diffusiontransport

Diffusion transport, or diffusion-driven transport, refers to the net movement of particles, energy, or chemical species caused by a gradient in concentration or temperature. In fluids and solids it describes how molecules spread from regions of high concentration to regions of lower concentration due to random thermal motion, typically in the absence of bulk flow. It is a fundamental transport mechanism alongside advection and convection and plays a central role in chemical kinetics, materials processing, and biological systems.

Governing equations and concepts are anchored in Fick's laws. 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 describes how concentration evolves in time: ∂c/∂t = ∇·(D ∇c) + S, with S representing sources or sinks. In multicomponent mixtures, diffusion is more complex and is often described by the Maxwell-Stefan framework, where diffusion is governed by a diffusivity matrix and coupling between species; Fick's law becomes a simplifying assumption for dilute, single-component systems. D generally depends on temperature, medium, and interactions.

Diffusion manifests in various forms, including molecular diffusion, Knudsen diffusion in porous media, and thermal diffusion (Soret effect). In many systems, diffusion competes with or is combined with advection, giving rise to dispersion in porous materials where velocity variations further spread tracers beyond molecular diffusion alone.

Applications span chemical engineering, materials science, biology, and electronics. Diffusion is critical for separations, alloy interdiffusion, dopant transport in semiconductors, membrane processes, and tracer studies. Experimental determination of D uses diffusion couples, tracer methods, or techniques like FRAP, depending on the system. Limitations include non-Fickian or anomalous diffusion when D depends on concentration or time, and complex boundary conditions at interfaces.