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Coagulation equations with mass loss

By Jonathan A.D. Wattis, D. Graham McCartney and Throstur Gudmundsson


We derive and solve models for coagulation with mass loss\ud arising, for example, from industrial processes in which\ud growing inclusions are lost from the melt by colliding with the wall of the vessel. We consider a variety of loss laws and a variety of coagulation kernels, deriving exact results\ud where possible, and more generally reducing the equations\ud to similarity solutions valid in the large-time limit.\ud One notable result is the effect that mass removal has on gelation: for small loss rates, gelation is delayed, whilst above a critical threshold, gelation is completely prevented. Finally, by forming an exact explicit solution for a more general initial cluster size distribution function, we illustrate how numerical results from earlier work can be interpreted in the light of the theory presented herein

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