Introduction to Physics I

For Biologists, Geoscientists, & Pharmaceutical Scientists

L14, 03.11.2017

Bernouilli equation

Tipler

wing and lift

Tipler

viscous fluid

Tipler

viscous fluid

Trautwein

turbulent flow

Biological systems & Reynolds nb

dynamical systems in aqueous environment at 310K constituted by small-size components

Stochastic (Brownian)FB 2/~ 10-9N

: viscosity, 10-3 Ns/m2

: density, 103 kg/m3

Friction (Stokes)FS=6pav ~ 10-12N

for a 1mm particle moving at 50mm/s

essentially no inertial forces

Living systems

• hydrodynamically speaking, we deal with fluids at low Reynolds number (Purcell, 1976)

R vL/

~1 g/cm3, ~1 g/(cm·s)

fish v ~ 1 m/s, L ~ 10 cm R ~ 105

(accelerates water to propel itself)

bacteria v ~ 10 mm/s, L ~ 1 mm R ~ 10-5

(uses viscous shear to move)

Living systems

Living systems

bacteria thus know nothing about inertia

what’s the distance it can coast when it stops swimming ?

m(-dv/dt)=6pav v(t)=v(0)·e-t/t

with t=2a2/9 ~ 2·10-7 s

the bacteria thus stops in about a micro-second coasting a distance v(0)·t ~ 0.04 Å (using v(0)=20 mm/s).

Further reading• E. M. Purcell, Life at low Reynolds number

Am. J. Phys. 45, 3 (1977)• H. C. Berg, Motile Behavior of Bacteria

Physics Today, January (2000)

So bacteria swimming in water is like us swimming in honey

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