Diffusive Growth of a Single Droplet with Three Different Boundary Conditions

Details Diffusive Growth of a Single Droplet with Three Different Boundary Conditions Diffusive Growth of a Single Droplet with Three Different Boundary Conditions

1999-12-13

arxiv.org/abs/cond-mat/9912225v1

Eur. Phys. J. B 14, 139-144 (2000)

Physics

Condensed Matter

Statistical Mechanics

21 pages, no figure, to be published in EPJ B

Scientific paper

10.1007/s100510050114

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.

Affiliated with

Also associated with

No associations

Rating

Diffusive Growth of a Single Droplet with Three Different Boundary Conditions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Diffusive Growth of a Single Droplet with Three Different Boundary Conditions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Diffusive Growth of a Single Droplet with Three Different Boundary Conditions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-529890