BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Bifurcations and control of bubbles in Hele-Shaw channels - Alice 
 Thompson\, University of Manchester
DTSTART:20220318T160000Z
DTEND:20220318T170000Z
UID:TALK168452@talks.cam.ac.uk
CONTACT:Prof. Jerome Neufeld
DESCRIPTION:The propagation of a deformable air finger or bubble into a fl
 uid-filled channel with an imposed pressure gradient was first studied by 
 Saffman and Taylor. Assuming large aspect ratio channels\, the flow can be
  depth-averaged and the free-boundary problem for steady propagation solve
 d by conformal mapping. Famously\, at zero surface tension\, fingers of an
 y width may exist\, but the inclusion of vanishingly small surface tension
  selects symmetric fingers of discrete finger widths. At finite surface te
 nsion\, Vanden-Broeck later showed that other families of 'exotic' states 
 exist\, but these states are all linearly unstable and cannot be directly 
 observed in experiments.\n\nIn this talk\, I will discuss the related prob
 lem of air bubble propagation into rigid channels with axially-uniform\, b
 ut non-rectangular\, cross-sections. By including a centred constriction i
 n the channel\, multiple modes of propagation can be stabilised\, includin
 g symmetric\, asymmetric and oscillatory states\, with a correspondingly r
 ich bifurcation structure. These phenomena can be predicted via depth-aver
 aged modelling\, and also observed in our experiments\, with quantitative 
 agreement between the two in appropriate parameter regimes. This agreement
  provides insight into the physical mechanisms underlying the observed beh
 aviour. I will outline our efforts to understand how the system dynamics i
 s affected by the presence of nearby unstable solution branches acting as 
 edge states. Finally\, I will discuss how feedback control and control-bas
 ed continuation could be used for direct experimental observation of stabl
 e or unstable modes.
LOCATION:MR2\, Centre for Mathematical Sciences\, Wilberforce Road\, Cambr
 idge
END:VEVENT
END:VCALENDAR