First observed by British botanist Robert Brown in 1827 (while studying pollen grains in water), Brownian motion (Wiener Process) refers to the continuous, zig-zag, random movement of colloidal particles in a dispersion medium.
Real-time Simulation (2D Brownian Motion)
Particle Steps: 0 Collision Frequency:
Stable Sol
Adjust the electrolyte concentration. High concentration neutralizes the particle charge, overcoming the Energy Barrier and causing coagulation.
1. The Physical Cause
The motion is caused by the unbalanced bombardment of the colloidal particles by the fast-moving molecules of the dispersion medium. Because the colloidal particles are small (1–1000 nm), the impact from one side is often greater than the other at any given moment, resulting in a net displacement.
2. Factors Affecting Brownian Motion
- Particle Size: Smaller particles move faster because they are easier to displace by molecular collisions.
- Viscosity: The motion is more vigorous in liquids with low viscosity. High viscosity acts as "internal friction" that slows the movement.
- Temperature: Increasing temperature increases the kinetic energy of the solvent molecules, leading to more frequent and forceful collisions.
3. Significance in Stability
4. Mathematical Perspective (Einstein’s Relation)
Albert Einstein later proved that the mean square displacement ($\overline{x^2}$) of a particle is related to time ($t$) and the diffusion coefficient ($D$):
$$\overline{x^2} = 2Dt$$
Where $D$ is defined by the Stokes-Einstein equation: $$D = \frac{kT}{6\pi\eta r}$$
- $k$ = Boltzmann constant
- $T$ = Absolute temperature
- $\eta$ = Viscosity of the medium
- $r$ = Radius of the particle
Summary Table
| Property | Effect on Brownian Motion |
|---|---|
| Increase Temperature | Motion Increases ⬆️ |
| Increase Particle Size | Motion Decreases ⬇️ |
| Increase Viscosity | Motion Decreases ⬇️ |