COVID infection pathways include droplets (blue) and aerosols (green, yellow, and red) as schematically represented in...

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COVID infection pathways include droplets (blue) and aerosols (green, yellow, and red) as schematically represented in the image below Both droplets and aerosols travel through the air from the infected person to the susceptible person, but ballistic droplets infect by impact, and aerosols infect by inhalation. A distinguishing feature is the droplet settling time. Key Respirable Aerosol ≤ 5μm Thoracic Aerosol s 10μm Nasopharyngeal Aerosol ≤ 100μm Fomite INDEX CASE Sprayborne Drops EXPOSED CONTACT a) Droplets will descend due to gravity. In the limit of low Reynolds number, derive an equation to estimate their steady state settling velocity V, using Stokes drag on a sphere F = 6лμVR. b) From your answer in part (a), estimate the time to settle from a height of 1.5 m for three drop diameters: 1 µm, 10 μm, and 100 µm. Use interpretable units for your answers. Comment on how sensitive the result is to diameter. c) Check our assumptions by estimating the Reynolds number for each of the three drop diameters. Comment. COVID infection pathways include droplets (blue) and aerosols (green, yellow, and red) as schematically represented in the image below Both droplets and aerosols travel through the air from the infected person to the susceptible person, but ballistic droplets infect by impact, and aerosols infect by inhalation. A distinguishing feature is the droplet settling time. Key Respirable Aerosol ≤ 5μm Thoracic Aerosol s 10μm Nasopharyngeal Aerosol ≤ 100μm Fomite INDEX CASE Sprayborne Drops EXPOSED CONTACT a) Droplets will descend due to gravity. In the limit of low Reynolds number, derive an equation to estimate their steady state settling velocity V, using Stokes drag on a sphere F = 6лμVR. b) From your answer in part (a), estimate the time to settle from a height of 1.5 m for three drop diameters: 1 µm, 10 μm, and 100 µm. Use interpretable units for your answers. Comment on how sensitive the result is to diameter. c) Check our assumptions by estimating the Reynolds number for each of the three drop diameters. Comment.

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Solution a The settling velocity of a droplet can be estimated using Stokes law which states that the force F on a sphere moving through a fluid is given by F 6VR where is the dynamic viscosity of the ... View the full answer