diffusion

Net spreading from high to low concentration through random molecular motion.

Flux (Fick’s first law):

$$J=-D\frac{\partial c}{\partial x}$$

Diffusion equation (Fick’s second law):

$$\frac{\partial c}{\partial t}=D\frac{{\partial }^{2}c}{\partial x^2}$$

where:

• $J$: diffusive flux,
• $c$: concentration,
• $D$: diffusion coefficient (m² s⁻¹),
• $x$, $t$: position and time.

Spreading distance after a time $t$: $\sim \sqrt{Dt}$. Turbulent mixing is often modelled with the same equation and a much larger effective $D$.