Brownian Motion 2D — Nanoparticle Diffusion Simulator

Particle & Fluid

Temperature 300 K

Particle radius 10 nm

Particle count 30

Fluid viscosity (η)

Live Readout

D (diffusion)

— nm²/μs

Fluid

Water

MSD (measured)

— nm²

RMS displacement

— nm

Step σ

— nm

Elapsed time

0.0 s

How it works

Each particle takes a random step every frame drawn from the Einstein-Smoluchowski diffusion coefficient:

D = kB*T / (6*pi*eta*r)
MSD(t) = 4*D*t   (2D)
sigma_step = sqrt(2*D*dt)

Smaller radius, higher temperature or lower viscosity all raise D, so particles jitter further per frame. The right-hand plot accumulates the measured mean-squared displacement of all particles and compares it against the theoretical straight line 4Dt — a close match confirms the simulated random walk reproduces real diffusive behaviour.