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Brownian Motion. Image Credit: University of Pennsylvania
Brownian motion was discovered by the botanist Robert Brown in 1827. Brown was studying pollen particles floating in water under the microscope. He then observed minute particles within the vacuoles of the pollen grains executing a jittery motion. By repeating the experiment with particles of dust, he was able to rule out that the motion was due to pollen particles being ‘alive’, although the origin of the motion was unexplained.
In physics, the diffusion equation yields an approximation of the time evolution of the probability density function associated to the position of the particle going under a Brownian movement under the physical definition. The approximation is valid for short timescales. The time evolution of the position of the Brownian particle itself is best described using Langevin equation, which involves a random force field representing the effect of the thermal fluctuations of the solvent on the particle.
The displacement of a particle undergoing Brownian motion is obtained by solving the diffusion equation under appropriate boundary conditions and finding the rms of the solution. This shows that the displacement varies as the square root of the time, which explains why previous experimental results concerning the velocity of Brownian particles gave nonsensical results. A linear time dependence can not be used.
In stellar dynamics, a massive body like a star or black hole can experience Brownian motion as it responds to gravitational forces from surrounding stars. The gravitational force from the massive object causes nearby stars to move faster than they otherwise would. The Brownian velocity of the supermassive black hole at the center of the Milky Way(SgrA) is thought to be less than 1km/s-1. If you do a little more research, you will find even more applications for Brownian motion.
We have written many articles about the Brownian Motion for Universe Today. Here’s an article discussing the effect of temperature on the movement of atoms, and here’s an article about mapping the hidden dark matter.
If you’d like more info on the Brownian Motion, check out NASA: Physicists Discover Temperature Key to Avalanche Movement, and here’s a link to a discussion about Brownian Motion.
We’ve also recorded an entire episode of Astronomy Cast all about the Atom. Listen here, Episode 164: Inside the Atom.
Source:
Wikipedia
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