Self-similar particle-size distributions during coagulation: theory and experimental verification

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Abstract
A quantitative theory for particle coagulation in continuous particle size distributions is presented and experimentally verified. The analysis, following Friedlander (1960a, b), assumes a local equilibrium in the size distribution maintained by a particle flux through the size distribution, Only particle collisions caused by Brownian motion, fluid shear and differences in settling velocities are considered. For intervals of particle size where only one coagulation mechanism is dominant, dimensional analysis predicts self-similar size distributions that contain only one dimensionless constant for each mechanism. Experiments were designed to test these predictions with clay particles in artificial seawater sheared in the gap between concentric rotating cylinders. Particle-size distributions measured over time were self-similar in shape and agreed with the Brownian- and shear-coagulation prediction in terms of shape and dependence on fluid shear rate and particle volume flux through the size distribution.