A sea urchin sperm cell swims at through seawater of viscosity and density ; its…

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

Forces, Machines and Signals, Ch Numbers and noise in a small system

Problem

A sea urchin sperm cell swims at

v = 200\,\mathrm{\mu m\,s^{-1}}

through seawater of viscosity

\eta = 1.0\times10^{-3}\,\mathrm{Pa\,s}

and density

\rho = 1.0\times10^3\,\mathrm{kg\,m^{-3}}

; its head-plus-flagellum forms a swimming body of characteristic length

L = 40\,\mathrm{\mu m}

. It swims up a gradient of a small chemoattractant peptide of diffusion coefficient

D = 2.0\times10^{-10}\,\mathrm{m^2\,s^{-1}}

. Recall the definitions

\mathrm{Re}=\rho v L/\eta

and

\mathrm{Pe}=vL/D

. ((a)) Evaluate

\mathrm{Re}

for this sperm cell and state what its size tells you about whether inertia matters for its motion. ((b)) Evaluate

\mathrm{Pe}

for the chemoattractant and state whether, over the length

L

, the sperm cell's own swimming or the peptide's diffusion dominates the transport of the peptide past it.