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

Kenzler, Rainer; Eurich, Frank; Maass, Philipp; Rinn, Bernd; Schropp, Johannes; Bohl, Erich; Dieterich, W.

doi:10.1016/s0010-4655(00)00159-4

Cited by 109 publications

(105 citation statements)

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“…Exact analytical treatments based on these equations are possible for the linear short-time regime and can become rather rich for thin films [4]. On the other hand, the exploration of the large-scale dynamics by numerical means is hard even within Ginzburg-Landau type treatments [5]. Nevertheless, numerous theoretical studies have been carried out in the past, in particular for investigating the behavior in confined geometries (for a recent review on this subject, see [6]).…”

Section: Introductionmentioning

confidence: 99%

Soft ellipsoid model for Gaussian polymer chains

Eurich

Maass

2001

The Journal of Chemical Physics

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A soft ellipsoid model for Gaussian polymer chains is studied, following an idea proposed by Murat and Kremer [J. Chem. Phys. 108, 4340 (1998)]. In this model chain molecules are mapped onto ellipsoids with certain shapes, and to each shape a monomer density is assigned. In the first part of the work, the probabilities for the shapes and the associated monomer densities are studied in detail for Gaussian chains. Both quantities are expressed in terms of simple approximate formulae. The free energy of a system composed of many ellipsoids is given by an intramolecular part accounting for the internal degrees of freedom and an intermolecular part following from pair interactions between the monomer densities. Structural and kinetic properties of both homogeneous systems and binary mixtures are subsequently studied by Monte-Carlo simulations. It is shown that the model provides a powerful phenomenological approach for investigating polymeric systems on semi-macroscopic time and length scales.

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Section: Introductionmentioning

confidence: 99%

Soft ellipsoid model for Gaussian polymer chains

Eurich

Maass

2001

The Journal of Chemical Physics

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“…This problem has been extensively studied for many years with Neumann boundary conditions. Recently, physicists [4,5,7] have introduced new boundary conditions, usually called dynamic boundary conditions, to account for the effective interaction between the wall and the two mixture components for a confined system. With these dynamic boundary conditions, the Cahn-Hilliard system is written as follows: …”

Section: Introductionmentioning

confidence: 99%

Finite-volume method for the Cahn-Hilliard equation with dynamic boundary conditions

Nabet

2014

ESAIM: ProcS

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“…Nevertheless, there were some contributions to the subject: Given a domain Q with boundary Γ and the mass concentration c of fluid 1, an early derived dynamic boundary condition for the Cahn-Hilliard equation [3,9,17] without convection on the surface reads (1.2)…”

Section: Introductionmentioning

confidence: 99%

“…[17] used Ginzburg-Landau theory to derive boundary conditions for the Cahn-Hilliard equation but did not study the full CHNS model. Numerical simulations can also be found in [9,17]. Mathematical studies of (1.1) 3 with (1.2) and υ = 0 can be found in Miranville and Zelik [23], Gilardi et.…”

Section: Introductionmentioning

confidence: 99%

On the derivation of thermodynamically consistent boundary conditions for the Cahn–Hilliard–Navier–Stokes system

Heida

2013

International Journal of Engineering Science

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Abstract.A new method will be introduced for the derivation of thermodynamically consistent boundary conditions for the full Cahn-Hilliard-Navier-Stokes-Fourier system for two immiscible fluids, where the phase field variable (order parameter) is given in terms of concentrations or partial densities. Five different types of models will be presented and discussed. The article can be considered as a continuation of a previous work by Heida, Málek and Rajagopal [16], which focused on the derivation and generalization of Cahn-HilliardNavier-Stokes models. The method is based on the assumption of maximum rate of entropy production by Rajagopal and Srinivasa [30]. This assumption will be generalized to surfaces of bounded domains using an integral formulation of the balance of entropy. Following [30], the calculations are based on constitutive equations for the bulk energy, the surface energy and the rates of entropy production in the bulk and on the surface. The resulting set of boundary conditions will consist of dynamic boundary conditions for the Cahn-Hilliard equation and either generalized Navier-slip, perfect slip or no-slip boundary conditions for the balance of linear momentum. Additionally, we will find that we also have to impose a boundary condition on the normal derivative of the normal component of the velocity field. The new approach has the advantage that the calculations are very transparent, the resulting equations come up very naturally and it is obvious how the calculations can be generalized to more than two fluids or more general constitutive assumptions for the energies. Additionally to former approaches, the approach also yields the full balance of energy for thewhole system. Finally, a possible explanation will be given for the "rolling" movement of the contact line, first observed in Dussan and Davis [8].

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

Cited by 109 publications

References 20 publications

Soft ellipsoid model for Gaussian polymer chains

Soft ellipsoid model for Gaussian polymer chains

Finite-volume method for the Cahn-Hilliard equation with dynamic boundary conditions

On the derivation of thermodynamically consistent boundary conditions for the Cahn–Hilliard–Navier–Stokes system

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