A polystyrene bead of diameter (density ) is suspended in water of viscosity at

PHYSICS · Subjective · Fermi University Physics · Thermal, Statistical & Complex Systems · Biophysics & Medical Physics · Physical foundations of the living cell

Forces, Machines and Signals, Ch Diffusion: friction, capture and the crowded cytoplasm

Problem

A polystyrene bead of diameter 2.0 μm2.0\,\mathrm{\mu m} (density 1050 kg m−31050\,\mathrm{kg\,m^{-3}}) is suspended in water of viscosity η=1.0 mPa s\eta = 1.0\,\mathrm{mPa\,s} at 293 K293\,\mathrm{K}. Using the Langevin equation's crossover time τm=m/ζ\tau_m = m/\zeta, with ζ=6πηa\zeta = 6\pi\eta a quoted for a sphere, find τm\tau_m for this bead.

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