Model-based description of droplet deformation into polyhedral shapes in liquid-liquid polydisperse dense-packed zones

Droplet deformation in liquid-liquid dense-packed zones (DPZs) significantly impacts the dispersed phase volume fraction and droplet coalescence, which is crucial to phase separation processes in various industrial equipment. This study introduces a modeling approach to describe droplet deformation into polyhedral shapes in polydisperse DPZs. Droplet deformation, characterized by the contact radius rf, the curvature radius ra, and the volume ratio Ei is modeled using equations based on pressure, geometric, and volumetric relationships for regular polyhedra as well as Bond number correlations. Moreover, generalized Bond number correlations are proposed to extend the approach to irregular convex polyhedral shapes. Simulations across technical Bond number ranges demonstrate that rf and Ei increases with the Bond number, while ra decreases, approaching zero at high Bond numbers. The Bond number correlations strongly agree with equation-based solutions, with mean absolute percentage errors below 3.0 %. Practical implications include enhanced predictions for DPZ behavior and integration into a common coalescence model.