A swimming alga such as Chlamydomonas is roughly a sphere of radius

PHYSICS · Multi-part · Fermi University Physics · Biophysics & Medical Physics · Physical foundations of the living cell · Physical foundations of the living cell

Forces, Machines and Signals, Ch Life at low Reynolds number

Problem

A swimming alga such as Chlamydomonas is roughly a sphere of radius a=5 μma = 5\,\mathrm{\mu m}, swimming at v=100 μm s−1v = 100\,\mathrm{\mu m\,s^{-1}} in water (η=1.0×10−3 Pa s\eta = 1.0\times10^{-3}\,\mathrm{Pa\,s}, ρ=1.0×103 kg m−3\rho = 1.0\times10^{3}\,\mathrm{kg\,m^{-3}}). Treat the cell's mass density as that of water, since a cell is mostly water. ((a)) Estimate the Reynolds number of this swimmer and say whether it is in the Stokes limit. ((b)) Estimate the stopping time τm=2ρa2/9η\tau_m = 2\rho a^2/9\eta and the coasting distance vτmv\tau_m after the flagella stop beating. ((c)) A small metabolite has diffusion coefficient D=1.0×10−9 m2 s−1D = 1.0\times10^{-9}\,\mathrm{m^2\,s^{-1}} in water. Estimate the Peclet number Pe=va/D\mathrm{Pe} = va/D for nutrient capture by this alga and say, in words, whether swimming meaningfully increases its uptake compared with diffusion alone.

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