This thesis focuses on the modeling and simulation of multi-phase flow on solid surfaces with moving contact line. In particular, we develop a consistent model for N-phase flow (N ≥ 3). The thesis consists of three parts.

In the first part, Cahn-Hilliard coupled Navier Stokes equation together with relaxation boundary condition for phase parameter and generalized Navier boundary condition (GNBC) [81] on velocity on the solid boundary is employed to simulate droplet impacting on a smooth, flat and chemically homogeneous solid surface with finite difference method. Different impacting phenomena, wetting, bouncing, partial bouncing and splashing, are observed numerically and their dependence on individual dimensionless parameters, Reynolds number, Weber number, density ratio, vis...[ Read more ]

This thesis focuses on the modeling and simulation of multi-phase flow on solid surfaces with moving contact line. In particular, we develop a consistent model for N-phase flow (N ≥ 3). The thesis consists of three parts.

In the first part, Cahn-Hilliard coupled Navier Stokes equation together with relaxation boundary condition for phase parameter and generalized Navier boundary condition (GNBC) [81] on velocity on the solid boundary is employed to simulate droplet impacting on a smooth, flat and chemically homogeneous solid surface with finite difference method. Different impacting phenomena, wetting, bouncing, partial bouncing and splashing, are observed numerically and their dependence on individual dimensionless parameters, Reynolds number, Weber number, density ratio, viscosity ratio and equilibrium contact angle between interface of liquid/air and solid surfaces are also investigated. In addition, we also use the model above to simulate two-phase flow in a bumpy channel with finite element method using unstructured mesh.

In the second part, the model of two-phase flow with moving contact line problem is generalized to that of three-phase flow. Difficulty of this problem lies in how to deal with constraints introduced to let the model give physically relevant results. We solve this problem by developing a gradient projection approach. A new model of Cahn-Hilliard coupled Navier Stokes equation together with the boundary condition on solid surfaces is proposed for three-phase flow on solid surfaces. The energy decay of the model is satisfied. An unconditional stable numerical scheme is then designed to solve the equation system we derive for the three phase flow on solid surfaces. The discrete energy law of the numerical scheme is proved. Some interesting numerical simulations of dynamics of triple junction and four phase contact line are performed.

In the third part, a systematical derivation of continuum model for the dynamics of multi-component system coupled with flow field on solid surfaces is presented based on thermodynamics principles and Onsager’s reciprocal relations. In addition, following the ideas of projection we used in the second part, derivation of a model that satisfies constrains to let the model give physically relevant results is straightforward. At last, we have verified that the model for multi-phase (N-phase) system is equivalent to model of two-phase flow with moving contact line problem derived in [82] and model of three-phase flow on solid surfaces we get above for N = 2 and N = 3 respectively.