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## Q. 12.2

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 tube.

## Verified Solution

$\tau = m/6\pi \nu \rho _{a} r=2r^{2} \rho_{p} /9v \rho _{a}$,

i. $\tau = 2\times (10\times 10^{-6} )^{2} \times 1 \times 10^{6} /(9\times 15\times 10^{-6} \times 1.2\times 10^{3} ) = 1.23 \times 10^{-3} \; s$.

$S= \tau V_{0} = 1.23\times 10^{-3} \times 2.0=2.5\; mm$. Hence the probability of deposition from turbulent flow in a bronchus of diameter 4 mm would be high.

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