带表面活性剂的两相流相场模型建模与数值求解

表面活性剂能明显地改变流体间的表面张力，生成表面张力梯度，引起流体沿着界面流动的传质效应，即马兰戈尼效应。借助这种效应，表面活性剂在大量的多相流问题中都发挥着很重要的作用，在制药、石油、生命科学等众多领域表面活性剂也发挥着重要的应用价值。本项目拟建立一个满足热力学一致性的多相流相场模型研究表面活性剂对多相流流动的影响。模型将考虑变密度、粘度的多相流，并考虑表面活性剂在流体内和流体界面上的扩散过程。设计高精度的能量稳定算法，使用申请人自主研发的带矩形自适应网格的多重网格计算软件BSAM实现算法，进行数值模拟，通过一些实际算例研究表面活性剂对于多相流流动的影响。

The presence of surfactants at fluid interfaces can reduce the surface tension, and lead to a gradient in surface tension, which gives rise to tangential forces dragging the fluid flow along the interface. Through this so-called Marangoni effect, surfactants can play an important role in several physical phenomena, and is very important in many industrial applications, including pharmacy, petrochemical engineering, and life science. This project intends to derive a thermodynamically consistent phase-field model for multiphase phase flows to study the effects of the surfactant on the fluid dynamics. The model will consider a multiphase fluid with variable density and viscosity, along with the bulk and interfacial surfactant concentrations. A second order accurate, energy stable numerical method will be designed for the model equations. The method will be implemented by using a Blocked Structured Adaptive Multigrid (BSAM) numerical package that is designed by the applicant. The effects of surfactants on the fluid dynamics will be studied through several numerical examples.