Abstract:

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.