diffusive

The term diffusive refers to processes governed by diffusion, the net movement of particles from regions of high concentration to regions of lower concentration due to their random thermal motion. Diffusion is a passive transport mechanism and is often contrasted with advection, which involves transport by bulk flow.

In mathematical models, diffusion is described by Fick's laws. The diffusion equation ∂C/∂t = D ∇^2 C expresses how concentration C changes in time, with D representing the diffusion coefficient. If D is constant, solutions depend on initial and boundary conditions; in one dimension this reduces to ∂C/∂t = D ∂^2C/∂x^2. For Brownian particles, the mean square displacement grows linearly with time, ⟨r^2⟩ = 2dDt, where d is the dimensionality.

Diffusive transport occurs in many contexts: molecular diffusion of gases and liquids, diffusion of solutes in porous media, and eddy or turbulent diffusion in fluids. In solids, diffusion describes atomic or vacancy motion leading to alloying, precipitation, or creep. In biology, diffusion moves nutrients, gases, and signaling molecules across membranes and within tissues.

Real-world diffusion is influenced by temperature, medium structure, and interactions, and is characterized by the diffusion coefficient D, which can depend on temperature and composition. When D is not constant or when transport involves memory effects, diffusive behavior may be non-Fickian or anomalous, with MSD scaling nonlinearly with time.

Historically, diffusion models date to Adolf Fick in the 1850s. In probability and statistical physics, diffusion is linked to Brownian motion and described by stochastic equations such as the Langevin and Fokker–Planck formalisms.