NGDE: Software for Solution of Nucleation, Surface Growth and Coagulation Problems

A. Prakash, A. P. Bapat, and M. R. Zachariah

Departments of Mechanical Engineering and Chemistry, University of Maryland

Abstract: We have developed a simple numerical method to solve the General Dynamic Equation (GDE) and the software made available. The model solution described is suitable for problems involving gas to particle conversion due to supersaturation, coagulation, and surface growth of particles via evaporation or condensation of monomers. The model is based on simplifying the sectional approach to discretizing the particle size distribution with a nodal form. The GDE developed here is an extension of the coagulation equation solution method developed by Kari Lehtinen (Lehtinen and Zachariah, 2001) wherein particles exist only at nodes, as opposed to continuous bins in the sectional method. The results have been tested by comparison where simple analytical solutions are available, and are shown to be in excellent agreement. By example we apply the model to the formation and growth of Aluminum particles. The important features of the model is that it is simple to comprehend, the software which we call Nodal-GDE Solver (NGDE) is relatively compact, and the code is well documented internally, so that users may apply it to their specific needs or make modifications as required. The software is being distributed as freeware, with the request and expectation that attribution be provided for work performed using the code.

A. Prakash, A. P. Bapat, and M. R. Zachariah

Departments of Mechanical Engineering and Chemistry, University of Maryland

Abstract: We have developed a simple numerical method to solve the General Dynamic Equation (GDE) and the software made available. The model solution described is suitable for problems involving gas to particle conversion due to supersaturation, coagulation, and surface growth of particles via evaporation or condensation of monomers. The model is based on simplifying the sectional approach to discretizing the particle size distribution with a nodal form. The GDE developed here is an extension of the coagulation equation solution method developed by Kari Lehtinen (Lehtinen and Zachariah, 2001) wherein particles exist only at nodes, as opposed to continuous bins in the sectional method. The results have been tested by comparison where simple analytical solutions are available, and are shown to be in excellent agreement. By example we apply the model to the formation and growth of Aluminum particles. The important features of the model is that it is simple to comprehend, the software which we call Nodal-GDE Solver (NGDE) is relatively compact, and the code is well documented internally, so that users may apply it to their specific needs or make modifications as required. The software is being distributed as freeware, with the request and expectation that attribution be provided for work performed using the code.

*Download files below.*Paper Describing Theory## NGDE CODE

The numerical algorithm has been implemented in C. The example problem is specific for a growth of aluminum aerosol by the evaporation-condensation method, however, the software is designed to allow the user to apply it to other systems where property data such as saturation vapor pressures and surface tension are known. The program code performs four main types of calculations:

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- Pure coagulation
- Coupled nucleation and coagulation
- Pure surface growth
- Unified GDE containing all of the above

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