diffusion

Diffusion is the net movement of particles from regions of higher concentration to lower concentration, driven by random thermal motion. It occurs in gases, liquids, and solids and tends toward uniform distribution. Unlike bulk flow, diffusion is a passive process that does not require external energy. The rate depends on the concentration gradient, temperature, the diffusing species, and the medium.

Fick's laws describe diffusion quantitatively. Fick's first law states that the diffusive flux J is proportional to the negative gradient of concentration: J = -D ∇C, where D is the diffusion coefficient. Fick's second law, ∂C/∂t = D ∇^2 C, governs how concentration changes over time. D increases with temperature and decreases with viscosity and particle size. In gases, diffusion is relatively rapid; in liquids and solids it is slower and may proceed via mechanisms such as vacancy diffusion in crystals.

Brownian motion underlies diffusion at the microscopic level. In biology, diffusion across membranes can occur by simple diffusion or by facilitated diffusion through channels or carrier proteins; both are passive, while active transport uses energy. In materials science, diffusion controls alloying, sintering, and dopant migration in semiconductors. Diffusion typically follows an Arrhenius relation D = D0 exp(-Ea/RT).

Examples include gas exchange in the lungs, diffusion of nutrients and wastes in tissues, and dialysis. Osmosis, the diffusion of water across a semipermeable membrane, is a related process driven by osmotic pressure. Understanding diffusion is essential across physiology, chemistry, and materials science.