A new examination of volume fraction effects during particle coarsening |
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| Affiliation: | 1. Peter the Great St. Petersburg Polytechnic University, Polytechnicheskaya Street, 29, St. Petersburg 195251, Russian Federation;2. Bauman Moscow State Technical University, 2nd Baumanskaya Street, 5, Moscow 105005, Russian Federation;3. Laboratory of Biopolymer Physical Chemistry, A.N. Nesmeyanov Institute of Organoelement Compounds of the Russian Academy of Sciences, Vavilova Street, 28, Moscow 119991, Russian Federation;1. Laboratory for Morphogenetic Signaling, RIKEN Center for Biosystems Dynamics Research, 2-2-3 Minatojima-minamimachi, Chuo-ku, Kobe, Hyogo 650-0047, Japan;2. Laboratory for Physical Biology, RIKEN Center for Biosystems Dynamics Research, 2-2-3 Minatojima-minamimachi, Chuo-ku, Kobe, Hyogo 650-0047, Japan;1. Department of Cell Biology, Research Drive, Duke University School of Medicine, Durham, NC 27710, USA;2. Laboratoire de Physique de l’École Normale Supérieure, CNRS, PSL Research University, Sorbonne Université, 24 Rue Lhomond, 75005 Paris, France;3. Department of Physics, University of California, San Diego, 9500 Gillman Drive, La Jolla, CA 92093, USA |
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| Abstract: | All previous studies of particle coarsening have shown that only one possible steady state particle size distribution (P.S.D.) is possible at any given volume fraction of the second phase and that the mean particle size follows a cubic growth law with time. Thus all initial P.S.D.'s will gradually approach this P.S.D. and growth rate on ageing. The present paper shows theoretically that there appear to be many possible P.S.D.'s at a given volume fraction and these all show cubic growth with time, although at different rates. It has been possible to study the effect of volume fraction on growth rates of similar P.S.D.'s. It is found that the growth rate increases with volume fraction but that the rate varies with the actual P.S.D. considered. Numerical analysis of coarsening has been carried out integrating both forwards and backwards with time. This has confirmed the existence of multiple steady state P.S.D.'s at a given volume fraction. It has also been shown that any arbitrary P.S.D. will develop towards that steady state distribution which has a similar size distribution at large radius values. Coarsening can be minimized by ensuring that the particles formed initially are all of comparable radius. |
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