Three-Dimensional Numerical Study of a Fluid-Kinetic Model for Respiratory Aerosols with Variable Size and Temperature

Abstract

In this paper, we extend to the three-dimensional case the numerical study previously performed in a two-dimensional framework for a complex coupled fluid-kinetic model describing respiratory aerosols. The specificity of this model lies in the fact that it takes into account the airway humidity and the resulting hygroscopic effects on the aerosol droplets, namely their size variation. The air is described through a system of partial differential equations: the incompressible Navier–Stokes equations for the air velocity, convection-diffusion equations on its temperature, and water vapor mass fraction. The aerosol distribution function obeys a Vlasov-type equation and depends on the standard kinetic variables, but also on radius and temperature variables. After discussing again the implementation strategy, we perform numerical experiments, mainly in a branched structure looking like the trachea and the first lung generation. This allows the presentation of various statistics on the aerosol behavior in terms of particle deposition, temperature, and size variation of the droplets. We observe that the outcome appears coherent with the two-dimensional case. Finally, we discuss several assumptions which may lead to model simplifications, such as the fact that the water vapor mass fraction in the air may be considered to be constant throughout the branched structure in standard breathing conditions.

Keywords:

• Fluid-kinetic models
• numerical simulation
• hygroscopic effects
• particle deposition

Acknowledgments

The authors want to thank Dr. Bérénice Grec and Prof. Sébastien Martin, from MAP5 at Université de Paris, for their input on the model and the computational aspects, as well as for their fruitful remarks on this work.

The first author wants to thank Dr. Laurent Vecellio, PST Director at Université de Tours and Prof. Stephan Ehrmann from CHRU Tours, as well as Prof. Céline Grandmont, from INRIA Paris and LJLL, for the various discussions they shared on the topic of aerosol size variation.

Notes

1 Note that we had to use version 3.43 as opposed to version 4.4.2 which is currently available because the function convect did not seem to properly behave in three dimensions.