We present a numerical model for the simulation of complex planar interfaces at which moving solid objects can be immersed, reproducing a wide variety of experimental conditions. The mathematical model consists of the Navier-Stokes equations governing the incompressible viscous flow in the liquid subphase, the transport equation for the evolution of the surfactant concentration at the interface, and the interfacial stress balance equation. The equations are simplified by treating the problem as isothermal and the surfactant as insoluble. The bulk flow equations are discretized using a collocated finite volume method, while the interfacial flow equations are discretized using a finite area method. The Boussinesq-Scriven interface constitutive model and a variant form accounting for extensional viscosity are used to describe the extra surface stress tensor. The coupling between surfactant concentration, interfacial velocity, and bulk velocity is treated implicitly by solving the interfacial and bulk equations sequentially at each time step until a stopping criterion is satisfied. The motion of the solid is treated by an arbitrary Lagrangian-Eulerian method. The model has been implemented in the OpenFOAM framework and allows the incorporation of new interface models and solvers, making the developed new package a versatile and powerful tool in the field of computational rheology. Applications of the model include the numerical simulation of flow around objects, such as probes, immersed at a complex interface, reproducing given experimental conditions, and its use as a tool in the analysis and design of interfacial stress rheometers. Several test cases have been performed to validate the model by comparing the results obtained with analytical solutions and with numerical and experimental results available in the literature.

中文翻译：

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用于模拟复杂平面牛顿界面的数值模型


我们提出了一个用于模拟复杂平面界面的数值模型，其中移动的固体物体可以浸入其中，并再现了各种实验条件。该数学模型由控制液体亚相中不可压缩粘性流的 Navier-Stokes 方程、界面处表面活性剂浓度演变的输运方程和界面应力平衡方程组成。通过将问题视为等温并将表面活性剂视为不溶性来简化方程。本体流方程使用并置有限体积法进行离散化，而界面流方程使用有限面积法进行离散化。Boussinesq-Scriven 界面本构模型和解释拉伸粘度的变体形式用于描述额外表面应力张量。表面活性剂浓度、界面速度和体速度之间的耦合通过在每个时间步长按顺序求解界面方程和体方程来隐式处理，直到满足停止标准。固体的运动由任意拉格朗日-欧拉方法处理。该模型已在 OpenFOAM 框架中实现，并允许合并新的接口模型和求解器，使开发的新软件包成为计算流变学领域的多功能和强大工具。该模型的应用包括对浸没在复杂界面上的物体（如探针）周围的流动进行数值模拟，再现给定的实验条件，以及将其用作界面应力流变仪分析和设计中的工具。 通过将获得的结果与解析解以及文献中提供的数值和实验结果进行比较，已经执行了几个测试用例来验证模型。