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We consider a model for phase separation in binary viscous liquids that allows for material transport due to cross-diffusion of unlike particles and convection by the hydrodynamic bulk flow. Typically, during the evolution, the average size of domains of the pure phases increases with time — a phenomenon called coarsening. Siggia [24] predicts that at an initial stage, coarsening proceeds mainly by diffusion, which leads to the well-known evaporation-recondensation growth law