# Brownian motion

## Description of the brownian motion

Updated November 06, 2013

Robert Brown (1773 - 1858) botanist of the 19th century, friend of Charles Darwin (1809 - 1882), had already discovered in 1827 with a microscope that plant cells had a nucleus. But it is by looking in the fluid located inside the pollen grains, that he observes very small particles in erratic movements going in all directions for no apparent reason. It reminds him of the vital principle, that is to say the cause which produces all the phenomena of life. It is therefore not surprising, pollen is a plant that contains life, and therefore it is normal for it to move.
But Robert Brown repeats the experiment with grains of pebbles, grains of metal and even grains of the stone of the Giza sphinx. He observes on these inert grains jerky, incessant movements, identical to those of the pollen grains.
In 70 years many physicists have repeated the experiment with more efficient microscopes, removing all measurement biases (air currents in the room, currents in the water in which the pollen grains are immersed, vibrations, disturbance by light, etc.) but none finds an explanation because the existence of molecules, were not discovered.
So how is it that these pollen grains are agitated?

It is Albert Einstein (1879 - 1955) who will find the reason for this agitation. Einstein explains this Brownian movement by the molecular and atomic hypothesis and calculates the size of the molecules.
This incessant movement of the grain, called "Brownian movement", is due to the very existence of the atoms. The Brownian particle is constantly shaken by the atoms of water.
The speed and position of the particle is subjected to a friction force depending on the viscosity of the bath and the square root of time.
This amount was calculated by Einstein (1905) :
D = RT/6πηaΝ
R = ideal gas constant (this number is 8)
T temperature
π = 3.141 592 653
η = viscosity of the fluid
a = diameter of the grain
Ν = 6,022 140 76 × 1023 mol−1 (number of Avogadro)
1/Ν is the mass of the hydrogen atom since there are Ν hydrogen atoms in 1 gram.
It is the first great formula which mixes the microscopic world with the macroscopic world.
Among all these values there is an immense number, the number of Avogadro and it is he who brings up the atomic structure of matter.
Pollen in water is continuously subjected to friction and disorderly movements explained by the presence of atoms in water molecules.
Brownian motion is universal, like the Gaussian curve.

## Brownian motion according Einstein

According to Einstein, molecules derive their kinetic energy from heat. Particle movement and temperature are linked.
The temperature causes a disordered movement of the particles.
The 1905 article provides theoretical proof of the existence of atoms and molecules.
These are the works of Jean Baptiste Perrin (1870 - 1942) who in 1908 will verify Einstein's predictions.
Atoms have only been "visible" since the 1980s, thanks to electronic telescopes.

NB: The Brownian movement was first described in 1827 by the botanist Robert Brown, by observing the movements of the pollen grains of Clarkia pulchella (a species of North American wildflower).
Brownian motion or Wiener's process is a mathematical description of the random motion of a "big" particle immersed in a fluid and which is not subjected to any other interaction, than shocks with the "small" molecules of the surrounding fluid. The result is a disorderly movement of the large particle.

### Image: Brownian motion of a particle.

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