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hele-shaw cell

European Journal of Applied Mathematics (1)

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On the breakup of air bubbles in a Hele-Shaw cell
VLADIMIR ENTOV, PAVEL ETINGOF
Journal:

European Journal of Applied Mathematics / Volume 22 / Issue 2 / April 2011

Published online by Cambridge University Press:

21 December 2010, pp. 125-149
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We study the problem of breakup of an air bubble in a Hele-Shaw cell. In particular, we propose some sufficient conditions of breakup of the bubble, and ways to find the contraction points of its parts. We also study regulated contraction of a pair of bubbles (in which the rates of air extraction from the bubbles are controlled) and study various asymptotic questions (such as the asymptotics of contraction of a bubble to a degenerate critical point, and asymptotics of contraction of a small bubble in the presence of a big bubble)