An efficient finite element method for simulation of droplet spreading on a topologically rough surface

• Published in: Journal of computational physics 2017-11, Vol.349, p.233-252
• Main Authors: Luo, Li, Wang, Xiao-Ping, Cai, Xiao-Chuan
• Format: Article
• Language: English
• Subjects: Algorithms; Boundary conditions; Computational fluid dynamics; Computational physics; Computer simulation; Domain decomposition methods; Finite element analysis; Finite element method; Fluid flow; Mass compensation; Mathematical analysis; Mathematical models; Navier-Stokes equations; Parallel computing; Phase-field model; Qualitative analysis; Simulation; Solid surfaces; Spreading; Surface roughness; Three dimensional models; Topologically rough surface; Topology; Unstructured finite element method; Wettability; Wetting phenomenon
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2017.08.010

We study numerically the dynamics of a three-dimensional droplet spreading on a rough solid surface using a phase-field model consisting of the coupled Cahn–Hilliard and Navier–Stokes equations with a generalized Navier boundary condition (GNBC). An efficient finite element method on unstructured meshes is introduced to cope with the complex geometry of the solid surfaces. We extend the GNBC to surfaces with complex geometry by including its weak form along different normal and tangential directions in the finite element formulation. The semi-implicit time discretization scheme results in a decoupled system for the phase function, the velocity, and the pressure. In addition, a mass compensation algorithm is introduced to preserve the mass of the droplet. To efficiently solve the decoupled systems, we present a highly parallel solution strategy based on domain decomposition techniques. We validate the newly developed solution method through extensive numerical experiments, particularly for those phenomena that can not be achieved by two-dimensional simulations. On a surface with circular posts, we study how wettability of the rough surface depends on the geometry of the posts. The contact line motion for a droplet spreading over some periodic rough surfaces are also efficiently computed. Moreover, we study the spreading process of an impacting droplet on a microstructured surface, a qualitative agreement is achieved between the numerical and experimental results. The parallel performance suggests that the proposed solution algorithm is scalable with over 4,000 processors cores with tens of millions of unknowns.