Fick’s Laws

Fick’s laws (first and second Fick’s laws). These two laws of diffusion were originally postulated by the medical doctor Adolf Eugen Fick (1829–1901) (from whom they take their name) by analogy with energy transfer in conduction and not by experiment (Fick 1855; Bird et al. 2002).

First Fick’s law. For a generic species A in a mixture, first Fick’s law is referred to as the constitutive equation for mass flux of A stating the proportionality between flux and mass gradient in a certain domain, which can be used in solid, liquid, and gas phase (Bird et al. 2002; Krishna and Taylor 1993). This relationship can be expressed both in term of mass (Eq. 1) and molar quantities (Eq. 2) as

$$ \underline {j_A}=-\rho {D}_A\nabla {w}_A $$

(1)

$$ \underline {J_A}=-c{D}_A\nabla {x}_A $$

(2)

where j _A and J _A are the mass and molar flux of the species A, respectively; ρ [kg m⁻³] is the density of mixture; c [mol m⁻³] is its total concentration; w_A [kg_A kg⁻¹] and x_A [mol_A mol⁻¹] are the mass and molar...