Diffusionkoefficienten

Diffusionkoefficienten, commonly called diffusion coefficients, are parameters that quantify the rate at which particles spread through a medium due to random motion. They are typically denoted by D and appear in Fick's laws. In Fick's first law, the diffusive flux J is proportional to the negative gradient of concentration: J = -D ∇C. In the diffusion equation for a single species, ∂C/∂t = D ∂^2C/∂x^2 in one dimension, or more generally ∂C/∂t = ∇·(D ∇C). In isotropic, homogeneous media D is a scalar; in anisotropic media it is a tensor.

D depends on temperature, the properties of the medium, and the size and interactions of the diffusing species. Generally, higher temperature and lower viscosity promote faster diffusion. Empirical models include Arrhenius-type relations, D = D0 exp(-Ea/RT), and, for dilute solutions of small spheres in viscous fluids, the Stokes–Einstein relation D = kB T / (6 π η r). In complex media, D may vary with position and time, and in anisotropic materials the diffusion equation uses a tensor D.

Units are square meters per second (m^2/s). Values span many orders of magnitude: gases often diffuse faster than liquids, and diffusion in solids tends to be much slower. Typical liquid values for small solutes are around 10^-9 to 10^-10 m^2/s; in solids, diffusion coefficients can range from about 10^-20 to 10^-12 m^2/s depending on mechanism.

Applications cover chemical engineering, materials science, biology, environmental science and geophysics. Measurements employ tracer techniques, pulse-field gradient NMR, impedance methods, or radioactive tracers. Diffusionkoefficienten thus serve as key descriptors of transport processes in diverse systems.