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

We investigate a non-isothermal diffuse-interface model that describes the dynamics of two-phase incompressible flows with thermo-induced Marangoni effect. The governing PDE system consists of the Navier--Stokes equations coupled with convective phase-field and energy transport equations, in which the surface tension, fluid viscosity and thermal diffusivity are allowed to be temperature dependent functions. First, we establish the existence and uniqueness of local strong solutions when the spatial dimension is two and three. Then, in the two-dimensional case, assuming that theL∞-norm of the initial temperature is suitably bounded with respect to the coefficients of the system, we prove the existence of global weak solutions as well as the existence and uniqueness of global strong solutions.

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Sharp interface limit of a diffuse interface model for tumor-growth

Communications in Mathematical Sciences ◽

10.4310/cms.2019.v17.n6.a4 ◽

2019 ◽

Vol 17 (6) ◽

pp. 1557-1593

Author(s):

Mingwen Fei ◽

Tao Tao ◽

Wei Wang

Keyword(s):

Tumor Growth ◽

Sharp Interface ◽

Diffuse Interface ◽

Interface Model ◽

Diffuse Interface Model ◽

Sharp Interface Limit

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

Metals ◽

10.3390/met9090944 ◽

2019 ◽

Vol 9 (9) ◽

pp. 944

Author(s):

Liu ◽

Zhang ◽

Lei ◽

Li ◽

Li

Keyword(s):

Sharp Interface ◽

Diffuse Interface ◽

Theoretical Formula ◽

Interface Model ◽

Sharp Interface Model ◽

Diffuse Interface Model ◽

Formula Derivation ◽

Dominant Condition ◽

Special Case

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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