A bacterium with a diameter of 5 microns is able to generate a maximum force of 1000 pN. How fast will it swim in water at 293K where viscosity = 1*10^-3 kg/ms?
Stokes:
\(
Drag coefficient = 6 \pi \eta R = 4.7E-8 kg/s
\)
\(
v_{drift} = \frac{f}{Drag coefficient} = \frac{1000E-12 N}{4.7E-8 kg/s} = 2.1 cm/s\)
All too fast, isn't it?
Calculate how far the same bacteria will travel in 1s due to Brownian motion.
\(D=\frac{k_BT}{Drag coefficient}=8.7E-14 m^2/s\)
\(
sqrt{<x^2>}=sqrt{2Dt} = 418 nm
\)
Stokes:
\(
Drag coefficient = 6 \pi \eta R = 4.7E-8 kg/s
\)
\(
v_{drift} = \frac{f}{Drag coefficient} = \frac{1000E-12 N}{4.7E-8 kg/s} = 2.1 cm/s\)
All too fast, isn't it?
Calculate how far the same bacteria will travel in 1s due to Brownian motion.
\(D=\frac{k_BT}{Drag coefficient}=8.7E-14 m^2/s\)
\(
sqrt{<x^2>}=sqrt{2Dt} = 418 nm
\)
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