Brownian Motion

(0.5,1.1, and 1.9 polystyrene particles in water, from Exploring Squishy Mterials at Emory University)

Robert Brown, Phil. Mag. 4, 171 (1828)

• Irregular motions of small grains in water were observed soon after advent of microscopes.
• Early microscopy observations were interpreted as motions of living creatures.
• Brown showed that inorganic grains in suspension show similiar irregular motion.

  Exploring Squishy Mterials at Emory University (Brownian Motion Movies - offline)

A. Einstein, Ann. d. Physik 17, 549 (1905)

• "Investigations on the theory of the Brownian Movement:"
• The large particle performs random motion as a result of collisoins with smaller (unseen) particles.
• A plethora of Java Applets to demostrate this:
• Michael Fowler Physics Applets (Virginia) (offline)
• Sturm/Dolgert (UCSB) (offline)
• Wolfgang Christian (Davidson)
• Mai Zhou (Kentucky)

   Langevin (C.R. Acad. Sci 146 530, 1908) equation for the particle:

• For a sphere of radius  a , in a fluid of viscosity  η  , the mobility is given by  μ=1/(6πηa)
• The stochastic force is uncorrelated at different times, <f(t) f(t')>∝δ(t-t')D  ,

   where  D  is the diffusion coefficient.

• To ensure the correct Maxwell-Boltzmann distribution at a temperature  T ,

   

  mobility and diffusion must be related by

   Jean Baptiste Perrin was awarded the 1926 Nobe Prize (lecture, offline) for expeimental verification (1905-12)

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