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The irregular motion of a body arising from the thermal motion of the molecules of the material in which the body is immersed. Such a body will of course suffer many collisions with the molecules, which will impart energy and momentum to it. Because, however, there will be fluctuations in the magnitude and direction of the average momentum transferred, the motion of the body will appear irregular and erratic.
In principle, this motion exists for any foreign body suspended in gases, liquids, or solids. To observe it, one needs first of all a macroscopically visible body; however, the mass of the body cannot be too large. For a large mass, the velocity becomes small. See Kinetic theory of matter
the disorderly motion of small particles (dimensions of several microns or less) suspended in a liquid or gas; takes place under the influence of collisions of molecules of the surrounding medium. It was discovered by R. Brown in 1827. The suspended particles, visible only under a microscope, move independently of each other and describe complex zigzag trajectories. Brownian movement does not diminish with time and does not depend on the chemical properties of the medium. The intensity of Brownian movement increases with the temperature of the medium and with the reduction of its viscosity and the particle size.
A systematic explanation of Brownian movement was given by A. Einstein and M. Smoluchowski in 1905-06 on the basis of kinetic molecular theory. According to this theory, the molecules of a liquid or gas exist in constant thermal movement, and the momenta of various molecules do not have the same magnitude and direction. If the surface of a particle placed in such a medium is small, as is the case for a Brownian particle, then the impacts experienced by the particles—caused by the surrounding molecules—will not be exactly compensated. Consequently, as a result of this “bombardment” by molecules, the Brownian particle falls into disorderly motion, changing the magnitude and direction of its velocity approximately 1014 times per second.
In observation of Brownian movement (see Figure 1), the position of a particle is recorded after equal time intervals. Of course, between observations the particle moves non-rectilinearly, but the connection of the successive positions by straight lines yields an arbitrary picture of the motion.
The principles of Brownian movement serve as graphic confirmation of the fundamental hypotheses of kinetic molecular theory. The general picture of Brownian movement is described by Einstein’s law for the mean square displacement of the particle Δx2 in any direction x. If within the time between two measurements a sufficiently large
number of collisions of the particle with molecules takes place, then Δx2 is proportional to this time τ:
(1) Δx2 = 2Dτ
Here D is the diffusion coefficient, which is determined by the resistance exerted by any medium in which the particle moves. For a specific particle of radius a, it is equal to
(2) D = kT/6πηa
where k is the Boltzmann constant, T is the absolute temperature, and η is the dynamic viscosity of the medium.
The theory of Brownian movement explains the random motion of a particle under the influence of random forces caused by molecules and frictional forces. The random character of the force implies that its action during the time interval τ1 is completely independent of the action during the time interval τ2, unless these intervals overlap. The average force, after a sufficiently large period of time, is equal to zero, and the average displacement Δx of a Brownian particle is also found to be zero.
The conclusions of the theory of Brownian movement agree brilliantly with experiments. Formulas (1) and (2) were corroborated by the measurements of J. Perrin and T. Svedberg (1906). On the basis of these relations, the Boltzmann constant and Avogadro’s number were experimentally determined to be in accordance with their values obtained by other methods.
The theory of Brownian movement has played an important role in the justification of statistical mechanics; it is of practical significance as well. Above all, Brownian movement limits the accuracy of measuring instruments—for example, the limit of accuracy of the readings of a mirror galvanometer is determined by the chatter of the mirror, which is similar to that of a Brownian particle being bombarded by air molecules; the laws of Brownian movement determine the random movement of electrons, which causes the noise in electric circuits; the dielectric losses in dielectrics are explained by the random motions of the molecule-dipoles that make up the dielectric; and the random motion of ions in solutions of electrolytes increases their electrical resistance.
REFERENCESEinstein, A., and M. Smoluchowski. Braunovskoe dvizhenie. Moscow-Leningrad, 1936. (Translated from German; with supplementary articles by Iu. A. Krutkov and B. I. Davydov.)
Feynman, R., R. Leighton, and M. Sands. Feinmanovskie lektsii po fizike, vol. 4. Moscow, 1965. (Translated from English.)