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Title: | Diffusive growth of a single droplet with three different boundary conditions |
Authors: | Tavassoli, Z Rodgers, GJ |
Keywords: | Statistical mechanics;Soft condensed matter |
Issue Date: | 1999 |
Publisher: | Springer |
Citation: | Eur. Phys. J. B 14: 139-144 (2000) |
Abstract: | We study a single, motionless three-dimensional droplet growing by adsorption of diffusing monomers on a 2D substrate. The diffusing monomers are adsorbed at the aggregate perimeter of the droplet with different boundary conditions. Models with both an adsorption boundary condition and a radiation boundary condition, as well as a phenomenological model, are considered and solved in a quasistatic approximation. The latter two models allow particle detachment. In the short time limit, the droplet radius grows as a power of the time with exponents of 1/4, 1/2 and 3/4 for the models with adsorption, radiation and phenomenological boundary conditions, respectively. In the long time limit a universal growth rate as $[t/\ln(t)]^{1/3}$ is observed for the radius of the droplet for all models independent of the boundary conditions. This asymptotic behaviour was obtained by Krapivsky \cite{krapquasi} where a similarity variable approach was used to treat the growth of a droplet with an adsorption boundary condition based on a quasistatic approximation. Another boundary condition with a constant flux of monomers at the aggregate perimeter is also examined. The results exhibit a power law growth rate with an exponent of 1/3 for all times. |
URI: | http://www.springerlink.com/content/1434-6036/ http://bura.brunel.ac.uk/handle/2438/314 |
Appears in Collections: | Mathematical Physics Dept of Mathematics Research Papers Mathematical Sciences |
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Diffusive Growth.pdf | 326.52 kB | Adobe PDF | View/Open |
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