, partial occlusion of a rectangular cross-section can force a transition from a steadily-propagating centred finger to a state that exhibits spatial oscillations via periodic sideways motion of the interface at a fixed location behind the finger tip. We characterize the dynamics of the oscillations and show that they arise from a global homoclinic connection between the stable and unstable manifolds of a steady, symmetry-broken solution. 2) Growth of complex dendritic fingers at the interface of air and a viscous fluid in the narrow gap between two parallel plates is an archetypical problem of pattern formation. We find a surprisingly effective means of suppressing this instability by replacing one of the plates with an elastic membrane. The resulting fluid-structure interaction fundamentally alters the interfacial patterns that develop and considerably delays the onset of fingering. We analyse the dependence of the instability on the parameters of the system and present scaling arguments to explain the experimentally observed behaviour.