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A novel multi-scale theoretical model for coalescence rate of droplets induced by turbulence has been developed. This model proposed two kinds of interaction mechanisms between the underlying turbulent flow and droplets and can be a kernel function required for population balance model (PBM). Most previous models only considered the contribution of the eddies of size equal to the droplets to the coalescence since the velocity of droplet was assumed to be equal to that of eddies of same size; the sizes of droplets was usually assumed to fall in the inertial sub-range of turbulent energy spectrum and only considered the eddies in this sub-range to coalescence. But the distribution of the sizes of droplets may be quite wide in the device, considering the entire energy spectrum (i.e. containing the dissipation sub-range, the inertial sub-range and the energy-containing sub-range) may be more reasonable. The above assumptions in the previous models are no more needed in this work. A novel model based on the entire energy spectrum and the collisions between two droplets and between eddy and droplet has been derived. The contribution of eddies of different sizes to the coalescence has been considered. The results predicted by coupling novel model with PBM agree with experimental data.
coalescence rate, droplet, entire energy spectrum, multiscale turbulent eddies, turbulence
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