Editing Fick's laws of diffusion (section)

=== Fick's flow in liquids ===
When two [[miscibility|miscible]] liquids are brought into contact, and diffusion takes place, the macroscopic (or average) concentration evolves following Fick's law. On a mesoscopic scale, that is, between the macroscopic scale described by Fick's law and molecular scale, where molecular [[random walk]]s take place, fluctuations cannot be neglected. Such situations can be successfully modeled with Landau-Lifshitz fluctuating hydrodynamics. In this theoretical framework, diffusion is due to fluctuations whose dimensions range from the molecular scale to the macroscopic scale.<ref>{{cite journal | vauthors = Brogioli D, Vailati A | title = Diffusive mass transfer by nonequilibrium fluctuations: Fick's law revisited | journal = Physical Review E | volume = 63 | issue = 1 Pt 1 | pages = 012105 | date = January 2001 | pmid = 11304296 | doi = 10.1103/PhysRevE.63.012105 | bibcode = 2000PhRvE..63a2105B | arxiv = cond-mat/0006163 | s2cid = 1302913 }}</ref>

In particular, fluctuating hydrodynamic equations include a Fick's flow term, with a given diffusion coefficient, along with hydrodynamics equations and stochastic terms describing fluctuations. When calculating the fluctuations with a perturbative approach, the zero order approximation is Fick's law. The first order gives the fluctuations, and it comes out that fluctuations contribute to diffusion. This represents somehow a [[tautology (logic)|tautology]], since the phenomena described by a lower order approximation is the result of a higher approximation: this problem is solved only by [[renormalization|renormalizing]] the fluctuating hydrodynamics equations.