Coalescence and breakage processes. (English) Zbl 1074.82534

Summary: We extend a model for coalescence and breakage of liquid-liquid dispersions proposed by Fasano/Rosso. The main feature is that the experimentally observed fact of a maximal droplet mass is taken into account. Our model includes spontaneous breakage as well as collisional fragmentation. Existence and uniqueness of solutions is proved and the long-time behaviour is investigated.


82C22 Interacting particle systems in time-dependent statistical mechanics
45K05 Integro-partial differential equations
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[1] A new model for the dynamics of dispersions in a batch reactor: theory and numerical simulation. In Lectures on Applied Mathematics: Proceedings of the Symposium on the Occasion of Karl-Heinz Hoffmann’s 60th Birthday, (eds), Munich, June 30-July 1, 1999, Springer: Berlin, Heidelberg, New York, 2000; 123-141.
[2] Separation of crude oil-water emulsions: experimental techniques and models. Ph.D. Thesis, ETH Zurich, 1998.
[3] Valentas, I&E C Fundamentals 5 pp 271– (1966)
[4] Valentas, I&E C Fundamentals 5 pp 533– (1966)
[5] Cheng, Physical Review Letters 60 pp 2450– (1988)
[6] Laurençot, Journal of Statistical Physics 104 pp 193– (2001) · Zbl 1126.82320
[7] Gewöhnliche Differentialgleichungen (2. Auflage.). de Gruyter: Berlin, New York, 1995.
[8] Functional Analysis and Semigroups, vol. XXXI (Revised edn.) American Mathematical Society Colloquium Publications: Providence, RI, 1957.
[9] McGrady, Physical Review Letters 58 pp 892– (1987)
[10] Vigil, Journal of Colloid and Interface Science 133 pp 257– (1989)
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