TABLE OF CONTENTS Gas-to-particle conversion, coagulation and particle transport have been discussed in previous chapters. These processes determine the change in the size distribution function with time and position. A general dynamic equation (GDE) for n( r, v, t) that includes all of these processes is set up in this chapter. This equation is sometimes referred to as a population balance equation. By solving the equation for different initial and boundary conditions, the size distribution function can be calculated for geometries and flow conditions of practical interest. The GDE is of fundamental importance to understanding and modeling industrial and atmospheric processes.
At the beginning of the chapter it is shown that the usual models for coagulation and nucleation presented in Chapters 7 and 10 are special cases of a more general theory for very small particles. An approximate criterion is given for determining whether nucleation or coagulation is rate-controlling at the molecular level. The continuous form of the GDE is then used to derive balance equations for several moments of the size distribution function.
Because the GDE is a nonlinear, partial integrodifferential equation, numerical solutions are usually required. Simple analytical solutions, some approximate, are given for several cases in which two or more processes that modify the size distribution are occurring at the same time. As examples, we consider simultaneous condensation and coagulation, turbulent diffusion and growth, and coagulation with transport to surfaces. Various terms that appear in the GDE such as the collision frequency function and migration...
