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As part of the mathematical model of the human respiratory system, a submodel is considered for the study of the non-steady airflow with solid particles (suspended particulate matter (PM) / dust particles) and the deposition of particles of various sizes in the human nasal cavity. It is assumed that the nasal cavity is divided by the bone-cartilaginous septum into two symmetrical (relative to the nasal septum) parts; the average geometry of the right part of the human nasal cavity is considered. The inhaled air is considered as a multiphase mixture of homogeneous single-component gas and solid dust particles. The Eulerian-Lagrangian approach to modeling the motion of a multiphase mixture is used: a viscous liquid model is used to describe the motion of the carrier gas phase; the carried phase (dust particles) is modeled as separate inclusions of various sizes. The process of heating the inhaled air due to its contact with the walls is also taken into account. The features of the unsteady flow of a multiphase air mixture with dust particles were obtained using Ansys CFX for several scenarios. It has been noted that when studying the airflow in the nasal cavity, it is necessary to take into account the presence of turbulence, for which it is proposed to use the k-ω model. The velocity fields of inhaled air in the nasal cavity have been obtained; presented temperature distributions in the nasal cavity at different time points; made estimates of air heating at different temperatures of inhaled air; gave estimates of the proportion of deposited particles in the nasal cavity depending on the particle size for real machine-building production; presented trajectories of movement of suspended particles. Thus, it is shown that more than 99.7 % of particles with a diameter of more than 10 microns deposit in the human nasal cavity; as the particle diameter and mass decrease, the proportion of deposited particles decreases. Suspended particles with a size of less than 2.5 microns almost do not deposit in the nasal cavity. They can penetrate deeper into the lower airways and lungs of a person with the inhaled air and, having fibrogenic and toxic effect, can cause diseases. The results obtained are in good agreement with the results of individual studies performed by other scientists. Further development of the model involves studying airflow in the human lungs and modeling the formation of diseases caused by the harmful effects of environmental factors (including dust particles) entering the human body by inhalation.

Mathematical Model of Airflow and Solid Particles Transport in The Human Nasal Cavity