Diffusionskonstante

Diffusionskonstante, often denoted D and also called the diffusion coefficient, is a parameter that quantifies the rate at which particles spread due to diffusion. In a homogeneous, isotropic medium, Fick's first law expresses the diffusive flux J as proportional to the negative concentration gradient: J = -D ∇c. If the medium is anisotropic, D becomes a second-order tensor and diffusion is described by ∂c/∂t = ∇·(D ∇c). For constant D, this reduces to the diffusion equation ∂c/∂t = D ∇^2 c.

The diffusion constant has units of area per time (SI: m^2/s). It sets a characteristic diffusion length; after time t, particles have typically spread by a length on the order of sqrt(2 D t) in one dimension, or sqrt(6 D t) in three dimensions. In random Brownian motion, the mean squared displacement is ⟨r^2⟩ = 2 d D t, where d is the number of spatial dimensions.

D is influenced by temperature, the medium, and the size of diffusing particles. It often increases with temperature and decreases with viscosity or particle size. Common models include the Arrhenius form D = D0 exp(-Ea/(RT)) and, for small spherical particles in liquids, the Stokes–Einstein relation D = k_B T/(6 π η r), where η is the dynamic viscosity and r the particle radius.

Diffusion can be classified as self-diffusion (diffusion of identical particles in a pure substance) or mutual (binary) diffusion in mixtures. In solids or porous media, diffusion may be anisotropic, requiring a tensor D. Diffusion constants are measured by tracer methods, NMR diffusometry, FRAP, or related techniques, and are fundamental in fields ranging from materials science to biology and geology.