Brownian motion is the random movement of particles in a gas or liquid caused by the unequal bombardment of other molecules in the medium. In 1827, Robert Brown first noticed that a pollen grain suspended in water was moving in a random pattern. Later in 1905, Albert Einstein derived a quantitative expression for Brownian motion using the kinetic theory of molecules.

Here’s how Brownian motion works: Let us say that a ping pong ball inside a container represents the particles of a liquid. According to the kinetic theory of molecules, atoms are constantly in motion, which leads to collisions and causes random movements. So, when you have another larger particle in the liquid, like a red ball, you can see that it jiggles randomly due to the other ping pong balls. Therefore, the red ball represents a particle that is undergoing Brownian motion.

Using statistical analysis and empirical evidence, Einstein derived that the displacement x, the shortest distance from the initial to final position of particle, of a Brownian particle is equal to the square root of 2Dt, where t is time and D is the diffusion constant that is determined by the Stokes-Einstein formula and depends primarily on viscosity and temperature of a fluid. A greater diffusion constant means that the displacement of a Brownian particle will be greater as well.

We can see that diffusion is a macroscopic manifestation of Brownian motion. In boiled water and regular tap water, we will see the diffusion constant at work using dye: the dye spreads faster in boiled water than the regular water since a greater amount of random collisions occur due to the higher temperature, forcing the dye to move in a random path that spreads out faster. That is Brownian motion!

There are two types of Brownian motion: unbiased random walks and biased random walks. Let us think of the Brownian particle as a tourist who is lost in a big city. They have absolutely no idea where they should go, so the probability of them moving in any direction is equal since they are so lost. This is called an unbiased random walk.

However, most cases of Brownian motion are biased random walks, meaning that they have a probability to travel in a preferred direction. This bias is mainly due to the presence of the diffusion coefficient. It is like handing a map to the tourist; they finally gain a sense of direction and have a higher probability of reaching the right destination. An example of biased Brownian motion is seen in the travel of neurotransmitters throughout neurons as well as gel electrophoresis because the particles have an affinity for a certain direction.

The best part about Brownian motion is that it’s all around us! The Brownian motion model is applicable to everyday life: it explains how molecules are transferred throughout a cell to the navigation of robots on random terrain to computing genetic drift in biology to the prediction of stock prices in finance. It is amazing how physics and science have given humanity a way to deal with random situations. All thanks to Brownian motion.

References

- Fowler, Michael.
*Brownian Motion*. (n.d.). http://galileo.phys.virginia.edu/classes/152.mf1i.spring02/BrownianMotion.htmAPS News. *Einstein and Brownian Motion.*American Physical Society. February 2005. https://www.aps.org/publications/apsnews/200502/history.cfm- Koberlein, Brian.
*Shake, Skate, and Roll*. May 5, 2015. https://briankoberlein.com/2015/05/05/shake-rattle-and-roll/

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