Phase separation in confined geometries: Solving the Cahn–Hilliard equation with generic boundary conditions

We apply implicit numerical methods to solve the Cahn–Hilliard equation for confined systems. Generic boundary conditions for hard walls are considered, as they are derived from physical principles. Based on a detailed stability analysis an automatic time step control could be implemented, which mak...

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Bibliographic Details
Published in:	Computer physics communications Vol. 133; no. 2; pp. 139 - 157
Main Authors:	Kenzler, R., Eurich, F., Maass, P., Rinn, B., Schropp, J., Bohl, E., Dieterich, W.
Format:	Journal Article
Language:	English
Published:	Amsterdam Elsevier B.V 15-01-2001 Elsevier Science
Subjects:	Classical statistical mechanics Condensed matter: structure, mechanical and thermal properties Dynamic and nonequilibrium phase transitions (general) Equations of state, phase equilibria, and phase transitions Exact sciences and technology Initial value and time-dependent initial-boundary value problems Method of lines Partial differential equations Physics Solubility, segregation, and mixing; phase separation Statistical physics, thermodynamics, and nonlinear dynamical systems Thermodynamics Time-dependent statistical mechanics (dynamics and nonequilibrium) 82C26 Partial differential equations Method of lines Initial value and time-dependent initial-boundary value problems 65M20 Time-dependent statistical mechanics (dynamics and nonequilibrium) Dynamic and nonequilibrium phase transitions (general) Time dependence Differential equations Theoretical study Boundary-value problems Initial value problems Line (geometry) Statistical mechanics Phase transitions
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Summary:	We apply implicit numerical methods to solve the Cahn–Hilliard equation for confined systems. Generic boundary conditions for hard walls are considered, as they are derived from physical principles. Based on a detailed stability analysis an automatic time step control could be implemented, which makes it possible to explore the demixing kinetics of two thermodynamically stable phases over many orders in time with good space resolution. The power of the method is demonstrated by investigating spinodal decomposition in two-dimensional systems. At early times of the decomposition process the numerical results are in excellent agreement with analytical predictions based on the linearized equations. Due to the efficiency of the variable time step procedure it is possible to monitor the process until a stable equilibrium is reached.
ISSN:	0010-4655 1879-2944
DOI:	10.1016/S0010-4655(00)00159-4