Transfer of respiratory pathogens: Wells curve derivation (ASIDE)

TL;DR

This content explains the mathematical equations and principles behind drop settling and evaporation, including the Wells curve and the effect of diffusion and solutes.

Transcript

PROFESSOR: So now, let me make the first of our technical asides, which you can skip over if you're not interested in the mathematical details or for those of you that have a higher-level, say, upper-level-undergraduate or even graduate-level understanding of transport phenomena and fluid mechanics. I'd like to show you some of the equations that a... Read More

Key Insights

• 💦 The Wells curve provides a graphical representation of the settling time of droplets based on their size, demonstrating that smaller droplets take longer to settle.
• 💦 Settling velocity is influenced by factors such as droplet size, fluid viscosity, and the gravitational force acting on the droplet.
• 💦 Evaporation of droplets is limited by the diffusion of water vapor, with a concentration gradient existing between the droplet surface and the ambient air.

Questions & Answers

Q: How does the Wells curve illustrate the settling of droplets?

The Wells curve shows the relationship between droplet size and settling time, indicating the time it takes for a droplet to settle out of the air based on its size.

Q: What factors determine the settling velocity of a droplet?

The settling velocity depends on the radius of the droplet, gravity, viscosity of the surrounding fluid, and the Stokes drag coefficient.

Q: How is evaporation of droplets affected by diffusion of water vapor?

The evaporation process is limited by the diffusion of water vapor away from the droplet, with a gradient of water vapor concentration existing from the droplet surface to the surrounding air.

Q: What limits the evaporation of biological fluids in respiratory droplets?

In the case of respiratory droplets containing biological fluids, evaporation can be limited by solutes and salts, which can impede the evaporation process and potentially attract more water.

Summary & Key Takeaways

• The Wells curve is derived through the theory of drop settling, showing the relationship between droplet size and settling velocity.

• The settling velocity of a droplet is determined by a force balance between gravitational force and drag force.

• Evaporation of droplets is limited by the diffusion of water vapor away from the droplet, and the process is influenced by factors such as temperature and relative humidity.