A generalized model for breakage and coalescence kernels valid for the entire spectrum of turbulence is proposed and validated. Most of the available kernels in the literature indeed assume that in a turbulent liquid-liquid dispersion, the dispersed droplets have dimension in the inertial subrange, and are affected by eddies with size in the same subrange. These kernels are based on the Kolmogorov second-order structure function, which is valid only in the inertial subrange. However, in most industrially encountered situations, many droplets may have a size in the dissipation range, where the Kolmogorov second-order structure function does not apply. Therefore, a more general description of the energy transferred between these droplets and the turbulent eddies is needed to properly model breakage and coalescence events.
In this work, the Coulaloglou and Tavlarides (1977) breakage and coalescence kernels have been modified through the implementation of the second-order structure function proposed by Davidson (2004), along with the Pope (2000) energy spectrum. Turbulent liquid-liquid dispersion experiments at high continuous phase viscosity are performed to test and validate the model. The generalized model is able to predict the experimental Sauter mean diameters at different viscosities, turbulent conditions and dispersed-phase volume fraction without any adjustment of the kernel parameters.