Brownian Motion Simulation

Interactive simulation of Brownian motion demonstrating random particle movement and diffusion

Time: 0.00 s
Displacement: 0.00 μm
Mean Square Displacement: 0.00 μm²
Diffusion Coefficient: 0.00 μm²/s

Parameters

Physical Equations

Mean Square Displacement: <x²> = 2Dt
Einstein Relation: D = k_BT/(6πηr)
Stokes' Law: F = 6πηrv
Random Step: dx = √(2Ddt)·ξ

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What is Brownian Motion?

Brownian motion is the random motion of particles suspended in a medium (liquid or gas). It was first observed by Robert Brown in 1827 when studying pollen grains in water. This phenomenon results from the collision of the large particles with the rapidly moving molecules in the fluid.

Einstein's Theory (1905)

Albert Einstein provided a theoretical explanation for Brownian motion in 1905. He showed that the motion is caused by thermal fluctuations and derived the diffusion equation: <x²> = 2Dt, where <x²> is the mean square displacement, D is the diffusion coefficient, and t is time. This work provided crucial evidence for the existence of atoms and molecules.

Diffusion Coefficient

The diffusion coefficient D = k_BT/(6πηr) depends on temperature (T), particle radius (r), and fluid viscosity (η). k_B is the Boltzmann constant (1.38×10⁻²³ J/K). Higher temperature, smaller particles, or lower viscosity increase the diffusion rate.

Stokes' Law and Drag

Stokes' law F = 6πηrv describes the drag force on a spherical particle moving through a viscous fluid. This friction balances the random thermal forces, determining how far the particle moves in each time step.

Applications

Brownian motion is fundamental to many fields: statistical mechanics, polymer science, finance (stock price models), biology (cell membrane dynamics), and engineering (nanoparticle behavior). It demonstrates the connection between microscopic thermal motion and macroscopic diffusion.