In this paper, a thermal-dynamical consistent model for mass transfer across permeable moving interfaces is proposed by using the energy variation method. We consider a restricted diffusion problem where the flux across the interface depends on its conductance and the difference of the concentration on each side. The diffusive interface phase-field framework used here has several advantages over the sharp interface method. First of all, explicit tracking of the interface is no longer necessary. Secondly, the interfacial condition can be incorporated with a variable diffusion coefficient. A detailed asymptotic analysis confirms the diffusive interface model converges to the existing sharp interface model as the interface thickness goes to zero. A decoupled energy stable numerical scheme is developed to solve this system efficiently. Numerical simulations first illustrate the consistency of theoretical results on the sharp interface limit. Then a convergence study and energy decay test are conducted to ensure the efficiency and stability of the numerical scheme. To illustrate the effectiveness of our phase-field approach, several examples are provided, including a study of a two-phase mass transfer problem where drops with deformable interfaces are suspended in a moving fluid.
翻译:在本文中,通过使用能源变异法,提出了跨渗透移动界面大规模传输的热动力一致模式。我们考虑了一个有限的扩散问题,因为界面的通量取决于其导演和每个侧面的集中程度差异。此处使用的 diffusive界面相位场框架比尖锐界面法具有若干优点。首先,对界面的清晰跟踪不再必要。第二,可以将界面的跨动性条件与可变扩散系数结合起来。详细的时间分析证实,当界面厚度降至零时,该硬性界面模式会与现有的尖性界面模式相融合。我们制定了一个分解的能源稳定数字方案,以有效解决这个系统。数字模拟首先显示锐性界面限制的理论结果的一致性。随后,进行了一项趋同研究和能源衰变试验,以确保数字方法的效率和稳定性。为了说明我们阶段化方法的有效性,提供了几个例子,包括一项两阶段质量转移问题的研究,即移动液中与可变式界面悬浮。