  We consider transversely modulated fronts in a directionally quenched
Cahn-Hilliard equation, posed on a two-dimensional infinite channel, with both
parameter and source-term type heterogeneities. Such quenching heterogeneities
travel through the domain, excite instabilities, and can select the pattern
formed in their wake. We in particular study striped patterns which are oblique
to the quenching direction and checkerboard type patterns. Under generic
spectral assumptions, these patterns arise via an $O(2)$-Hopf bifurcation as
the quenching speed is varied, with symmetries arising from translations and
reflections in the transverse variable. We employ an abstract functional
analytic approach to establish such patterns near the bifurcation point.
Exponential weights are used to address neutral continuous spectrum, and a
co-domain restriction is used to address neutral mass-flux. We also give a
method to determine the direction of bifurcation of fronts. We then give an
explicit example for which our hypotheses are satisfied and for which
bifurcating fronts can be investigated numerically.
