Numerical modeling of diffusion-controlled phase transformation using the Darken method: Application to the dissolution/precipitation processes in materials
Résumé
Many material phase transformations are controlled by mass transport induced by diffusion. To better understand such transformations, numerous modeling strategies at the scale of the moving interfaces exist, with their strengths and weaknesses. Phase-field approaches are based on diffuse interfaces that do not require any interface tracking, as opposed to those based on fixed-grid sharp interface tracking. In the case of binary two-phase systems, in this paper we address the key point of the mass balance equation at the interface involving a concentration jump, which determines the interface moving velocity. We propose a unique diffusion equation for both phases and their interface, based on the component’s chemical potentials which are continuous through the interface and a smooth volume-of-fluid phase representation. This model is achieved in the framework of the Darken method, which involves intrinsic diffusion of components and a drift velocity to which all compounds are subjected. This drift velocity is shown to be that of the interface displacement as well. This methodology is verified for 1D and 3D dissolution/precipitation problems and has a first-order spatial convergence. The 3D simulations of precipitation and dissolution processes of more complex microstructures clearly show a bifurcation of the particle morphology from the initial spherical shape when the diffusion edges of each particle interact with each other. An extension of the diffusion potential to mechanical driving forces should make it possible to deal with mechano-chemical coupling of mass transport.
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