Paramecium, a ciliate about across, swims forward at and randomly reorients (an…

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

Many Parts, One Behaviour, Ch Emergence and self-organisation: collective order from local rules

Problem

Paramecium, a ciliate about 50 μm50\,\mu\mathrm m across, swims forward at v=1.0 mm s−1v=1.0\,\mathrm{mm\,s^{-1}} and randomly reorients (an 'avoiding reaction') with a mean interval τ=1.5 s\tau=1.5\,\mathrm s between reorientations; this is treated as three-dimensional run-and-tumble motion. It swims in water at T=293 KT=293\,\mathrm K, viscosity η=1.0 mPa s\eta=1.0\,\mathrm{mPa\,s}. ((a)) Find its effective diffusion coefficient Deff=v2τ/3D_{\rm eff}=v^2\tau/3, in μm2 s−1\mu\mathrm m^2\,\mathrm s^{-1}. ((b)) Find the thermal diffusion coefficient of a sphere of radius a=25 μma=25\,\mu\mathrm m (its own size) in the same fluid, and compare the two by their ratio. Use kB=1.381×10−23 J K−1k_{\rm B}=1.381\times10^{-23}\,\mathrm{J\,K^{-1}}.

Browse the problem library