VISCOUS PARALLEL FLOWS IN FINITE ASPECT RATIO HELE-SHAW CELL - ANALYTICAL AND NUMERICAL RESULTS

The parallel flow of one or two fluids of contrasted viscosities throu gh a rectangular channel of large aspect ratio is studied. The usual r esult for an infinite aspect ratio is that the velocity profile is par abolic throughout the gap and flat in the other direction. For a finit e aspect ratio a deviation from this usual profile is found in boundar y layers along the edges of the channel or close to the interface. The extension of these boundary layers is of the order of the small dimen sion of the channel. In the two-fluid case we find, however, that the velocity profile at the interface is strictly a parabola. The velocity profiles obtained by a 3-D lattice BGK simulation are successfully co mpared to the analytical results in the one- and two-fluid cases. (C) 1997 American Institute of Physics.