Simulations of inertial liquid-lens coalescence with the pseudopotential lattice Boltzmann method

TL;DR

This paper uses the pseudopotential lattice Boltzmann method to simulate the coalescence of liquid lenses, revealing how contact angles influence bridge growth dynamics in two and three dimensions, with results aligning with experiments and theory.

Contribution

It introduces a detailed numerical investigation of liquid-lens coalescence across a range of contact angles using the pseudopotential lattice Boltzmann method, including comparisons with experimental and theoretical models.

Findings

Quantitative agreement with experiments for small contact angles in 2D.

Thin-sheet equations accurately predict dynamics up to 40° contact angle.

Bridge growth in 3D is initially independent of contact angle.

Abstract

The coalescence of liquid lenses is relevant in various applications, including inkjet printing and fog harvesting. However, the dynamics of liquid-lens coalescence have been relatively underexplored, particularly in the case of liquid lenses with larger contact angles. We numerically investigate the coalescence of low-viscosity liquid lenses by means of the pseudopotential multi-component lattice Boltzmann method over a wide range of contact angles. In two-dimensional simulations, our numerical results on the growth of the bridge height are in quantitative agreement with experimental measurements for small contact angles. In addition, by comparing our simulation results with a theoretical approach based on the thin-sheet equations for liquid lenses, we find that the thin-sheet equations accurately capture the bridge-growth dynamics up to contact angles of approximately $\theta < 40^{\circ}$. For the three-dimensional case, the growth of the bridge radius is independent of the equilibrium contact angle of the liquid lenses at the initial stage of growth. The dependency between the growth of the bridge height and the bridge radius exhibits a non-linear to linear transition.