Science lab / statistical motion

Brownian motion, one collision at a time.

Track a massive probe through a crowd of moving marbles, then change its size, density, launch direction, and surroundings to see how its path responds.

Model notes

A small mechanical model of random-looking motion

This laboratory uses a two-dimensional hard-disc model inspired by Brownian motion. Each marble has a radius and an areal density (mass per unit area), giving it a mass of m = ρπr2. Larger or denser marbles therefore carry more inertia than smaller or lighter ones.

Every collision is treated as elastic: momentum is exchanged along the line joining the two centres while tangential motion is retained. The repeated impacts make a tracked probe follow an irregular path even though every individual collision obeys a deterministic rule.

From a botanical puzzle to evidence for atoms

In 1827, botanist Robert Brown watched tiny particles released from pollen grains wander continually in water. He repeated the observation with non-living materials, helping to rule out a specifically biological cause. The phenomenon later took his name.

Albert Einstein's 1905 treatment connected this visible wandering to countless unseen molecular impacts and predicted measurable diffusion. Jean Perrin's painstaking experiments tested those predictions and provided evidence for the molecular nature of matter. His 1926 Nobel Prize in Physics recognised his work on the discontinuous structure of matter, especially sedimentation equilibrium.

Where similar motion appears

Brownian motion can be observed in sufficiently small pollen or mineral particles in water, pigment particles in colloidal suspensions, and fine smoke or dust suspended in still air. Thermal jostling also contributes to microscopic motion inside cells, though real cells add flows, binding, and active molecular transport that this model omits.

What this model leaves out

This is an idealised teaching model, not a complete molecular-dynamics simulation of a real fluid. It is two-dimensional, uses perfectly hard circular particles, and omits attractive molecular forces, explicit viscous drag, rotation, and three-dimensional effects.

Things to try

  • Raise the temperature and compare the probe's path and speed history.
  • Increase probe density while keeping its radius fixed, then select Reset probe to give each impact less influence on its velocity.
  • Change the probe radius and select Reset probe to compare paths with a larger collision cross-section and mass.
  • Compare the canvas trail with the full-space trajectory and speed history.

Sources and further reading

Updated · factual and copy review

Deep instrument

Hard-disc collision workbench

Updated

Configure the bath and probe, then compare its live trail with its trajectory in position space. Select Reset probe to apply the probe settings.

Simulation running

Particle bath
Probe particle

Under the hood

The mathematics used in this simulation

Updated

Each particle is a circular hard disc. Its mass is its density multiplied by its two-dimensional area. Positions advance with a fixed 1/120-second physics step; rendering can happen at a different rate without changing the collision calculation.

Mass and motion

m = ρπr2

xt+Δt = xt + vΔt

A wall collision reverses only the velocity component perpendicular to that wall.

Elastic collision impulse

j = −(1 + e) (vb − va) · n / (1/ma + 1/mb)

Here n points between the particle centres and e = 1 for a perfectly elastic collision. The equal and opposite impulse changes both velocities, conserving the pair's total momentum and kinetic energy apart from floating-point error. The walls exchange momentum with the discs, so the particles' total momentum is not conserved.

Keeping contacts stable

Overlaps are reduced in inverse proportion to mass, so the lighter disc moves farther. A spatial grid checks only particles in the same or neighbouring cells instead of comparing every possible pair. Contacts are detected after each fixed step, so fast discs can pass through one another between checks; this is not exact collision timing.

Assumptions and limits

The model is two-dimensional, uses circular particles with no rotation, and does not include explicit viscous drag, long-range molecular forces, thermal reservoirs, or three-dimensional fluid structure. Temperature is relative to the default setting, with background speeds proportional to its square root. Doubling the setting doubles the background particles' kinetic energy at the instant of adjustment. The probe responds through collisions. This control does not maintain a fixed temperature or measure kelvin.

Further mathematics

All science experimentsNavigation updated