General Dynamic Equation

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. 

As already noted, the present study of dynamic fuel cell behavior involves the analysis of systems with capacitive elements. These elements control the rate at which process parameters change due to net forces imposed by other coupled process parameters. A general dynamic equation showing capacitance behavior is ... 

A similar result holds true for any general dynamic equation of elasticity theory and for equations of compressional and shear waves as well. 

The General Dynamic Equation for the Particle Size Distribution Function. ... 

GENERAL DYNAMIC EQUATION FOR THE DISCRETE DISTRIBUTION FUNCTION... 

Figure 11.1 Processes taking place in an elemental volume included in the general dynamic equation. Gas flows produce particle transport across the element bound-aric.s. In addition lo gravitation, olherforce lields that drive Iluacs not shown] aie electrical potential and temperature gradients.

The general dynamic equation di-scussed in this chapter does not include terms for the inertial transport of particles. Discuss possible methods of incorporating particle tran.spor1 by the inertial mechanism in the GDE. 

In the simplest cases, discussed below, a chemical reaction releases a large number of condensable molecules at r = 0. The dynamics of the system then depend on aero.sol processes alone. Landgrebe and Pratsinis (1989) gave criteria for determining when chemical kinetics must be taken into account. Floess et al, (1997) combined a detailed chemical kinetic model with the general dynamic equation in a. study of the synthesis of fumed silica in a hydrogen-air flame reactor. 

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). 

In the approach adopted in my first edition, the derivation and use of the general dynamic equation for the particle size distribution played a central role. This special form of a population balance equation incorporated the Smoluchowski theory of coagulation and gas-to-panicle conversion through a Liouville term with a set of special growth laws coagulation and gas-to-particle conversion are processes that take place within an elemental gas volume. Brownian diffusion and external force fields transport particles across the boundaries of the elemental volume. A major limitation on the formulation was the assumption that the panicles were liquid droplets that coalesced instantaneously after collision. 

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... 

The PBE is also known as the general dynamic equation in the aerosol literature. 

Zhao, H. B., Zheng, C. G. Xu, M. H. 2005a Multi-Monte Carlo approach for general dynamic equation considering simultaneous particle coagulation and breakage. Powder... 

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