Abstract
An analytical theory is given for the viscous wake behind a spherical
bubble rising steadily in a pure liquid at high Reynolds number, and for
that
wake's effect on
the motion of a second bubble rising underneath the first. Previous theoretical
work on this subject consists of just two papers: a first approximation
ignoring
wake vorticity diffusion between the bubbles, and a full numerical solution
avoiding
simplifying approximations (apart from that of spherical shape of the bubbles).
A
second approximation is now found; it removes much of the discrepancy between
the first approximation and the full solution. The leading-order calculation
of wake
vorticity diffusion uses a transformation of the independent variables
which appears
to be new. Experimental work to date has disagreed with all the theoretical
work, but
it addresses a somewhat different problem: a line of many bubbles.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
33 articles.
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