Coarsening dynamics of a one-dimensional driven Cahn-Hilliard system.

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. 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, where E is the driving field, and the separation, L, of the interfaces. For EL ≫ 1 the velocities of the interfaces are negligible, while in the opposite limit a travelling-wave solution is found with a velocity v ∝ E/L. For this latter case (EL ≪ 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 behaviour, and show that the system exhibits dynamical scaling from very early times. Typeset using REVTEX