Buoyancy driven motion of non-coalescing inertial drops: microstructure modeling with nearest particle statistics

TL;DR

This paper introduces a new algorithm integrated with the VoF method to simulate buoyant emulsions, analyzing how droplet microstructures depend on flow inertia, volume fraction, and viscosity ratio, with implications for understanding droplet clustering.

Contribution

The study develops a novel non-coalescing algorithm within the VoF framework and applies it to DNS, providing quantitative microstructure analysis based on nearest particle statistics across various parameters.

Findings

Droplets form isotropic clusters at moderate inertia ($Ga=10$).

High inertia ($Ga=100$) leads to non-isotropic structures like layers.

Viscosity ratio influences microstructure, favoring layering for less viscous droplets.

Abstract

In this study, we analyze the various arrangements that droplets can form within dispersed buoyant emulsions, which we refer to as the study of microstructure. To this end, we have developed a novel algorithm that effectively prevents numerical coalescence between drops while maintaining a reasonable computational cost. This algorithm is integrated into the Volume of Fluid (VoF) method and implemented using the open-source code http://basilisk.fr. Subsequently, we perform Direct Numerical Simulations (DNS) of statistically steady state mono-disperse buoyant emulsion over a broad range of dimensionless parameters, including the particle volume fraction ($\phi$), the Galileo number ($Ga$) and the viscosity ratio ($\lambda$). We make use of nearest particle statistics to quantify the microstructure properties. As predicted by Zhang et al. (2023), it is demonstrated that the second moment of the nearest particle pair distribution can effectively quantify microstructural features such as particle clusters and layers. Specifically, the findings are: (1) In moderately inertial flows ($Ga = 10$), droplets form isotropic clusters. In high inertial regimes ($Ga = 100$), non-isotropic clusters, such as horizontal layers, are more likely to form. (3) The viscosity ratio plays a significant role in determining the microstructure, with droplets that are less viscous or equally viscous as the surrounding fluid tending to form layers preferentially. Overall, our study provides a quantitative measure of the microstructure in terms of $Ga$, $\phi$ and $\lambda$.