diffusioncontrolled

Diffusion-controlled, in science and engineering, describes processes whose rate is governed by the transport of species through a medium by diffusion rather than by the intrinsic speed of a chemical or interfacial reaction. In diffusion-controlled processes, the supply of reactants to the reaction site is the limiting factor: if diffusion is slow, the overall rate is constrained even when the surface reaction is fast.

The theoretical framework often invokes Fick's laws of diffusion. In steady state, the diffusive flux J = -D ∂c/∂x supplies reactants to an interface; when the surface reaction proceeds rapidly, the observed rate mirrors this diffusive supply, yielding a diffusion-controlled rate. This contrasts with reaction-controlled (kinetically limited) processes, where the intrinsic rate constants of chemical steps determine the overall pace, independent of how quickly species can reach the interface.

Applications occur across disciplines. In electrochemistry, diffusion control arises when electrode reactions are fast and the current is limited by how quickly species reach the electrode surface. In materials science, diffusion control governs processes such as alloy formation, precipitation, crystal growth, and diffusion-limited aggregation, where growth or transformation rates depend on the transport of species through the material. In corrosion and catalysis, the rate may be set by the diffusion of oxidants, reactants, or inhibitors to reactive sites.

Practical implications include characteristic dependencies on concentration and diffusion coefficients, and a time scale often scaling with the square of a characteristic length (t ~ L^2/D) for simple diffusion. Identifying a diffusion-controlled regime informs strategies to modify rates, such as enhancing convection, reducing diffusion distances, or accelerating interfacial reactions.