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Theory of growth by differential sedimentation, with application to snowflake formation

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Westbrook, C. D., Ball, Robin, Field, P. R. and Heymsfield, Andrew J.. (2004) Theory of growth by differential sedimentation, with application to snowflake formation. Physical Review E, Vol.70 (No.2). ISSN 1063-651X

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Official URL: http://dx.doi.org/10.1103/PhysRevE.70.021403

Abstract

A simple model of irreversible aggregation under differential sedimentation of particles in a fluid is presented. The structure of the aggregates produced by this process is found to feed back on the dynamics in such a way as to stabilize both the exponents controlling the growth rate, and the fractal dimension of the clusters produced at readily predictable values. The aggregation of ice crystals to form snowflakes is considered as a potential application of the model.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Divisions:	Faculty of Science > Physics
Library of Congress Subject Headings (LCSH):	Aggregation (Chemistry) -- Mathematical models, Snowflakes -- Mathematical models
Journal or Publication Title:	Physical Review E
Publisher:	American Physical Society
ISSN:	1063-651X
Official Date:	25 August 2004
Volume:	Vol.70
Number:	No.2
Number of Pages:	7
Identification Number:	10.1103/PhysRevE.70.021403
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access
Funder:	Engineering and Physical Sciences Research Council (EPSRC), Great Britain. Meteorological Office
References:	[1] C.D. Westbrook, R.C. Ball, P.R. Field and A.J. Heymsfield, arXiv:physics/0310164 (2003) [2] P. Meakin, Phys. Rev. Lett 51, 1119 (1983) [3] R.C. Ball et al, Phys. Rev. Lett. 58, 274 (1987) [4] R. Jullien and M. Kolb, J. Phys. A 17, L639 (1984) [5] D.L. Mitchell, J. Atmos. Sci. 53 1710 (1996) [6] T. Vicsek and F. Family, Phys. Rev. Lett. 52 1669 (1984) [7] M. von Smoluchowksi, Phys. Z. 17 585 (1916) [8] P.G.J. Van Dongen and M.H. Ernst, Phys. Rev. Lett. 54, 1396 (1985) [9] P.G.J. Van Dongen, J. Phys. A 20, 1889 (1987) [10] R.C. Ball and T.A.Witten, Phys. Rev. A 29, 2966 (1984) [11] P.G.J. Van Dongen and M.H. Ernst Physica A 145, 15 (1987) [12] H.R. Prupappacher and J.D. Klett, ”Microphysics of clouds and precipitation”, 2nd ed., Kluwer, London (1997). [13] A.J. Heymsfield and R. Platt, J. Atmos. Sci. 41, 846 (1984) [14] P.R. Field and A.J. Heymsfield, J. Atmos. Sci. 60, 544 (2003) [15] A.J. Heymsfield et al, J. Atmos. Sci. 59, 3 (2002) [16] A. Korolev and G. Isaac, J. Atmos. Sci. 60, 1795 (2003) [17] R.C. Ball and C.D. Westbrook - work in progress [18] PB Warren, RC Ball and A Boelle, Europhys. Lett. 29 339-344 (1995).
URI:	http://wrap.warwick.ac.uk/id/eprint/8051