## A Level Set Method for the Simulation of Moving Contact Lines in Three Dimensions

Publication ,  Journal Article
Zhao, Q; Xu, S; Ren, W
Published in: Communications in Computational Physics
January 1, 2022

We propose an efficient numerical method for the simulation of the two-phase flows with moving contact lines in three dimensions. The mathematical model consists of the incompressible Navier-Stokes equations for the two immiscible fluids with the standard interface conditions, the Navier slip condition along the solid wall, and a contact angle condition (Ren et al. (2010) [28]). In the numerical method, the governing equations for the fluid dynamics are coupled with an advection equation for a level-set function. The latter models the dynamics of the fluid interface. Following the standard practice, the interface conditions are taken into account by introducing a singular force on the interface in the momentum equation. This results in a single set of governing equations in the whole fluid domain. Similarly, the contact angle condition is imposed by introducing a singular force, which acts in the normal direction of the contact line, into the Navier slip condition. The new boundary condition, which unifies the Navier slip condition and the contact angle condition, is imposed along the solid wall. The model is solved using the finite difference method. Numerical results are presented for the spreading of a droplet on both homogeneous and inhomogeneous solid walls, as well as the dynamics of a droplet on an inclined plate under gravity.

## Published In

Communications in Computational Physics

1991-7120

1815-2406

January 1, 2022

32

5

## Start / End Page

1310 / 1331

• Applied Mathematics
• 4601 Applied computing

### Citation

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Zhao, Q., Xu, S., & Ren, W. (2022). A Level Set Method for the Simulation of Moving Contact Lines in Three Dimensions. Communications in Computational Physics, 32(5), 1310–1331. https://doi.org/10.4208/cicp.OA-2022-0021
Zhao, Q., S. Xu, and W. Ren. “A Level Set Method for the Simulation of Moving Contact Lines in Three Dimensions.” Communications in Computational Physics 32, no. 5 (January 1, 2022): 1310–31. https://doi.org/10.4208/cicp.OA-2022-0021.
Zhao Q, Xu S, Ren W. A Level Set Method for the Simulation of Moving Contact Lines in Three Dimensions. Communications in Computational Physics. 2022 Jan 1;32(5):1310–31.
Zhao, Q., et al. “A Level Set Method for the Simulation of Moving Contact Lines in Three Dimensions.” Communications in Computational Physics, vol. 32, no. 5, Jan. 2022, pp. 1310–31. Scopus, doi:10.4208/cicp.OA-2022-0021.
Zhao Q, Xu S, Ren W. A Level Set Method for the Simulation of Moving Contact Lines in Three Dimensions. Communications in Computational Physics. 2022 Jan 1;32(5):1310–1331.

## Published In

Communications in Computational Physics

1991-7120

1815-2406

January 1, 2022

32

5

1310 / 1331