We implement a new solvent-bath computer simulation scheme to calculate effective interactions between two charged colloidal spheres with their counterions in a hard-sphere solvent in order to test the primitive model and a solvent-averaged primitive model. We show that the presence of a granular solvent significantly influences the effective colloidal interaction. For divalent counterions, the total effective force can become attractive, generated by counterion hydration, while for monovalent counterions the forces are repulsive and well described by a solvent-induced colloidal charge renormalization. Neither effect is contained in the traditional `primitive' approaches but both can be accounted for in a solvent-averaged primitive model.
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