一种用于表面活性剂的通用扩散界面建模框架
A universal diffuse interface modeling framework for surfactants
AI总结：
提出用于两相流中表面活性剂输运的通用扩散界面建模框架，基于三标量非平衡模型推导两个单标量模型，通过表面张力与纳维-斯托克斯方程耦合，经多种模拟验证，弥补了现有模型的不足。
AI中文摘要：
我们提出了一种用于两相流中表面活性剂输运的通用扩散界面建模框架，适用于所有溶解度情况和任何守恒相场方法。该框架基于一个通用的三标量非平衡模型，该模型基于我们之前的一致标量输运框架，具有局部和全局守恒、无泄漏、伽利略不变性和归约一致性等特性。在热化学平衡假设下，推导出两个单标量模型。所有模型通过包含由非均匀界面表面活性剂分布产生的马兰戈尼应力的表面张力与纳维-斯托克斯方程耦合。现有的扩散界面表面活性剂模型存在局限性，而本文框架通过多种模拟进行了验证。
英文摘要：
We propose a universal diffuse-interface modeling framework for surfactant transport in two-phase flows, applicable to all solubility scenarios and to any conservative phase field method. The foundation of our framework is a general three-scalar non-equilibrium model governing the surfactant concentrations in each bulk phase and at the interface, which builds on our prior consistent scalar transport framework and is locally and globally conservative, leakage-free, Galilean-invariant, and reduction-consistent. Assuming thermochemical equilibrium, we derive two one-scalar models: one for a surfactant in full equilibrium between both bulk phases and the interface, and one for a surfactant confined to a single bulk phase and the interface. All models are coupled to the Navier-Stokes equations through a surface tension force that incorporates the Marangoni stress arising from non-uniform interfacial surfactant distributions. While diffuse-interface surfactant models have been developed for the Cahn-Hilliard equation and, more recently, for the conservative Allen-Cahn (CAC) equation, existing models for CAC address only the insoluble and single-phase-soluble cases, leaving the general scenario of partial solubility in both bulk phases unaddressed; furthermore, these models lack Galilean invariance and reduction consistency, and are not applicable beyond the CAC setting. The framework is validated against analytical solutions in one-dimensional transport tests, assessed for convergence in two-dimensional advection-diffusion simulations, and demonstrated in fully-coupled drop-in-shear flow simulations covering insoluble, soluble, and partially-soluble surfactant scenarios.
