Buoyancy driven motion of non-coalescing inertial drops: microstructure modeling with nearest particle statistics
Résumé
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 reason-
able 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 Numeri-
cal Simulations (DNS) of statistically steady state mono-disperse buoyant emulsion over a broad range
of dimensionless parameters, including the particle volume fraction (φ), the Galileo number (Ga) and
the viscosity ratio (λ). We make use of nearest particle statistics to quantify the microstructure prop-
erties. 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, φ and λ.