The onset of thermal convection in a horizontal layer of a colloidal suspension is investigated in terms of a continuum model for binary-fluid mixtures where the viscosity depends on the local concentration of colloidal particles. With an increasing difference between the viscosity at the warmer and the colder boundary the threshold of convection is reduced in the range of positive values of the separation ratio ψ with the onset of stationary convection as well as in the range of negative values of ψ with an oscillatory Hopf bifurcation. Additionally the convection rolls are shifted downwards with respect to the center of the horizontal layer for stationary convection (ψ > 0 and upwards for the Hopf bifurcation (ψ < 0 .
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