Brownian motion was identified by Robert Brown in 1827 after looking at the jittery movement of pollen on water. It can be defined as the apparent random motion of particles suspended on a fluid. The term is often associated with the 'random walk' phenomenon.
Graphical representation of three dimensional Brownian motion.
Brownian motion, and the mathematical models that describe it, have been used for over a century to describe a multitude of phenomena. For example, Einstein used Brownian motion to describe both the existence of atoms, and the kinetic model of thermal equilibrium. Among other things, economists have been using Brownian motion since the early 20th century to model the stock market. For a study of the diffusion of brownian spheres, see Hydrodynamic Coupling of two brownian spheres to a planar survace.
In biology, Brownian motion can be the driving force behind supramolecular ratchets. The principle of operation is that polymerizing filaments can push on an object. When this object's position fluctuates due to Brownian motion, polymer subunits can attach to the growing filament, biasing the movement of the object in a certain direction. These filaments are cross-linked into a gel which provides the force for movement.
1. Einstein, A. "On the Movement of Small Particles Suspended in Stationary Liquids Required by the Molecular-Kinetic Theory of Heat", Annalen der Physik, 17, 1905, 549-560
Keyword in references:
Mechanoelectrical transduction assisted by Brownian motion: a role for noise in the auditory system
Brownian Dynamics of a Sphere Between Parallel Walls
Hydrodynamic Coupling of Two Brownian Spheres to a Planar Surface, E. R. Dufresne, T. M. Squires, M. P. Brenner and D. G. Grier, Phys. Rev. Lett,85, 3317 (2000).
Measuring Translational, rotational, and vibrational dynamics with digital holographic microscopy, J Fung, K Martin, R Perry, D Kaz, R McGorty, and V Manoharan. Optics Express. Vol. 19, No 9. (2011)
On The Movement of Small Particles Suspended in Stationary Liquids Required By The Molecular-Kinetic Theory of Heat
Single-particle Brownian dynamics for characterizing the rheology of fluid Langmuir monolayers
The Elementary Theory of the Brownian Motion
Like Charge Attraction through Hydrodynamic Interaction
Noise underlies switching behavior of the bacterial flagellum
The force-velocity relationship for the actin-based motility of Listeria-Monocytogenes
Gravitational stability of suspensions of attractive colloidal particles
Physiological and pathological population dynamics of circulating human red blood cells
Motility powered by supramolecular springs and ratchets
Rise of the Source-Sink Model
Single molecule statistics and the polynucleotide unzipping transition
Minimal model for kinetic arrest
New directions in mechanics
Patterned Colloidal Coating Using Adhesive Emulsions
Optical Measurements of Frequency-Dependent Linear Viscoelastic Moduli of Complex Fluids
Elasticity of Compressed Emulsions
Janus Microgels Produced from Functional Precursor Polymers
Perturbation Spreading in Many-Particle Systems: A Random Walk Approach
Dealing with mechanics: mechanisms of force transduction in cells
Actin Filament Length Tunes Elasticity of Flexibly Cross-Linked Actin Networks
Nanomechanics of vimentin intermediate filament networks
Surface roughness directed self-assembly of patchy particles into colloidal micelles
Does size matter? Elasticity of compressed suspensions of colloidal- and granular-scale microgels
Origin of de-swelling and dynamics of dense ionic microgel suspensions