An Introduction to Brownian Motion

Brownian motion is the random movement of particles in a fluid due to their collisions with other atoms or molecules. Brownian motion is also known as pedesis, which comes from the Greek word for "leaping." Even though a particle may be large compared to the size of atoms and molecules in the surrounding medium, it can be moved by the impact with many tiny, fast-moving masses. Brownian motion may be considered a macroscopic (visible) picture of a particle influenced by many microscopic random effects.

Brownian motion takes its name from the Scottish botanist Robert Brown, who observed pollen grains moving randomly in water. He described the motion in 1827 but was unable to explain it. While pedesis takes its name from Brown, he was not the first person to describe it. The Roman poet Lucretius describes the motion of dust particles around the year 60 B.C., which he used as evidence of atoms.

The transport phenomenon remained unexplained until 1905 when Albert Einstein published a paper that explained the pollen was being moved by the water molecules in the liquid. As with Lucretius, Einstein's explanation served as indirect evidence of the existence of atoms and molecules. At the turn of the 20th century, the existence of such tiny units of matter was only a theory. In 1908, Jean Perrin experimentally verified Einstein's hypothesis, which earned Perrin the 1926 Nobel Prize in Physics "for his work on the discontinuous structure of matter."

The mathematical description of Brownian motion is a relatively simple probability calculation, of importance not just in physics and chemistry, but also to describe other statistical phenomena. The first person to propose a mathematical model for Brownian motion was Thorvald N. Thiele in a paper on the least squares method that was published in 1880. A modern model is the Wiener process, named in honor of Norbert Wiener, who described the function of a continuous-time stochastic process. Brownian motion is considered a Gaussian process and a Markov process with continuous path occurring over continuous time.

What Is Brownian Motion?

Because the movements of atoms and molecules in a liquid and gas is random, over time, larger particles will disperse evenly throughout the medium. If there are two adjacent regions of matter and region A contains twice as many particles as region B, the probability that a particle will leave region A to enter region B is twice as high as the probability a particle will leave region B to enter A. Diffusion, the movement of particles from a region of higher to lower concentration, can be considered a macroscopic example of Brownian motion.

Any factor that affects the movement of particles in a fluid impacts the rate of Brownian motion. For example, increased temperature, increased number of particles, small particle size, and low viscosity increase the rate of motion.

Brownian Motion Examples

Most examples of Brownian motion are transport processes that are affected by larger currents, yet also exhibit pedesis.

Examples include:

• The motion of pollen grains on still water
• Movement of dust motes in a room (although largely affected by air currents)
• Diffusion of pollutants in the air
• Diffusion of calcium through bones
• Movement of "holes" of electrical charge in semiconductors

Importance of Brownian Motion

The initial importance of defining and describing Brownian motion was that it supported the modern atomic theory.

Today, the mathematical models that describe Brownian motion are used in math, economics, engineering, physics, biology, chemistry, and a host of other disciplines.

Brownian Motion Versus Motility

It can be difficult to distinguish between a movement due to Brownian motion and movement due to other effects. In biology, for example, an observer needs to be able to tell whether a specimen is moving because it is motile (capable of movement on its own, perhaps due to cilia or flagella) or because it is subject to Brownian motion. Usually, it's possible to differentiate between the processes because Brownian motion appears jerky, random, or like a vibration. True motility appears often as a path, or else the motion is twisting or turning in a specific direction. In microbiology, motility can be confirmed if a sample inoculated in a semisolid medium migrates away from a stab line.

Source

"Jean Baptiste Perrin — Facts." NobelPrize.org, Nobel Media AB 2019, July 6, 2019.