[Paper Review] Level-set method for accurate modeling of two-phase immiscible flow with moving contact lines

Moataz O. Abu-Al-Saud, Cyprien Soulaine+2 more|arXiv (Cornell University)|Aug 16, 2017

Surface Modification and Superhydrophobicity8 references3 citations

TL;DR

This paper presents a sharp-interface level-set method with piecewise linear reconstruction to accurately simulate two-phase immiscible flows with moving contact lines. By coupling the Cox-Voinov slip-based model with a ghost-fluid method for contact line treatment, the approach achieves grid-convergent spurious current suppression and machine-precision force balance, validated against theory and experiments for capillary rise and forced imbibition in tubes.

ABSTRACT

We developed a sharp interface level-set approach for two-phase immiscible flow with moving contact lines. The Cox-Voinov model is used to describe the moving contact line. A piecewise linear interface method is used to construct the signed distance function and to implement the contact angle boundary condition. Spurious currents are studied in the case of static and moving fluid interfaces, which show convergence behavior. Pressure and the surface tension force are balanced up to machine precision for static parabolic interfaces, while the velocity error decreases steadily with grid refinement when the interface is advected in a uniform flow field. The moving contact line problem is studied and validated through comparison with theory and experiments for an advancing interface and capillary rise in a tube.

Motivation & Objective

• To address the challenge of spurious currents and lack of grid convergence in moving contact line simulations using traditional level-set methods.
• To develop a sharp interface approach that accurately captures contact line dynamics with physical boundary conditions.
• To validate the method against theoretical predictions and experimental data for capillary rise and forced imbibition in porous-like geometries.
• To demonstrate the necessity of higher-order asymptotic terms in the Cox-Voinov model for accurate macroscopic contact angle prediction.

Proposed method

• A level-set function is reconstructed as a signed distance function using piecewise linear interface reconstruction to improve curvature accuracy.
• The Cox-Voinov model is employed to describe the dynamic contact line, relating macroscopic contact angle to microscopic slip length via matched asymptotic expansions.
• A ghost-fluid method is applied to enforce the contact angle boundary condition at solid walls with sharp treatment of the interface.
• The surface tension force is balanced with pressure gradient using a consistent formulation that minimizes spurious currents.
• Grid refinement studies are conducted to assess convergence of velocity error and spurious currents in static and dynamic cases.
• The method is validated against analytical solutions for capillary rise and experimental data for forced imbibition of viscous oil by water in capillary tubes.

Experimental results

Research questions

• RQ1 Can a level-set method with piecewise linear reconstruction achieve grid-convergent spurious current suppression in two-phase flows with moving contact lines?
• RQ2 Does the inclusion of higher-order asymptotic terms in the Cox-Voinov model improve agreement with theoretical predictions for small contact angles?
• RQ3 How accurately can the proposed method reproduce experimental capillary rise and forced imbibition dynamics in capillary tubes?
• RQ4 What is the impact of using a constant contact angle versus the Cox-Voinov model on interface shape and macroscopic contact angle prediction?

Key findings

• Spurious currents converge to machine precision in static interface cases with contact angle boundary conditions, demonstrating high numerical accuracy.
• Velocity error decreases steadily with grid refinement during interface advection in uniform flow, confirming grid convergence.
• The method matches theoretical predictions for advancing interfaces in capillary tubes when the higher-order term in the Cox-Voinov model is included.
• For capillary rise, the simulated interface height converges to the experimental equilibrium height with good agreement across different grid resolutions.
• In forced imbibition of viscous oil by water, the method correctly captures viscous fingering at Ca = 1.14×10⁻³ and periodic droplet formation at Ca = 4.02×10⁻⁴, matching experimental observations.
• Applying a constant contact angle instead of the Cox-Voinov model leads to significantly different and unphysical interface shapes, confirming the model's necessity.