Brownian motion, (Braunian motion), the disorderly motion of small particles suspended in a liquid or a gas, which takes place under the impacts of the molecules of the surrounding medium. It was studied in 1827 by the English scientist R. Brown, who observed through a microscope the motion of pollen suspended in water. The particles observed, of a size of ≈10-6 m and less, make disordered, independent movements, tracing out complicated zigzag paths. The intensity of Brownian motion does not depend on time, but increases as the temperature of the medium rises and as its viscosity and the size of the particles decrease (irrespective of their chemical nature). A complete theory of Brownian motion was given in 1905—06 by A. Einstein and the Polish physicist M. Smoluchowski.
The cause of Brownian motion is the thermal motion of the molecules of the medium and the absence of exact compensation of the impacts that the particle receives from the molecules surrounding it, that is, Brownian motion is due to fluctuations of pressure. The impacts of the molecules of the medium set the particle in disorderly motion: its velocity changes rapidly in magnitude and in direction. If the position of the particle is recorded at short equal intervals of time, the path constructed in this way turns out to be extremely complicated and tangled (Fig. ).
The Brownian motion of three different gamboge particles in water (after Perrin). The dots mark the positions of the particles at intervals of 30 s. The radius of the particles is 0.52·10-6 m, the distance between the divisions of the grid is 3.4·10-6 m.
Brownian motion is the most graphic experimental confirmation of the picture, given by the molecular-kinetic theory, of the chaotic thermal motion of atoms and molecules. If the interval of observation τ is long enough for the forces exerted on the particle by the molecules of the medium to change their direction many times, then the mean square of the projection Δx2 of its displacement on any axis (in the absence of other external forces) is proportional to the time τ (Einstein's law):
where D is the diffusion coefficient. For spherical particles of radius a it is D = kT/6πηa, where η is the dynamic viscosity of the medium. In deriving Einstein's law it is assumed that displacements of the particle in any direction are equally probable and that for large τ the inertia of the Brownian particle can be neglected in comparison with the effect of the friction forces. The relations for Δx2 and D were confirmed experimentally by the measurements of the French physicist J. Perrin and the Swedish physicist T. Svedberg. The Boltzmann constant and the Avogadro constant were determined experimentally from these measurements.
Besides translational Brownian motion there is also rotational Brownian motion — the disorderly rotation of a Brownian particle under the impacts of the molecules of the medium. For rotational Brownian motion the mean square angular displacement of the particle φ2 is proportional to the time of observation τ:
where the diffusion coefficient of rotational Brownian motion for a spherical particle is Drot=kT/8πηa3. Relation (2) was also confirmed by Perrin's experiments.
The theory of Brownian motion is applied in the physical chemistry of disperse systems; the kinetic theory of the coagulation of solutions (Smoluchowski, 1916) and the theory of sedimentation equilibrium (the equilibrium of disperse systems in a gravitational field or in a field of centrifugal force) are based on it. In metrology Brownian motion is regarded as the main factor that limits the accuracy of sensitive measuring instruments. The limit of measurement accuracy is reached when the fluctuational (Brownian) displacements of the moving parts of the instrument become, in order of magnitude, equal to the displacement caused by the effect being measured.