Brownian Motion - Mean Squared Displacement & Diffusion

Tracer Particle Radius

10 px

Number of Fluid Particles

200

Fluid Particle Radius

3 px

Temperature (K)

300 K

Viscosity (relative)

1.0

Show Tracer Trail

Highlight Collisions

Show Fluid Particles

Trail Length

200

The mean squared displacement grows linearly with time:

⟨r²⟩ = 2dDt

where d=2 in 2D. The diffusion coefficient:

D = k_BT / (6πηr)

relates thermal energy to particle mobility.

Tracer Particle

Fluid Molecules

MSD Data

Linear Fit

Mean Squared Disp.

0.00

Diffusion Coeff. D

0.00

Einstein Pred. D

0.00

Time Steps

Collisions

Distance from Origin

0.0

√(MSD)

0.0

R² (fit quality)