A ciliate such as Paramecium 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 ciliate such as Paramecium is roughly a sphere of radius a=60 μma = 60\,\mathrm{\mu m}, swimming at v=1.0 mm s−1v = 1.0\,\mathrm{mm\,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}}), its mass density taken equal to water's. ((a)) Estimate its Reynolds number and say whether it still lies safely 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 if its cilia suddenly stopped beating, and compare that distance with the cell's own size. ((c)) Dissolved oxygen has D=2.0×10−9 m2 s−1D = 2.0\times10^{-9}\,\mathrm{m^2\,s^{-1}}. Estimate the Peclet number Pe=va/D\mathrm{Pe} = va/D for oxygen uptake and say whether swimming is worth it for this cell.

Browse the problem library