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SUMMARY:Applying conformal mapping and exponential asymptotics to study tr
 anslating bubbles in a Hele-Shaw cell - Scott McCue (Queensland University
  of Technology)
DTSTART:20191029T090000Z
DTEND:20191029T100000Z
UID:TALK133276@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:In a traditional Hele-Shaw configuration\, the governing equat
 ion for the pressure is Laplace&#39\;s equation\; thus\, mathematical mode
 ls for Hele-Shaw flows are amenable to complex analysis.&nbsp\; We conside
 r here one such problem\, where a bubble is moving steadily in a Hele-Shaw
  cell.&nbsp\; This is like the classical Taylor-Saffman bubble\, except we
  suppose the domain extends out infinitely far in all directions.&nbsp\; B
 y applying a conformal mapping\, we produce numerical evidence to suggest 
 that solutions to this problem behave in an analogous way to well-studied 
 finger and bubble problems in a Hele-Shaw channel.&nbsp\; However\, the se
 lection of the ratio of bubble speeds to background velocity for our probl
 em appears to follow a very different surface tension scaling to the chann
 el cases.&nbsp\; We apply techniques in exponential asymptotics to solve t
 he selection problem analytically\, confirming the numerical results\, inc
 luding the predicted surface tension scaling laws. Further\, our analysis 
 sheds light on the multiple tips in the shape of the bubbles along solutio
 n branches\, which appear to be caused by switching on and off exponential
 ly small wavelike contributions across Stokes lines in a conformally mappe
 d plane.&nbsp\; These results are likely to provide insight into other wel
 l-known selection problems in Hele-Shaw flows.
LOCATION:Seminar Room 1\, Newton Institute
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