10th International Aerosol Conference September 2 - September 7, 2018 America's Center Convention Complex St. Louis, Missouri, USA
Abstract View
NGDE: A Simple, MATLAB-based Code for Solving the General Dynamic Equation
JAMES CORSON, George Mulholland, Michael Zachariah, University of Maryland
Abstract Number: 884 Working Group: Aerosol Education
Abstract The general dynamic equation governing aerosol particle nucleation, coagulation, and surface growth [1] is taught as part of undergraduate- and graduate-level college courses. This complicated integro-differential equation can only be solved analytically for a small number of special cases, so one must resort to numerical methods to solve the GDE. Unfortunately, the methods used to solve the equation often obscure the underlying physics: for example, moment methods (see e.g. [2]) transform the integro-differential equation into integrals that must be solved numerically for the various moments of the aerosol size distribution, while sectional methods [3-4] require assumptions about the size distribution within each bin. These considerations complicate efforts to understand the physics represented by the GDE.
To address these concerns, Prakash et al. [5] developed a code to solve the GDE using a nodal method, where aerosol particles exist only at discrete size nodes. This method is similar to the sectional method but obviates the need to consider intra-bin processes. Instead, the NGDE code uses a simple size-splitting algorithm – essentially, linear interpolation – to deal with particles that form or grow to sizes between two nodes. The original NGDE code was written in C; recently, we have converted the code to MATLAB. As part of the conversion, we have added several features to improve its function as a teaching tool, including implementation of a dynamic time-step algorithm that improves code stability and speeds up the calculation by orders of magnitude, and a post-processing tool that shows the evolution of the aerosol size distribution with time. We have also imbedded the Bohren Mie Code [6] in the post processing tool to show the evolution of the optical cross sections for the aerosol. Furthermore, because MATLAB is widely used in science and engineering curricula, users can more easily make changes to the code to add additional features or to implement different physics models for the constituent dynamic processes (e.g. substituting a different nucleation model in place of classical homogeneous nucleation theory with the self-consistent correction).
We will demonstrate the features of the NGDE code using sample problems including coagulation of an initially monodisperse aerosol, pure surface growth, and the full GDE for condensation of aluminum vapor. We will also discuss lessons-learned from including the NGDE code as part of an Aerosol Dynamics course at the University of Maryland.
[1] Friedlander, S. K. Smoke, Dust, and Haze: Fundamentals of Aerosol Dynamics. Oxford University Press, New York, 2nd edition, 2000. [2] Barrett, J. and Webb, N. A comparison of some approximate methods for solving the aerosol general dynamic equation. Journal of Aerosol Science, 29(1-2):31–39, 1998. [3] Gelbard, F., Tambour, Y., and Seinfeld, J. H. Sectional representations for simulating aerosol dynamics. Journal of Colloid and Interface Science, 76(2):541–556, 1980. [4] Gelbard, F. and Seinfeld, J. H. Simulation of multicomponent aerosol dynamics. Journal of colloid and Interface Science, 78(2):485–501, 1980. [5] Prakash, A., Bapat, A., and Zachariah, M. A simple numerical algorithm and software for solution of nucleation, surface growth, and coagulation problems. Aerosol Science & Technology, 37(11):892–898, 2003. [6] Bohren, C. F. and Huffman, D. R. Absorption and Scattering of Light by Small Particles. John Wiley & Sons, 1983.