  We study travelling-wave spatially periodic solutions of a forced
Cahn-Hilliard equation. This is a model for phase separation of a binary
mixture, subject to external forcing. We look at arbitrary values of the mean
mixture concentration, corresponding to asymmetric mixtures (previous studies
have only considered the symmetric case). We characterize in depth one
particular solution which consists of an oscillation around the mean
concentration level, using a range of techniques, both numerical and
analytical. We determine the stability of this solution to small-amplitude
perturbations. Next, we use methods developed elsewhere in the context of
shallow-water waves to uncover a (possibly infinite) family of multiple-spike
solutions for the concentration profile, which linear stability analysis
demonstrates to be unstable. Throughout the work, we perform thorough
parametric studies to outline for which parameter values the different solution
types occur.
