Scaling Function for the Diffusion Coefficient of a Critical Fluid in a Finite Geometry

The long wavelength diffusion coefficient of a critical fluid confined between two parallel plates separated by a distance L is strongly affected by the finite size. Finite size scaling leads us to expect that the vanishing of the diffusion coefficient as \xi^{-1} for \xi<<L, \xi being the correlation length, would crossover to \L^{-1} for \xi>>L. We show that this is not strictlytrue. There is a logarthmic scaling violation. We construct a Kawasaki like scaling function that connects the thermodynamic regime to the extreme critical (\xi>>L) regime.