Adaptive near-contact repulsion in conservative Allen-Cahn phase-field lattice Boltzmann multiphase model

Abstract

Unresolved thin-film dynamics often causes spurious coalescence in diffuse-interface simulations of multiphase flows. We address this issue by introducing a fully local repulsive near-contact flux in a conservative Allen--Cahn phase-field model coupled to lattice Boltzmann hydrodynamics. The interaction activates only for oppositely oriented nearby interfaces, with a strength that self-adjusts based upon an analytical estimate of the local film thickness extracted from the phase field. The resulting method circumvents nonlocal geometric procedures, preserves computational efficiency, and is well suited to massively parallel implementations. Tests on collision benchmarks and three-dimensional bubble swarms demonstrate robust suppression of artificial merging and physically consistent near-contact dynamics.

Figures (8)

• Figure 1: Graphical sketch of the head-on (a) and off-axis (b) collisions between equally sized droplets.
• Figure 2: Comparison between experimental results of Huang & Pan HuangPan2021JFM and the corresponding numerical simulations for two bouncing regimes. (a) Head-on collision of dodecane droplets with $D=300~\mu\mathrm{m}$ at $We = 4.60$. (b) Off-center collision of water droplets with $D=1000~\mu\mathrm{m}$, $B = 0.32$ and $We = 4.70$. In each case, experiments (top) and simulations (bottom) are shown for direct comparison. The time shown above each frame is given in milliseconds.
• Figure 3: Velocity field in the inter-droplet region during head-on impact. The color map denotes the normalized velocity magnitude ($u/u_{\max}$), and arrows indicate the flow direction.
• Figure 4: Velocity field and associated profiles at three stages of the collision. Panels (a–c) show the flow field at the pre-collision stage, at head-on contact, and the post-collision. Panel (d) reports the film-averaged normal velocity $\bar{w}_{\mathrm{film}}$, and panel (e) shows the centerline streamwise velocity $u_x(x)$ along $z = z_0$. In panels (d) and (e), the blue, orange, and yellow curves correspond to the stages shown in panels (a–c), respectively.
• Figure 5: Quantification of the near-contact interaction and the capillary contribution within the inter-droplet film at peak activation for different values of $A_{\mathrm{rep}}$, $\sigma$, and $D$. (a) Schematic of the inter-droplet thin-film region where the force balance is evaluated. (b) Ratio between the repulsive and capillary forces within the thin film, $R_n$, as a function of droplet diameter. (c) Maximum repulsive force magnitude $\max|\mathbf{F}_{\mathrm{rep}}|$ as a function of $\sigma$. (d) Film-averaged repulsive force magnitude $\langle|\mathbf{F}_{\mathrm{rep}}|\rangle_{\mathrm{film}}$ as a function of $\sigma$. (e) Activated film volume normalized by the square of the droplet diameter $V_{\mathrm{film}}/D^2$ as a function of $D$.