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.

中文翻译：

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具有沉淀和溶解的两相流的三元 Cahn-Hilliard-Navier-Stokes 模型

我们考虑两种不混溶流体在固相存在下的不可压缩流动，固相由于沉淀和溶解效应而随时间变化。基于开创性的尖锐界面模型，提出了一种相场方法，该方法将 Navier-Stokes 方程和固体离子浓度输运方程与相场的 Cahn-Hilliard 演化相结合。该模型显示保留了基本守恒约束和遵守热力学第二定律的新自由能公式。对消失界面宽度的扩展分析表明，在这个限制下，尖锐的界面模型被恢复，包括所有相关的传输条件。值得注意的是，新的相场模型能够在极限内实现固-流界面的纳维滑移条件。