COMPARISON OF ASYMPTOTIC SOLUTIONS OF PHASE-FIELD MODELS TO A SHARP-INTERFACE MODEL

We consider the incompressible flow of two immiscible fluids in the presence of a solid phase that undergoes changes in time due to precipitation and dissolution effects. Based on a seminal sharp interface model a phase-field approach is suggested that couples the Navier–Stokes equations and the solid’s ion concentration transport equation with the Cahn–Hilliard evolution for the phase fields. The model is shown to preserve the fundamental conservation constraints and to obey the second law of thermodynamics for a novel free energy formulation. An extended analysis for vanishing interfacial width reveals that in this limit the sharp interface model is recovered, including all relevant transmission conditions. Notably, the new phase-field model is able to realize Navier-slip conditions for solid–fluid interfaces in the limit.

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Non-axisymmetric growth of dendrite with arbitrary symmetry in two and three dimensions: sharp interface model vs phase-field model

The European Physical Journal Special Topics ◽

10.1140/epjst/e2020-000045-2 ◽

2020 ◽

Vol 229 (19-20) ◽

pp. 2899-2909

Author(s):

L. V. Toropova ◽

P. K. Galenko ◽

D. V. Alexandrov ◽

M. Rettenmayr ◽

A. Kao ◽

...

Keyword(s):

Phase Field ◽

Field Model ◽

Phase Field Model ◽

Sharp Interface ◽

Three Dimensions ◽

Interface Model ◽

Sharp Interface Model

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Sharp-interface formation during lithium intercalation into silicon

European Journal of Applied Mathematics ◽

10.1017/s0956792517000067 ◽

2017 ◽

Vol 29 (1) ◽

pp. 118-145 ◽

Cited By ~ 2

Author(s):

E. MECA ◽

A. MÜNCH ◽

B. WAGNER

Keyword(s):

Free Boundary ◽

Phase Field ◽

Field Model ◽

Phase Field Model ◽

Lithium Ion ◽

Sharp Interface ◽

Ion Concentration ◽

Interface Model ◽

Sharp Interface Model ◽

Time Dynamics

In this study, we present a phase-field model that describes the process of intercalation of Li ions into a layer of an amorphous solid such as amorphous silicon (a-Si). The governing equations couple a viscous Cahn–Hilliard-Reaction model with elasticity in the framework of the Cahn–Larché system. We discuss the parameter settings and flux conditions at the free boundary that lead to the formation of phase boundaries having a sharp gradient in lithium ion concentration between the initial state of the solid layer and the intercalated region. We carry out a matched asymptotic analysis to derive the corresponding sharp-interface model that also takes into account the dynamics of triple points where the sharp interface intersects the free boundary of the Si layer. We numerically compare the interface motion predicted by the sharp-interface model with the long-time dynamics of the phase-field model.

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A new phase-field model for strongly anisotropic systems

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2008.0385 ◽

2009 ◽

Vol 465 (2105) ◽

pp. 1337-1359 ◽

Cited By ~ 112

Author(s):

Solmaz Torabi ◽

John Lowengrub ◽

Axel Voigt ◽

Steven Wise

Keyword(s):

Phase Field ◽

Field Model ◽

Three Dimensional ◽

Phase Field Model ◽

Sharp Interface ◽

Interface Model ◽

Sharp Interface Model ◽

Anisotropic Surface ◽

Sharp Corners ◽

New Phase

We present a new phase-field model for strongly anisotropic crystal and epitaxial growth using regularized, anisotropic Cahn–Hilliard-type equations. Such problems arise during the growth and coarsening of thin films. When the anisotropic surface energy is sufficiently strong, sharp corners form and unregularized anisotropic Cahn–Hilliard equations become ill-posed. Our models contain a high-order Willmore regularization, where the square of the mean curvature is added to the energy, to remove the ill-posedness. The regularized equations are sixth order in space. A key feature of our approach is the development of a new formulation in which the interface thickness is independent of crystallographic orientation. Using the method of matched asymptotic expansions, we show the convergence of our phase-field model to the general sharp-interface model. We present two- and three-dimensional numerical results using an adaptive, nonlinear multigrid finite-difference method. We find excellent agreement between the dynamics of the new phase-field model and the sharp-interface model. The computed equilibrium shapes using the new model also match a recently developed analytical sharp-interface theory that describes the rounding of the sharp corners by the Willmore regularization.

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