Heil, M. (2001) Finite Reynolds number effects in the Bretherton problem.
Physics of Fluids 13, 2517-2521.
This paper investigates the effect of fluid inertia in the
classical Bretherton problem in which a semi-infinite air finger
displaces viscous fluid in a 2D channel. The governing free-surface
Navier-Stokes equations are discretised by a finite element method
and the system's behaviour is studied for capillary and Reynolds
numbers in the ranges 0.05 < Ca < 5 and 0 < Re < 280,
respectively. It is shown that at finite Reynolds number, a sequence
of closed vortices develops in the recirculating flow region ahead of
the bubble tip. The largest of these vortices is located near the bubble tip
where it significantly affects the pressure distribution and leads to
a noticeable increase in the overall pressure rise across the
bubble tip. The underlying physical mechanisms are discussed in detail.
Page last modified: August 31, 2001
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