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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:TALK133279AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/133279
DESCRIPTION:In a traditional Hele-Shaw configuration\, the gov
erning
equation for the pressure is Laplace'
\;s equation\; thus\, mathematical models for
H
ele-Shaw flows are amenable to complex analysis. W
e consider here one such problem\, where a
bubb
le is moving steadily in a Hele-Shaw cell.
This
is like the classical Taylor-Saffman bubble\, exc
ept we suppose the
domain extends out infinitel
y far in all directions. By applying a conformal m
apping\, we produce
numerical evidence to sugge
st that solutions to this problem behave in an
analogous way to well-studied finger and bubble pr
oblems in a Hele-Shaw
channel. However\, the se
lection of the
ratio of bubble speeds to backgr
ound velocity for our problem appears to follow
a very different surface tension scaling to the c
hannel cases. We apply techniques in exponentialasymptotics to solve the selection problem analy
tically\, confirming the
numerical results\, in
cluding the predicted surface tension scaling laws
.
Further\, our analysis sheds light on the mul
tiple tips in the shape of the
bubbles along so
lution branches\, which appear to be caused by swi
tching on and
off exponentially small wavelike
contributions across Stokes lines in a
conforma
lly mapped plane. These results
are likely to p
rovide insight into other well-known selection pro
blems in
Hele-Shaw flows.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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