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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Applying conformal mapping and exponential asympto
tics to study translating bubbles in a Hele-Shaw c
ell - Scott McCue (Queensland University of Techno
logy)
DTSTART;TZID=Europe/London:20191029T090000
DTEND;TZID=Europe/London:20191029T100000
UID:TALK133276AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/133276
DESCRIPTION:In a traditional Hele-Shaw configuration\, the gov
erning equation for the pressure is Laplace'\;s
equation\; thus\, mathematical models for Hele-Sh
aw flows are amenable to complex analysis. \;
We consider here one such problem\, where a bubble
is moving steadily in a Hele-Shaw cell. \; Th
is is like the classical Taylor-Saffman bubble\, e
xcept we suppose the domain extends out infinitely
far in all directions. \; By applying a confo
rmal mapping\, we produce numerical evidence to su
ggest that solutions to this problem behave in an
analogous way to well-studied finger and bubble pr
oblems in a Hele-Shaw channel. \; However\, th
e selection of the ratio of bubble speeds to backg
round velocity for our problem appears to follow a
very different surface tension scaling to the cha
nnel cases. \; We apply techniques in exponent
ial asymptotics to solve the selection problem ana
lytically\, confirming the numerical results\, inc
luding the predicted surface tension scaling laws.
Further\, our analysis sheds light on the multipl
e tips in the shape of the bubbles along solution
branches\, which appear to be caused by switching
on and off exponentially small wavelike contributi
ons across Stokes lines in a conformally mapped pl
ane. \; These results are likely to provide in
sight into other well-known selection problems in
Hele-Shaw flows.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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