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SUMMARY:Bifurcations and control of propagating bubbles in Hele-Shaw chann
 els - Dr. Alice Thompson (University of Manchester)
DTSTART:20220204T123000Z
DTEND:20220204T133000Z
UID:TALK169145@talks.cam.ac.uk
CONTACT:99736
DESCRIPTION:The propagation of a deformable air finger or bubble into a fl
 uid-filled channel with an imposed pressure gradient is a classical proble
 m first studied by Saffman and Taylor within the context of a depth-averag
 ed model. At zero surface tension\, fingers of any width may exist\, but t
 he inclusion of vanishingly small surface tension selects symmetric finger
 s of discrete finger widths. At finite surface tension\, Vanden-Broeck lat
 er showed that other families of 'exotic' states exist\, but these states 
 are all linearly unstable and cannot be observed directly in experiments.\
 n\nIn this talk\, I will discuss the related problem of air bubble propaga
 tion into rigid channels with axially-uniform\, but non-rectangular\, cros
 s-sections. By including a centred constriction in the channel\, multiple 
 modes of propagation can be stabilised\, including symmetric\, asymmetric 
 and oscillatory states\, with a correspondingly rich bifurcation structure
 . These phenomena can be predicted via depth-averaged modelling\, and also
  observed in our experiments\, with quantitative agreement between the two
  in appropriate parameter regimes. This agreement provides insight into th
 e physical mechanisms underlying the observed behaviour. I will outline ou
 r efforts to understand how the system dynamics is affected by the presenc
 e of nearby unstable solution branches acting as edge states. Finally\, I 
 will discuss our recent work on how feedback control and control-based con
 tinuation could enable direct experimental observation of stable or unstab
 le modes.
LOCATION:CUED\, LT6
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