Numerical Studies of Sessile Droplet Shape with Moving Contact Lines

Abstract

This paper numerically studies the equilibrium shape of a sessile droplet with moving contact lines. The Navier- Stokes equation was solved through the finite volume method on a Cartesian staggered grid. The level-set method was used to track free surface of the immiscible two-phase, gas and liquid. The Navier boundary condition is enforced on the entire solid surface away from the triple contact line to remove the force singularity. The continuum model formulated by Ren and E was used near the contact line [1]. Our code was validated by comparing it with other numerical results, and gave a lower mass loss of less than 2%. The method can easily be extended to a three dimensional model. Droplet spreading and recoiling were calculated and discussed with the presented numerical methods. Both two-dimensional and threedimensional simulation results agree well with experimental observations. Keywords: Sessile droplet, level-set method, triple contact line, Numerical Studies, Navier boundary, microfluidics, transition, discretization process, asymmetric model, reintialization