A brief History of Brownian Motion

• Jan Ingenhousz 1785 (1st to record an observation?).
• Robert Brown 1828 (1st to study systematically and publish).
• Various explanations and experiments:
  • Regnault 1858 (irregular heating by light?).
  • Weiner 1863 (not temperature differences or evaporation).
  • Cantoni and Oehl 1865 (persistence for over a year).
  • S. Exner 1867 (more rapid with smaller particles).
  • Jevons 1870 (electrical forces?).
  • Dancer 1870 (not electrical forces).
  • Delsaux 1877 (1st to say motion is from molecular bombardment).
  • Gouy 1888 (motion is more lively in less viscous liquid, illumination nor e.m. field has an effect, first experimental work).
  • Ramsay 1892 (not electrical, pressure differences?).
  • Maede Bache 1894 (confirmation of Gouy).
  • Quincke 1898 (temperature fluctuations?).
  • F. M. Exner 1900 (not temperature fluctuations, particle size and temperature dependence).
  • Louis Bachelier 1900 (correct mathematical theory in doctoral dissertation 'Theory of Speculation').
• A. Einstein 1905.
• Various explanations and experiments:
• Smoluchowski 1905 (similar results as Einstein using different methods).
• de Broglie et. al. 1908 (makes a movie from still photos at 1/20 sec. intervals).
• J. Perrin 1921 (Les Atoms) Nobel prize in 1926:
• Starts with the law of definite proportions and collects all known arguments in favor of the existence of atoms. A real tour de force.

Perrin's experiments

• Observations under a microscope, both horizontal and vertical orientations.
• Preparation of gamboge grains of various sizes.
• Measurement of grain size and mass by three techniques (direct camera measurments, weight, Stokes' law).
  

In the following:

• N_A is Avogadro's number.
• g is the acceleration of gravity.
• R is the ideal gas constant.
• T is the absolute temperature.
• a is the radius of the particles.
• is the viscosity of the liquid.

1. Vertical distribution in emulsions (balance between Brownian motion and gravity)

Here n is the concentration of particles, n_o is the concentration at hight h, m the mass of the particles, d the density of the liquid, D the density of the material of the particles.

Experimental value of Avogadro's number is determined to be 68.2 x 10²².

2. Direct random walk displacement measurements (Einstein)

Here x is the the projection of the horizontal displacement along an arbitrary axis in time t.

Experimental value of Avogadro's number is determined to be 64 x 10²².

3. Brownian rotation (Einstein)

Here A is the change in the angle of rotation in time t.

Experimental value of Avogadro's number is determined to be 65 x 10²².

4. Diffusion (Einstein)

Here D is the diffusion coefficient.

Experimental value of Avogadro's number is determined to be 69 x 10²².

Perrin's summary in 1923:

• Brownian motion has now been investigated by Perrin or others under various conditions:
  • Temperature variations.
  • Light intensity variations.
  • Light color variations.
  • Disturbances due to local mechanical vibrations.
  • In other fluids (acids, bases, salts).
  • In fluids with other viscosities (glycerin, gases).
  • Water droplets on soap films.
  • Over periods of days, weeks years and in quartz inclusions (i.e. 1000's of years).
  • With various size particles (0.2 microns up to 5.5 microns) of various materials (pollen, mastic, gamboge).
• Brownian motion is truly random, eternal, spontaneous; an essential property of fluids in equilibrium.
• Brownian motion breaks the 2nd law of thermodynamics ('Carnot's Principle') on a microscopic scale (Perrin anticipates Feynman's thermal ratchet problem).
• Agreement of various methods of calculating Avogadro's number, N_A is proof of the atomic theory.

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