Mathematical modeling of monodisperse nanoparticle concentration in aerosols subject to electric field using the Poisson–Nernst–Planck equation

In recent decades, the study of particulate materials has gained significant attention from the scientific community. This is due to applications that can be developed, among which we can cite the risks to human health and the environment. As a consequence of this concern, classifying nanoparticles is a topic of considerable interest. One of the most used devices to classify nanoparticles in aerosols is the Differential Mobility Analyzer. From a mathematical point of view, particle concentration profiles have been obtained, preferably, considering constitutive relationships. In this contribution, the Poisson–Nernst–Planck equation is used to determine the concentration of monodisperse nanoparticles in aerosols subjected to an electric field. For this purpose, an inverse problem is proposed and solved considering real data and the Differential Evolution algorithm as an optimization tool. The results demonstrate that the proposed methodology was able to obtain good estimates considering the phenomenological model in relation to experimental points, as well as accurate estimates for intermediate profiles considering the Kriging approach. Finally, it is important to mention that the novelty of this contribution lies in predicting the concentration of monodisperse nanoparticles in aerosols subjected to an electric field using the Poisson–Nernst–Planck equation.