Título: Mathematical Modeling of Monodisperse Nanoparticle Concentration in Aerosols Subject to Electric Field using the Poisson–Nernst–Planck Equation
Autores: LOBATO, F. S.; DAMASCENO, J. J. R.; AROUCA, F. O.
Revista: Ciência e Natura, 47, 1-26, 2025.
Resumo: In recent decades, the study of particulate materials has gained significant attention from the scientificcommunity. This is due to applications that can be developed, among which we can cite the risks tohuman health and the environment. As a consequence of this concern, classifying nanoparticles is atopic of considerable interest. One of the most used devices to classify nanoparticles in aerosols is theDifferential Mobility Analyzer. From a mathematical point of view, particle concentration profiles havebeen obtained, preferably, considering constitutive relationships. In this contribution, thePoisson–Nernst–Planck equation is used to determine the concentration of monodisperse nanoparticlesin aerosols subjected to an electric field. For this purpose, an inverse problem is proposed and solvedconsidering real data and the Differential Evolution algorithm as an optimization tool. The resultsdemonstrate that the proposed methodology was able to obtain good estimates considering thephenomenological model in relation to experimental points, as well as accurate estimates forintermediate profiles considering the Kriging approach. Finally, it is important to mention that thenovelty of this contribution lies in predicting the concentration of monodisperse nanoparticles inaerosols subjected to an electric field using the Poisson–Nernst–Planck equation.

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