Find the relaxation times and stopping distances of spores of 10 µm radius and aerosol particles of 0.5 µm radius in a gas moving at 2 m s^−1. Hence confirm that the spores would be deposited rapidly to the walls of a bronchus 4 mm diameter while the aerosol would penetrate effectively along the

Question

Find the relaxation times and stopping distances of spores of 10 µm radius and aerosol particles of 0.5 µm radius in a gas moving at 2 m [latex]s^{−1}[/latex]. Hence confirm that the spores would be deposited rapidly to the walls of a bronchus 4 mm diameter while the aerosol would penetrate effectively along the tube.

Accepted Answer

[latex] au = m/6\pi u ho _{a} r=2r^{2} ho_{p} /9v ho _{a} [/latex],

i. [latex] au = 2 imes (10 imes 10^{-6} )^{2} imes 1 imes 10^{6} /(9 imes 15 imes 10^{-6} imes 1.2 imes 10^{3} ) = 1.23 imes 10^{-3} \; s [/latex].

[latex] S= au V_{0} = 1.23 imes 10^{-3} imes 2.0=2.5\; mm [/latex]. Hence the probability of deposition from turbulent flow in a bronchus of diameter 4 mm would be high.

ii. τ = 3 × [latex]10^{−6}[/latex] s, and S = 6 µm. The probability of deposition would be low.

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