Mathematical Model of Dust Particle Dispersion Based on Air Temperature And Humidity

This article addresses the dispersion of dust particles influenced by temperature and humidity using an extended advection-diffusion model. Dust particles suspended in the air pose significant risks to public health and the environment, especially in industrial or densely populated urban areas. The proposed model incorporates temperature- and humidity-dependent velocity and diffusion coefficients, along with a source term that captures emission or absorption processes. By applying standard partial differential equation theory and well-known numerical methods, the model is shown to be well-posed under reasonable assumptions. Simulations demonstrate that higher temperatures tend to accelerate dust transport, while increased humidity can slow the diffusive spreading or promote particle aggregation. Although real-world scenarios often involve more complex, nonlinear interactions, these findings provide a foundational understanding that can be refined through experimental validation. Future research aims to incorporate gravitational settling, turbulence, and more detailed particle characteristics, ultimately supporting the design of air pollution mitigation strategies and ventilation systems.