Fickképlet

Fickképlet, or Fick’s equation, refers to the mathematical expressions that describe diffusion, the net movement of particles from regions of higher concentration to lower concentration. The concept was introduced by the German physiologist Adolf Eugen Fick in the 1850s. The equations come in two related forms: Fick's first law, which relates a steady-state diffusive flux to the concentration gradient, and Fick's second law, which describes how concentration changes with time due to diffusion.

Fick's first law states that the diffusive flux J is proportional to the negative gradient of concentration: J = −D dC/dx in one dimension, where J is the flux (amount per unit area per unit time), C is concentration, and D is the diffusion coefficient. More generally, J = −D ∇C, with D treated as a scalar or a tensor in anisotropic media.

Fick's second law describes the time evolution of concentration: ∂C/∂t = D ∇^2 C for constant D. In one dimension, this becomes ∂C/∂t = D ∂^2C/∂x^2. These forms assume non-reactive diffusion and, for the second law, constant diffusion properties; variations account for concentration-dependent D or nonlinearity.

Applications of Fickképlet span environmental science, biology, pharmacology, materials science, and semiconductor processing. They are used to model pollutant spreading, drug release, grain-boundary diffusion, and the smoothing of concentration profiles in solids. In practice, boundary and initial conditions, variable diffusion coefficients, and anisotropy may require generalized or numerical solutions. Fick's laws remain foundational to diffusion theory and its wide range of practical problems.