Fick Transport — Non-Equilibrium Diffusion

Fick's second law ∂c/∂t = D∇²c governs concentration spreading. Non-equilibrium steady states arise under maintained gradients, producing entropy at rate σ = D(∇c)²/c — a hallmark of irreversible thermodynamics.

Controls

Diffusivity D 1.0 Drift velocity v 0.0 Source rate q_src 0.5 Boundary c_R 0.1

Total mass: —

Entropy prod: —

t: 0.00

Green: c(x,t).
Source at x=0.2L.
Sink (fixed BC) at right.
Steady state: Gaussian-
broadened profile.