• DOI:10.1103/PhysRevE.63.061704
• Corpus ID: 24040381

Grain-boundary motion in layered phases.

@article{Boyer2001GrainboundaryMI,
  title={Grain-boundary motion in layered phases.},
  author={Denis Boyer and Jorge Vi{\~n}als},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2001},
  volume={63 6 Pt 1},
  pages={
          061704
        }
}

• D. Boyer, J. Viñals
• Published 1 March 2001
• Physics
• Physical review. E, Statistical, nonlinear, and soft matter physics

We study the motion of a grain boundary that separates two sets of mutually perpendicular rolls in Rayleigh-Bénard convection above onset. The problem is treated either analytically from the corresponding amplitude equations, or numerically by solving the Swift-Hohenberg equation. We find that if the rolls are curved by a slow transversal modulation, a net translation of the boundary follows. We show analytically that although this motion is a nonlinear effect, it occurs in a time scale much shorter than that of the linear relaxation of the curved rolls. The total distance traveled by the boundary scales as epsilon(-1/2), where epsilon is the reduced Rayleigh number. We obtain analytical expressions for the relaxation rate of the modulation and for the time-dependent traveling velocity of the boundary, and especially their dependence on wave number. The results agree well with direct numerical solutions of the Swift-Hohenberg equation. We finally discuss the implications of our results on the coarsening rate of an ensemble of differently oriented domains in which grain-boundary motion through curved rolls is the dominant coarsening mechanism.