A model for droplet size distribution in wall-bounded emulsion flows

This study introduces a model for the droplet size distribution in wall-bounded turbulent emulsion. The model assumes an equilibrium state, at which droplets breakup and coalescence balance. The shear stress induced deformation process is modeled through a simple first-order ordinary differential equation. Breakup occurs when sustained stress drives deformation beyond a critical threshold θ_c, with fragmentation modeled as successive binary splitting events that exhibit characteristics analogous to turbulent energy cascade. The process of droplet coalescence, on the other hand, is modeled probabilistically analogous to the intermolecular collisions in the kinetic theory of gases based on the classical Coulaloglou & Tavlarides (1977) framework. Predictions from the baseline model which considers only the collision probability yield mean droplet size satisfying the〈D〉∽Re^-1.2 scaling across Reynolds numbers Re_τ=180 to 1000. Equilibrium droplet size distribution also aligns well with existing literature data in experiments.