Mathematical Model of Emergency Indoor Air Purification by Powder Aerosol

The rapid removal of fine contaminant particles (0.1-5 µm), including bioaerosols, from indoor air remains a critical challenge, particularly in emergency scenarios such as industrial accidents or biological incidents. This study develops a novel mathematical model that integrates the kinetic evolution of an impulse-sprayed powder aerosol (as an example, TiO₂, particle size 5-10 µm) with contaminant-capture efficiency, accounting for Brownian diffusion, inertial impaction, interception, and electrostatic attraction. The model incorporates the triboelectric charge acquired by sorbent particles during pneumatic spraying. Parametric calculations demonstrate that for uncharged particles, capture efficiency in the Greenfield gap is low (η = 0.1-0.3). However, when sorbent particles carry an opposite charge to the contaminants, the efficiency increases to over 0.7, and the characteristic capture time becomes substantially shorter than the gravitational settling time. A model-based criterion for sorption completeness is derived, indicating that, under the specified assumptions, sorbent particles with diameters of 5-7 µm satisfy the criterion at concentrations of approximately 1-2 g/m³. The model provides a theoretical and parametric framework for estimating the required sorbent concentration, capture efficiency, and characteristic purification time under specified room and particle conditions. The results can support the preliminary design of rapidly deployable emergency air-cleaning systems.