The phase-field-based lattice Boltzmann (LB) model has been developed to accurately simulate multiphase flows. This model is particularly useful for handling large density differences and surface tension effects, which are crucial for simulating capillary flows. As a result, it can reliably reproduce flow patterns like slug flow, droplet flow, and film flow, which are important in engineering applications. In this study, we improved the LB model by incorporating a conservative Allen-Cahn equation and volumetric boundary conditions to handle complex geometries in PowerFLOW®. Additionally, we implemented an optimized wettability and friction model to enhance accuracy. We tested benchmark cases, including dynamic contact angle measurement, a droplet moving in a sinusoidal channel, a slug moving in a micro-channel, and air-driven multiphase flow in a micro-channel. Our solver produced results that closely match both theoretical predictions and experimental data.

Schematics of wettability model (image credit to Dr. Hiroshi Otomo, Dassault Systemes). The order parameter φ conveys the phase information of the water (φ=1) and the air (φ=0). The schematics shows the computation of the gradient and Laplacian of φ at yellow point near the wall (red). The contact angle θ determines the iso-surface of ideal φ. In this study, this wettability model was implemented along with the volumetric boundary condition.

Example run of single drop moving in a microchannel. The following figures show the simulation set-up and the contour map of order parameter (or ‘water vapor mass fraction’) along with the pressure profile inside of the slug. The moving slug experiences three types of pressure drop: (a) viscous pressure drop at wall, (2) capillary pressure drop due to Laplace pressure, and (c) viscous dissipation at the wedges (or triple points).

We also investigated an air-driven multiphase flow case with separate air and water inlets. Water droplets pinch off from the water inlet, with their length and frequency varying based on the flow rates. The flow behavior is significantly influenced by surface wettability:

• When the inner surface is hydrophobic, the flow exhibits slug formation.
• With a hybrid surface property (hydrophobic bottom surface and hydrophilic top and side walls), a thin water film forms along the walls.

To assess flow characteristics, we measured the time evolution of fluid velocity and pressure, allowing us to compare the pressure drop with experimental data when the flow reaches a quasi-steady state

The details of this work can be found in this link: https://doi.org/10.1063/5.0249034

Thirumalaisamy R., Kim S., Otomo H., Jilesen J., & Zhang R. Capillary flow simulation with the phase-field-based lattice Boltzmann solver, Physics of fluids.