A Comparative Study of the Diffuse-Interface Model and Sharp-Interface Model in the Soldering Related Wetting Spreading Systems

A typical dissolution wetting system, Bi-Sn eutectic filler metal over a Bi substrate in a high-purity argon atmosphere was investigated first using real-time in situ hot stage microscopy for the extensive use of the sharp-interface model and the diffuse-interface model in the modeling of brazing/soldering related wetting systems. Subsequently, the similarities and differences between the aforementioned models in describing the issues of the wetting and spreading interfaces were discussed in terms of soldering definition and theoretical formula derivation. It is noted that (i) the mutual dissolution diffusion between the liquid Bi-Sn solder and Bi substrate were obvious. As a result, the composition and volume of the liquid solder is constantly changing during the wetting and spreading process; (ii) the sharp-interface model is a special case of the diffuse-interface model of the Cahn-Hilliard nonlinear diffuse-equation under the convective dominant condition; (iii) although there are differences between the sharp-interface model and the diffuse-interface model, both of them could be used in brazing/soldering related processes; and, (iv) the agreement between the experimental and simulation results of the sharp-interface model is not as good as that of the diffuse-interface model, which can be attributed to the effects of the elements’ diffusion and the phase transformation.

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A Rigorous Sharp Interface Limit of a Diffuse Interface Model Related to Tumor Growth

Journal of Nonlinear Science ◽

10.1007/s00332-016-9352-3 ◽

2016 ◽

Vol 27 (3) ◽

pp. 847-872 ◽

Cited By ~ 8

Author(s):

Elisabetta Rocca ◽

Riccardo Scala

Keyword(s):

Tumor Growth ◽

Sharp Interface ◽

Diffuse Interface ◽

Interface Model ◽

Diffuse Interface Model ◽

Sharp Interface Limit

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A diffuse interface model for quasi–incompressible flows : Sharp interface limits and numerics, ,

ESAIM Proceedings ◽

10.1051/proc/201238004 ◽

2012 ◽

Vol 38 ◽

pp. 54-77 ◽

Cited By ~ 2

Author(s):

Gonca Aki ◽

Johannes Daube ◽

Wolfgang Dreyer ◽

Jan Giesselmann ◽

Mirko Kränkel ◽

...

Keyword(s):

Incompressible Flows ◽

Sharp Interface ◽

Diffuse Interface ◽

Interface Model ◽

Diffuse Interface Model

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Simulations of Nonlinear Strongly Anisotropic, Misfitting Crystals and Thin Films

MRS Proceedings ◽

10.1557/proc-1087-v02-01 ◽

2008 ◽

Vol 1087 ◽

Cited By ~ 3

Author(s):

Solmaz Torabi ◽

Steven Wise ◽

Shuwang Li ◽

Axel Voigt ◽

John Lowengrub ◽

...

Keyword(s):

Thin Films ◽

Surface Energy ◽

Excellent Agreement ◽

Elastic Energy ◽

Equilibrium Shape ◽

Relative Strength ◽

Sharp Interface ◽

Diffuse Interface ◽

Interface Model ◽

Sharp Interface Model

AbstractWe present a new approach for modeling strongly anisotropic crystal and epitaxial growth using regularized, anisotropic Cahn-Hilliard-type equations as a model for the growth and coarsening of thin films. When the surface anisotropy is sufficiently strong, sharp corners form and unregularized anisotropic Cahn-Hilliard equations become ill-posed. Our models contain a high order Willmore regularization to remove the ill posedness at the corners. A key feature of our approach is the development of a new formulation in which the interface thickness is independent of crystallographic orientation. In our previous work, we have provided matched asymptotic analysis to show the convergence of our diffuse interface model to the analytical sharp interface model. In previous models there was no such convergence to sharp interface model when the Willmore energy was considered. We present 2D numerical results using an adaptive, nonlinear multigrid finite-difference method. In particular, we find excellent agreement between the computed shapes using the Cahn-Hilliard approach, with a finite but small Willmore regularization, with dynamical numerical simulations of a sharp interface model. The equilibrium shapes from our diffuse model are compared with an analytical sharp-interface theory recently developed by Spencer [1] at the corners, and there is excellent match. Away from the corners there is an excellent agreement between the diffuse model and the classical Wulff shape. Finally, in order to model the misfit and displacement strains, we add the elastic energy and corresponding forces to our diffuse model. We analyze numerically the effect of elastic stress on the corner regularization in terms of two parameters: one parameter that describes the relative strength of the elastic energy to surface energy and the second that characteristics the strength of the surface energy anisotropy. Adding elastic energy modifies the equilibrium shape and in particular affects the shape of the corners. We can predict different Qdot shapes, such as pyramids and domes, based on the strength of the elastic interactions.

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