DYNAMIC SIMULATION OF DROPS BY THE PARTICLE FINITE ELEMENT

Abstract

Liquid drop dynamics on solid surfaces play an important role both in nature and engineered applications. The prediction of drop spreading and/or sliding motions has far reaching implications in many fields of application, including microfluidics, phase change applications, or coating technology. Modeling liquid drop spreading, sliding, deformation, and detachment is an active area of research, involving contact line motion, wetting, and interfacial effects. Many analytical models have been established to predict and analyze thin liquid film and droplet dynamics. However, these models are valid only for predefined geometries and do not accurately account for gravitational and interfacial effects. Numerical models have proven to be more effective tools for predicting single-phase and two-phase flows, as they can take into account complex geometries and many physical effects such as gravity, surface tension, and interfacial forces in the vicinity of moving contact lines. One of the widely used numerical approaches to simulate two-phase flows is the Volume of Fluid (VOF) method, a front-capturing, mass-conserving Eulerian scheme. However, it requires small time-marching steps, as a result of the explicit treatment of the surface tension term. Furthermore, the VOF approach is based on a fixed background computational mesh, which makes it challenging to track the free-surface of a fluid due to its high geometric complexity and time-evolving nature. In addition to the VOF method, level-set Eulerian methods can also be used to enhance tracking of the air-water interface by using larger time steps. Furthermore, these methods are not considered mass conserving for free surface hydrodynamics problems. An alternative approach to computing two-phase flows implicitly is the Lagrangian method. Its advantage stems from its ability to accurately track fluid interfaces, its implicit treatment of surface tension, thus allowing large time steps, and finally its ability to conserve mass. Its main disadvantage is due to the requirement of remeshing the entire computational domain after each time step to avoid mesh degradation, thereby increasing the computational cost. By combining the advantages of both the Eulerian and the Lagrangian methods, it is possible to develop a powerful scheme, known as the Eulerian-Lagrangian scheme. It is found to be effective for the accurate tracking of the gas-liquid interface and to account for the changes in material properties, such as viscosity, density, and surface tension. It also properly deals with the jump discontinuity of pressure across the interface, and it allows for the use of a large time step when compared to the pure Eulerian approach. This dissertation presents a multidimensional numerical model based on one of the most recent Lagrangian frameworks, namely the Particle Finite Element Method (PFEM), for the prediction of the spreading and sliding motion of liquid drops (single-phase). The model includes the effect of the physical dissipative force acting at the solid-liquid interface, and of a retention force that acts in the vicinity of the drop’s moving contact line. The proposed model is validated by using experimental data, covering a wide range of applications, drop size, and physical properties. Our numerical results are found to be mesh-independent and in very good agreement with experiments. An embedded two-phase flow is also considered in this work. Examples of two-phase flow can be found in many applications of natural and industrial importance. Of particular interest in this work are two-phase flows which involve drops, and for which surface tension and partial wetting are key factors to predict their spatiotemporal evolution. As a relevant engineering example, we consider the dynamics of drops injected into the channels of Proton Exchange Membr