  We study the one-dimensional Cahn-Hilliard equation with an additional
driving term representing, say, the effect of gravity. We find that the driving
field $E$ has an asymmetric effect on the solution for a single stationary
domain wall (or `kink'), the direction of the field determining whether the
analytic solutions found by Leung [J.Stat.Phys.{\bf 61}, 345 (1990)] are
unique. The dynamics of a kink-antikink pair (`bubble') is then studied. The
behaviour of a bubble is dependent on the relative sizes of a characteristic
length scale $E^{-1}$, where $E$ is the driving field, and the separation, $L$,
of the interfaces. For $EL \gg 1$ the velocities of the interfaces are
negligible, while in the opposite limit a travelling-wave solution is found
with a velocity $v \propto E/L$. For this latter case ($EL \ll 1$) a set of
reduced equations, describing the evolution of the domain lengths, is obtained
for a system with a large number of interfaces, and implies a characteristic
length scale growing as $(Et)^{1/2}$. Numerical results for the domain-size
distribution and structure factor confirm this behavior, and show that the
system exhibits dynamical scaling from very early times.
