Each sphere is a nanoparticle suspended in a real 3D fluid volume. Every frame it takes a genuine Brownian step in x, y and z drawn from the Stokes-Einstein diffusion coefficient, plus a deterministic drift from the van der Waals force exerted by every other particle within range — a Lennard-Jones-like law with a steep repulsive core (particles can't overlap) and a long ~1/r⁶ attractive tail (particles clump once close enough).
D = k_BT / (6πηr) (Stokes-Einstein)
F(r) = 24ε/r · [2(σ/r)^12 - (σ/r)^6] (Lennard-Jones-like)
dx = μ·F·dt + 𝒩(0, 2Dt) (overdamped Langevin step)
- Temperature — raises kBT, speeding up random thermal steps; hot enough and clusters get shaken apart.
- Particle radius — larger r slows diffusion (1/r in the mobility) but also raises the effective van der Waals well depth, since bigger nanoparticles present more surface for attraction.
- Attraction strength (ε) — the Hamaker-like well depth; above a critical value it overwhelms thermal jitter and particles irreversibly aggregate.
- Viscosity presets — water, glycerol and oil set η directly in the denominator of D, matching real fluid values.
Orbit the camera to see cluster geometry from any angle — real nanoparticle aggregation in colloids and drug-delivery carriers is a genuinely 3D process that a flat view can hide.