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We construct rigorously suitable approximate solutions to theStokes/Cahn-Hilliard system by using the method of matched asymptoticsexpansions. This is a main step in the proof of convergence given in the firstpart of this contribution, where the rigorous sharp interface limit of acoupled Stokes/Cahn-Hilliard system in a two dimensional, bounded and smoothdomain is shown. As a novelty compared to earlier works, we introducefractional order terms, which are of significant importance, but share theproblematic feature that they may not be uniformly estimated in $\epsilon$ inarbitrarily strong norms. As a consequence, gaining necessary estimates for theerror, which occurs when considering the approximations in theStokes/Cahn-Hilliard system, is rather involved.

Sharp Interface Limit of a Stokes/Cahn-Hilliard System, Part II: Approximate Solutions