We calculate the effective diffusion coefficient in convective flows which are well described by one spatial mode. We use an expansion in the distance from onset and homogenization methods to obtain an explicit expression for the transport coefficient. We find that spatially periodic fluid flow enhances the molecular diffusion D by a term proportional to D^-1. This enhancement should be easy to observe in experiments, since D is a small number.
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Sagués et al. (1986) studied this question.