Scaling function for the critical 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. We show that this is not strictly true. There is a logarithmic scaling violation. We construct a Kawasaki-like scaling function that connects the thermodynamic regime to the extreme critical (xi>>L) regime.