Surface viscosity in multiphase flow - modeling, numerical analysis and simulations

我们的目标是得到一个通用的多相流的扩散界面模型，包括可溶性表面活性剂，表面反应，传质和相变，这将适用于广泛的一类问题，在微过程工程，微流体和材料科学。扩散界面模型的推导是基于一个发达的一般概念，以耦合偏微分方程在复杂的和不断变化的散装域与偏微分方程在不断变化的表面。我们将通过匹配渐近分析来分析所得到的模型，以显示收敛到尖锐的界面极限。我们解决由此产生的非线性方程组的自适应有限元和能量耗散时间离散计划。这些算法将在工具箱AMDiS中实现，该工具箱允许在高性能计算机上进行高效计算。我们将验证模型和模拟结果的实验数据的化学Marangoni对流和空气释放的液压泵。感兴趣的一个应用是混沌混合，我们将解决一组方程在一个隐式定义的域。

Our goal is to derive a general diffuse-interface model for multi-phase flow, including soluble surfactants, surface reactions, mass transfer and phase change which will be applicable for a wide class of problems in microprocess engineering, mirofluidics and material science. The derivation of the diffuse-interface model is thereby based on a developed general concept to couple PDEs in complicated and evolving bulk domains with PDEs on evolving surfaces. We will analyse the resulting models by means of matched asymptotic analysis to show the convergence to the sharp interface limit. We solve the resulting system of nonlinear equations by adaptive finite elements and energy dissipative time discretization schemes. The algorithms will be implemented in the toolbox AMDiS, which allows for efficient computations on high performance computers. We will validate the models and simulation results on experimental data for chemo-Marangoni convection and air release in hydraulic pumps. An application of interest is chaotic mixing for which we will solve the set of equations in an implicitly defined domain.