Analytical solutions to validate 3D numerical methods for solving direct ultraviolet photoionization and charge recombination of aerosol nanoparticles with laminar flow in circular ducts

• Published in: Journal of applied physics Vol. 128; no. 8
• Main Authors: Fernández-Díaz, Julio M., Palacios, Sergio L., Menéndez-Blanco, Alberto
• Format: Journal Article
• Language: English
• Published: Melville American Institute of Physics 28.08.2020
• Subjects: Applied physics; Charged particles; Dimensional analysis; Ducts; Electric fields; Exact solutions; Laminar flow; Mathematical models; Method of lines; Methods; Nanoparticles; Numerical analysis; Numerical methods; Numerical models; Photoionization; Rarefaction; Three dimensional models
• ISSN: 0021-8979; 1089-7550
• DOI: 10.1063/5.0017098

This work analyzes UV photocharging of aerosol particles in a cylindrical duct and develops analytical solutions to particular cases. A three-dimensional (3D) numerical method is also developed in order to be used as an example of validation. These methods consider diffusion, photoionization, recombination, and advection by both a fluid and an electric field in a three-dimensional space. In the first place, governing equations are developed to clarify misleading equations found in a previous literature. These equations are then used in analytical methods to find solutions for these particular cases: diffusion only, electric field only, electric field plus photoionization, and, finally, electric field plus recombination. An analysis of these solutions shows the existence of shock/rarefaction waves in the evolution of charged particles’ concentration inside the duct, a very interesting phenomenon that cannot be captured using zero-dimensional (0D) numerical models or a dimensional analysis. The numerical method of lines is applied to generate an axisymmetrical 3D numerical model that is validated using the analytical solutions. A good agreement between the numerical and analytical solutions was obtained despite the simplicity of the numerical method. The paper also comments on the advantages of using the presented methods for the prediction of concentration values against the use of non-dimensional parameters in 0D models.