  In a viscous lock-exchange gravity current, which describes the reciprocal
exchange of two fluids of different densities in a horizontal channel, the
front between two Newtonian fluids spreads as the square root of time. The
resulting diffusion coefficient reflects the competition between the buoyancy
driving effect and the viscous damping, and depends on the geometry of the
channel. This lock-exchange diffusion coefficient has already been computed for
a porous medium, a 2D Stokes flow between two parallel horizontal boundaries
separated by a vertical height, H, and, recently, for a cylindrical tube. In
the present paper, we calculate it, analytically, for a rectangular channel
(horizontal thickness b, vertical height, H) of any aspect ratio (H/b) and
compare our results with experiments in horizontal rectangular channels for a
wide range of aspect ratios (1/10-10). We also discuss the 2D Stokes-Darcy
model for flows in Hele-Shaw cells and show that it leads to a rather good
approximation, when an appropriate Brinkman correction is used.
