A dual resolution phase‐field solver for wetting of viscoelastic droplets

Abstract

We present a new and efficient phase‐field solver for viscoelastic fluids with moving contact line based on a dual‐resolution strategy. The interface between two immiscible fluids is tracked by using the Cahn‐Hilliard phase‐field model, and the viscoelasticity incorporated into the phase‐field framework. The main challenge of this approach is to have enough resolution at the interface to approach the sharp‐interface methods. The method presented here addresses this problem by solving the phase field variable on a mesh twice as fine as that used for the velocities, pressure, and polymer‐stress constitutive equations. The method is based on second‐order finite differences for the discretization of the fully coupled Navier–Stokes, polymeric constitutive, and Cahn–Hilliard equations, and it is implemented in a 2D pencil‐like domain decomposition to benefit from existing highly scalable parallel algorithms. An FFT‐based solver is used for the Helmholtz and Poisson equations with different global sizes. A splitting method is used to impose the dynamic contact angle boundary conditions in the case of large density and viscosity ratios. The implementation is validated against experimental data and previous numerical studies in 2D and 3D. The results indicate that the dual‐resolution approach produces nearly identical results while saving computational time for both Newtonian and viscoelastic flows in 3D.

Wetting Effect on Patterned Substrates

“…Most models on the wetting phenomenon in literature are based on Equation ( 9), such as the work of Jacqmin, [167] Cahn, [173] de Gennes, [174] and many other references. [175][176][177][178][179] This equation is sometimes called natural boundary condition. At static equilibrium when d𝜌/dt = 0, it has been demonstrated that this boundary condition is equivalent to the Young's law.…”