ORCID

0009-0008-9474-4831

Subject Area

Mathematics, Applied

Abstract

We investigate trajectories of microscale evaporating droplets in a stagnation point flow near a wall of a respiratory airway. The configuration is motivated by the problem of advection and deposition of microscale droplets of respiratory fluids in human airways during transmission of infectious diseases such as tuberculosis and COVID-19. Laminar boundary layer equations are solved to describe the air flow while the equations of motion of the droplet include contributions from gravity, aerodynamic drag, and Saffman force. Evaporation is accounted for at both the droplet surface and the wall of the respiratory airway and is shown to delay droplet deposition as compared to the predictions of isothermal models. Evaporation at the airway wall has a stronger effect on droplet trajectories than evaporation at the droplet surface, leading to droplets being advected away by the flow and thus avoiding deposition in the stagnation point flow region.

The model was expanded to account for the simultaneous transport of vapor concentrations produced by evaporation at both the droplet surface and the airway walls. A concentration boundary layer formulation was then used to couple this concentration field to the flow field in order to investigate how the presence of humidity and concentration gradients affect the rate of droplet evaporation, droplet trajectory, and deposition pattern. Results indicated that as a result of evaporation droplet sizes decrease and their inertia decreases and therefore they move toward areas of high vapor concentration which occur closer to the airway walls. Finally, the effect of an unsteady stagnation point flow was examined using time dependent similarity formulations. Unsteady velocity and concentration fields were found to be different than steady state velocity and concentration fields. These differences affected droplet trajectories, evaporation rates, and the location of where the droplets deposited compared to steady state conditions.

Degree Date

Summer 8-4-2026

Document Type

Dissertation

Degree Name

Ph.D.

Department

Mathematics

Advisor

Vladimir Ajaev

Second Advisor

Andrea Barreiro

Third Advisor

Sheng Xu

Fourth Advisor

David A. Willis

Number of Pages

93

Format

.pdf

Creative Commons License

Creative Commons Attribution-Noncommercial 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License

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