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The droplet size distribution in the late stage of phase separation
Institution:1. Department of Immunology and Microbial Science, The Scripps Research Institute, La Jolla, CA 92037, USA;2. Department of Pathology and Immunology, Washington University School of Medicine, St. Louis, MO 63110, USA;1. Department of Biomedical Engineering;2. Lorry I. Lokey Interdisciplinary Center for Life Sciences and Engineering;3. Department of Electrical Engineering, Technion – Israel Institute of Technology, Haifa, Israel;4. Raymond & Beverly Sackler School of Chemistry;5. Department of Physiology and Pharmacology, Sackler Faculty of Medicine;6. Sagol School of Neuroscience;7. Raymond & Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel;1. Fédération de Recherche FERMAT, Université de Toulouse, CNRS, Toulouse, France;2. Institut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS, Toulouse, France;3. Laboratoire des IMRCP, Université de Toulouse, CNRS UMR 5623, Université Toulouse III - Paul Sabatier, Toulouse, France;1. Cellular and Molecular Biology Program, University of Michigan, Ann Arbor, MI 48103, USA;2. Department of Computational Medicine and Bioinformatics, University of Michigan, Ann Arbor, MI 48103, USA;3. Department of Biological Chemistry, University of Michigan, Ann Arbor, MI 48103, USA;4. Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48103, USA;5. Department of Biomedical Engineering, University of Michigan, Ann Arbor, MI 48103, USA
Abstract:We consider a collection of droplets during the late stage of phase separation in a closed system. Its coarsening is driven by surface energy and leads asymptotically to a linear growth of the mean droplet volume with time (Ostwald ripening). The droplets grow either from the supersaturated uncondensed phase (coalescence) or by collisions with subsequent fusion (coagulation). The combination of both mechanisms leads asymptotically to a self-similar evolution of the size distribution of the droplets when the coagulation kernel is homogeneous with degree zero. We calculate the scaled droplet size distribution for Brownian and constant kernel and compare the effects of coagulation with the effects of correlation and screening discussed in the literature. We compare our results for the asymptotic scaled distribution with computer simulations for the combined coalescence and coagulation processes.
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