The process of particle growth in a warm cloud caused by coalescence is studied. The purely probabilistic model introduced by Gillespie [J. Atmos. Sci. 29 (1972) 1496-1510j is used and solved exactly by the aid of the Monte Carlo algorithm developed by Gillespie [J. Atmos. Sci. 32 (1975) 1977-1989]. Another approach uses the kinetic coalescence equation which is solved numerically using finite difference methods. It is known that the stochastic completeness of the kinetic coalescence equation depends on the extent of correlations between particles. Our objective is to compare these two models and analyze the suitability of the kinetic coalescence equation to simulate the coalescence process using a Brownian diffusion collision kernel.
The stochastic coalescence model introduced by Gillespie is discussed in detail. A description of Gillespie's Monte Carlo simulation procedure and the numerical code that implements this algorithm in Fortran are provided. This algorithm is applied to the coalescence kernel for Brownian diffusion and initial Poisson and uniform droplet size distributions. Numerical methods which can he applied to the continuous and the discrete forms of the kinetic equation are described. The discrete form of this equation is solved by using Euler's and the fourth order Runge-Kutta methods. Solutions from the two models at early and later times are examined and the effect of the number of droplets used in simulations is investigated. It is shown that solutions agree well for early and later times using large and relatively small number of droplets initially.
The problem of the growth of a large particle as it settles through a monodisperse suspension of small elemental particles is considered. It is demonstrated that the solution to the stochastic equation predicts about twice the growth rate of a large particle than the kinetic model.
To validate solutions obtained by the stochastic algorithm, the convergence of the solution to Poisson distribution as time increases is studied. It is shown that the normalized average concentration obtained from the initial uniform and Pois¬son distributions in the stochastic coalescence model can be approximated by the Marshall-Palmer distribution function well known in the cloud physics community.
The results of numerical simulations of the coalescence process using Brownian diffusion suggest that the kinetic equation in general produces an average size spec-trum that well matches the stochastic average spectrum. However, in the case of poorly mixed suspensions when correlations between particles are more important, these two models predict different size distributions, which is expected.
| Identifer | oai:union.ndltd.org:uvic.ca/oai:dspace.library.uvic.ca:1828/2299 |
| Date | 03 March 2010 |
| Creators | Bohun, Vasylyna |
| Contributors | Illner, Reinhard, Khouider, Boualem |
| Source Sets | University of Victoria |
| Language | English, English |
| Detected Language | English |
| Type | Thesis |
| Rights | Available to the World Wide Web |
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