Based on primitive model computer simulations with explicit microions, we calculate the effective interactions in a binary mixture of charged colloids with species $A$ and $B$ for different size and charge ratios. An optimal pairwise interaction is obtained by fitting the many-body effective forces. This interaction is close to a Yukawa (or Derjaguin-Landau-Verwey-Overbeek(DLVO)) pair potential but the $AB$ cross-interaction is different from the geometric mean of the two direct $AA$ and $BB$ interactions. As a function of charge asymmetry, the corresponding nonadditivity parameter is first positive, then getting significantly negative and is getting then positive again. We finally show that an inclusion of nonadditivity within an optimal effective Yukawa model gives better predictions for the fluid pair structure than DLVO-theory.
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