Implementing contact angle boundary conditions for second-order Phase-Field models of wall-bounded multiphase flows

Abstract

In the present work, a general formulation is proposed to implement the contact angle boundary conditions for the second-order Phase-Field models, which is applicable to N -phase (N 2) moving contact line problems. To remedy the issue of mass change due to the contact angle boundary condition, a Lagrange multiplier is added to the original second-order Phase-Field models, which is determined by the consistent and conservative volume distribution algorithm so that the summation of the order parameters and the consistency of reduction are not influenced. To physically couple the proposed formulation to the hydrodynamics, especially for large-density-ratio problems, the consistent formulation is employed. The reduction-consistent conservative Allen-Cahn models are chosen as examples to illustrate the application of the proposed formulation. The numerical scheme that preserves the consistency and conservation of the proposed formulation is employed to demonstrate its effectiveness. Results produced by the proposed formulation are in good agreement with the exact and/or asymptotic solutions. The proposed method captures complex dynamics of moving contact line problems having large density ratios.

A projection-based, semi-implicit time-stepping approach for the Cahn-Hilliard Navier-Stokes equations on adaptive octree meshes

“…Thus, in this case the resolution for interface is not very high and we do not anticipate a large efficiency gain. ng et al [57] and Voigt [58] m: ℎ = 4.0/2 11 4.0/2 7 to 4.0/2 11…”

“…We are particularly interested in the coupled Cahn-Hilliard Navier-Stokes equations as a means to capture interfacial dynamics. Cahn-Hilliard Navier-Stokes (CHNS) models have received in-creasing attention for their ability to capture interface resolved two-phase phenomena in various applications [8][9][10][11][12]. Such an approach provides a thermodynamically consistent description of the interfacial processes and evolution [13].…”

Energy stable and conservative numerical schemes for simulating two-phase flows using Cahn-Hilliard Navier Stokes equations

“…We are particularly interested in the coupled Cahn-Hilliard Navier-Stokes equations as a means to capture interfacial dynamics. Cahn-Hilliard Navier-Stokes (CHNS) models have received increasing attention for their ability to capture interface resolved two-phase phenomena in various applications (Guo and Lin, 2015;Huang et al, 2021;Mirjalili and Mani, 2021). Such an approach provides a thermodynamically consistent description of the interfacial processes and evolution .…”