General dynamic equation for aerosols

This equation is called the continuous general dynamic equation for aerosols (Gelbard and Seinfeld 1979). Its initial and boundary conditions are... 

Gelbard, F., and Seinfeld J. H. (1979) The General Dynamic Equation for aerosols—theory and application to aerosol formation and growth, J. Colloid Interface Sci. 68, 363-382. 

Pilinis, C., and Seinfeld, J. H. (1987) Asymptotic solution of the aerosol general dynamic equation for small coagulation, J. Colloid Interface Sci. 115, 472-479. 

Barrett, J. C. and N. A. Webb (1998). A comparison of some approximate methods for solving the aerosol general dynamic equation. Journal of Aerosol Science 29, 31-39. 

In this section, basic concepts from aerosol dynamics and the general dynamic equation (GDE) are employed to explain important features of atmospheric size di.stribiition functions. The goal is to provide physical insight into these features. For the application of numerical methods to modeling atmospheric aerosol dynamics, the reader is referred to Wexler et al. (1994) and Jacobson (1997). 

Unsolved fundamental problems of great practical importance remain in aerosol dynamics. In addition to the need for rapid chemical measurement methods mentioned above, much more research is required on the effects of turbulence on coagulation and nucleation the general dynamic equation must be extended to include factors that determine the crystal state of primary particles. We also need to continue efforts to Jink aerogel formation and aerosol dynamics as initiated by A. A. Lushnikov (Karpov Institute), Experimental and... 

An aerosol distribution can be described by the number concentrations of particles of various sizes as a function of time. Let us define Nk(t) as the number concentration (cm-3) of particles containing k monomers, where a monomer can be considered as a single molecule of the species representing the particle. Physically, the discrete distribution is appealing since it is based on the fundamental nature of the particles. However, a particle of size 1 pm contains on the order of 1010 monomers, and description of the submicrometer aerosol distribution requires a vector (N2, N-j,..., N10io) containing 1010 numbers. This makes the use of the discrete distribution impractical for most atmospheric aerosol applications. We will use it in the subsequent sections for instructional purposes and as an intermediate step toward development of the continuous general dynamic equation. 

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