Each sphere is a Janus particle: one hemisphere carries a platinum catalyst, the other is bare silica. The Pt cap decomposes fuel (H₂O₂ → H₂O + ½O₂), building a local concentration gradient of reaction product around the particle. That gradient drives fluid slip along the surface — self-diffusiophoresis — which pushes the whole particle along its cap-to-body axis, away from the catalytic pole:
v_self = μ_ph · ∇c (phoretic slip from the local gradient)
v₀(C) = v_max · C / (K_M + C) (Michaelis–Menten catalytic turnover)
Meanwhile, ordinary Brownian motion still acts on the particle. Thermal collisions randomize both position and orientation, so the propulsion direction itself diffuses — this is what turns a "swimmer" into a persistent random walk instead of a straight line:
D_t = k_BT / (6πηr) translational diffusion (Stokes–Einstein)
D_r = k_BT / (8πηr³) rotational diffusion
τ_r = 1 / (2D_r) orientation persistence time (3D)
D_eff = D_t + v₀²τ_r/6 long-time effective diffusion of an active swimmer
- Fuel concentration — sets the catalytic turnover rate via Michaelis–Menten saturation; more fuel → faster propulsion, up to a plateau.
- Particle radius — larger particles rotate more slowly (D_r ∝ 1/r³), so they hold a heading longer and travel further ballistically before randomizing; smaller particles tumble almost immediately.
- Bath temperature — raises k_BT and lowers water's viscosity η (Vogel equation), boosting both translational and rotational diffusion.
- Catalytic cap toggle — switches v₀ to zero, turning every swimmer into a plain passive Brownian sphere, so you can compare active vs. passive spreading side by side.
This is the same mechanism used by real Pt/SiO₂ and Pt/polystyrene Janus micromotors studied since the mid-2000s (Golestanian, Howse et al.) as model autonomous "nanomotors" for cargo transport and targeted delivery. Simulated time is accelerated ~40× relative to a real H₂O₂ bath so the enhanced diffusion is visible within seconds rather than minutes.