Capillary flow simulation with the phase-field-based lattice Boltzmann solver

Abstract

The phase-field-based lattice Boltzmann (LB) model has been developed to perform high fidelity multiphase flow simulations. Its ability to accurately handle high density ratio and surface tension effects is expected to be beneficial for capillary flow simulation, leading to accurate reproduction of flow patterns such as slug flow, droplet flow, and film flow. This is critical in many engineering cases because the flow patterns significantly affect the velocity and pressure fields. In this study, on top of the LB models based on the conservative Allen-Cahn equation and the volumetric boundary conditions for the complex geometries, an optimized wettability and friction model are implemented. With these models, we conducted a set of benchmark test cases, including static and dynamic multiphase flow scenarios such as the droplet on the curved surfaces, water-filling channel for the Lucas-Washburn law, and the critical pressure in the three-dimensional channel, an air-driven multiphase flow in the experiments. In all of these cases, the solver produces results that are consistent with both theory and experiment, even with respect to the pressure field accuracy, which has often been overlooked in many previous studies.

Figures (23)

• Figure 1: Introduction of the wettability model. Consider the computation of the gradient and Laplacian of $\varphi$ at a yellow point in the first lattice point. The solid is colored red, and its normal direction is shown as $\vec{n}$. With the input contact angle $\theta$, we obtain the iso-surface of an ideal $\varphi$ variation, whose normal direction is shown with $\vec{w}$. The parallelograms/parallelepipeds from the surface are shown with the blue color.
• Figure 2: Schematic explanation of the sampled $\varphi$ calculation for complex geometry.
• Figure 3: (a) Schematic of a single slug moving in a three-dimensional duct. The airflow introduced through the inlet propels the slug. The inset shows the discretization in the cross-sectional area of the duct. (b) Three-dimensional view of a moving slug shows its curved interface as it moves forward driven by air pressure.
• Figure 4: (a) Order parameter contour maps of the slices along the centerline. Pressures were measured at four different locations near the two interfaces. (b) Pressure (blue) and the order parameter (orange) profile along the centerline of the slug.
• Figure 5: A schematic illustrates a setup for a slug flow in a two-dimensional channel with hydrophobic wall boundary conditions ($\theta=133^\circ$) at the top and bottom boundaries. The left boundary is a velocity inlet with velocity $u$, while the right boundary has a fixed pressure boundary condition.