An Extended Height-Function Method for 3D VOF Simulations of Wetting Phenomena on Super-Hydrophilic and Hydrophobic Surfaces

An extended height-function (HF) method that can be consistently utilized for 3D volume of fluid (VOF) simulations of wetting phenomena on super-hydrophilic and super-hydrophobic surfaces, is proposed. First, the standard HF method is briefly explained. Then, 2D and 3D HF methods that reflect the contact angles reported so far are described, with their limitations discussed. Finally, specific treatments of contact line identification and HF construction reflecting the contact angle boundary condition, required to overcome such limitations, are presented in detail. Numerical tests for a sessile droplet reveal that the contact line identification and HF construction are conducted appropriately with respect to the imposed contact angles ranging from $15^{\circ }$ to $165^{\circ }$ in the proposed numerical scheme. Additionally, the present method shows approximately first- or second-order convergence of the curvature at the contact line for a wide range of contact angles. Moreover, simulations of droplet spreading driven by surface tension reveal that the proposed method can reasonably reproduce the behavior of a droplet reaching an equilibrium state defined by an imposed contact angle.