A mean-field theory of the electrodynamics of a turbulent fluid is formulated under the assumption that the molecular electric conductivity is correlated with the turbulent velocity fluctuation in the (radial) direction, g. It is shown that for such homogeneous fluids a strong turbulence-induced field advection anti-parallel to g arises almost independently of rotation. For rotating fluids, an extra alpha effect appears with the known symmetries and with the expected maximum at the poles. Fast rotation, however, with Coriolis number exceeding unity suppresses this term. Numerical simulations of forced turbulence using the nirvana code demonstrate that the radial advection velocity, gamma, always dominates the alpha term. We show finally with simplified models that alpha(2) dynamos are strongly influenced by the radial pumping: for gamma < alpha the solutions become oscillatory, while for gamma > alpha they become highly exotic if they exist at all. In conclusion, dynamo models for slow and fast solid-body rotation on the basis of finite conductivity-velocity correlations are unlikely to work, at least for alpha(2)omega dynamos without strong shear.