Brownian motion

A small particle in a liquid or gas is struck continually by molecules moving because of thermal energy. The impacts arrive from all directions, but at any instant their forces do not balance perfectly. The resulting small, unpredictable changes of momentum produce the particle’s jittery path. This is not caused by the suspended particle being alive, nor is it the same as bulk fluid flow. The details of observed motion depend on factors such as particle size, temperature and the fluid’s viscosity.

In 1827, botanist Robert Brown described the irregular motion of microscopic particles associated with pollen suspended in water. He also observed similar movement in nonliving material, showing that the phenomenon was not limited to living pollen. In 1905, Albert Einstein developed a quantitative account relating the visible motion of suspended particles to the molecular theory of matter. Jean Perrin’s experimental work later tested predictions of the theory and helped establish the physical reality of atoms and molecules.

In the idealized model of Brownian motion, successive random displacements accumulate over time. For a particle undergoing ordinary diffusion in one dimension, the mean squared displacement grows in proportion to elapsed time; in several dimensions, the total mean squared displacement scales with the number of dimensions. These statistical properties describe ensembles or repeated observations, not a forecast of one particle’s exact path. The model has become a foundation for stochastic calculus and is used in physical and mathematical models of systems subject to random fluctuations.

The classic physical example concerns a particle much larger than the molecules of the surrounding fluid, with its observed motion emerging from molecular impacts. Brownian motion is also used as a mathematical model well beyond colloids, but a successful mathematical analogy does not mean that every random process has the same physical cause. Real particles can experience fluid inertia, boundaries, interactions with nearby particles and other effects that are absent from the simplest ideal model.