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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:TALK133279@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:In a traditional Hele-Shaw configuration\, the governing<br>eq
 uation for the pressure is Laplace&#39\;s equation\; thus\, mathematical m
 odels for<br>Hele-Shaw flows are amenable to complex analysis. We consider
  here one such problem\, where a<br>bubble is moving steadily in a Hele-Sh
 aw cell.<br>This is like the classical Taylor-Saffman bubble\, except we s
 uppose the<br>domain extends out infinitely far in all directions. By appl
 ying a conformal mapping\, we produce<br>numerical evidence to suggest tha
 t solutions to this problem behave in an<br>analogous way to well-studied 
 finger and bubble problems in a Hele-Shaw<br>channel. However\, the select
 ion of the<br>ratio of bubble speeds to background velocity for our proble
 m appears to follow<br>a very different surface tension scaling to the cha
 nnel cases. We apply techniques in exponential<br>asymptotics to solve the
  selection problem analytically\, confirming the<br>numerical results\, in
 cluding the predicted surface tension scaling laws.<br>Further\, our analy
 sis sheds light on the multiple tips in the shape of the<br>bubbles along 
 solution branches\, which appear to be caused by switching on and<br>off e
 xponentially small wavelike contributions across Stokes lines in a<br>conf
 ormally mapped plane. These results<br>are likely to provide insight into 
 other well-known selection problems in<br>Hele-Shaw flows.
LOCATION:Seminar Room 1\, Newton Institute
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