FickGesetzen

FickGesetzen, commonly referred to as Fick's laws in English, describe diffusion as the net movement of particles from regions of higher concentration to regions of lower concentration due to random motion. They were formulated by Adolf Fick in the 1850s and provide a foundational framework for understanding mass transfer in gases, liquids, and solids. The laws apply to many physical, chemical, and biological processes where diffusion is the dominant transport mechanism, assuming appropriate conditions such as a homogeneous medium and no bulk flow.

Fick's first law states that the diffusive flux J (amount per unit area per unit time) is proportional to the negative gradient of concentration: J = -D ∇C. Here D is the diffusion coefficient, which depends on the temperature, medium, and the diffusing species. In one dimension, this becomes J_x = -D dC/dx. The negative sign reflects movement from high to low concentration.

Fick's second law describes how concentration changes with time in a diffusing system: ∂C/∂t = ∇·(D ∇C). If D is constant, this simplifies to ∂C/∂t = D ∂^2 C/∂x^2 in one dimension. This law predicts the evolution of concentration profiles and underlies many diffusion problems, such as pollutant spreading and material processing.

Assumptions include constant D, a homogeneous and isotropic medium, and negligible convection or chemical reactions. Real systems may exhibit non-Fickian diffusion, where D varies with position or time, or where other transport mechanisms dominate. Fick's laws remain widely used in engineering, pharmacology, materials science, and geology to model diffusion-driven processes.