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Ink Drop Diffusion: Fick's Law in a Swirling Flow (2D)

2D ink-diffusion lab: a real finite-difference solver for Fick's second law advected by a divergence-free stream-function flow field, with live mass-conservation and spread-radius (σ²=4Dt) diagnostics.

Fluid Dynamics & Aerodynamics2DModerate60 FPS📱 Mobile-adapted⇄ 3D version

This 2D companion replaces the 3D version's orbiting curl-noise particle cloud with an actual numerical solver for Fick's second law: a concentration grid diffuses under an explicit finite-difference Laplacian and is advected by a divergence-free stream-function flow field, so clicking the water drops real dye that spreads, mixes and thins exactly as the mass-conservation and σ²=4Dt readouts predict, with diffusion strength, flow strength, vortex count and drop size all live-adjustable.

⚙ Under the hood

2D ink-diffusion lab: a real finite-difference solver for Fick's second law (∂C/∂t = D∇²C − (u·∇)C), advected by a divergence-free stream-function flow field (u = ∂ψ/∂y, v = −∂ψ/∂x), with live mass-conservation, peak-concentration and spread-radius (σ²=4Dt) diagnostics.

fick's lawdiffusion equationfinite differencedivergence-free flowmass conservationstream function

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install