Diffusionsläge

Diffusionsläge, or the diffusion regime, describes a transport state in which the spread of particles, heat, or chemical species is governed primarily by diffusion rather than by advection or convection. In this regime, the movement results from concentration gradients and random molecular motion rather than bulk flow.

The behavior of diffusion is commonly described by Fick’s laws. Fick’s first law states that the diffusive flux J is proportional to the negative gradient of concentration: J = -D ∇C, where D is the diffusivity. Fick’s second law describes the time evolution of concentration: ∂C/∂t = D ∇^2 C for constant D. Together, these equations capture how a localized source or interface spreads into surrounding material.

Diffusionsläge occurs when diffusion dominates over advection, typically quantified by a small Peclet number Pe = UL/D, where U is a characteristic velocity, L a length scale, and D the diffusivity (Pe ≪ 1). It is common at small length scales, short times, or in still fluids. The hallmark is a smooth, isotropic spreading of concentration without a directed bulk flow.

Characteristic scales in diffusion include the diffusion length, L_d ≈ √(2Dt) (or √(Dt) depending on dimensionality), and a timescale t ~ L^2/D for significant mixing. Real-world examples include diffusion of solutes in gels or soils, odor dispersion in still air, dopant diffusion in semiconductors during annealing, and nutrient diffusion in biological tissues.

In modeling, diffusionsläge is treated with diffusion equations, while regimes where advection or convection dominates are described by convection-diffusion equations and related formulations. The distinction helps in choosing appropriate analytical or numerical approaches for transport problems.