Sieverts-Fick law

Hydrogen flux through the membrane according to Sieverts-Fick law... 

When the pressure is relatively low, the diffusion is assumed to be the rate-limiting step and the factor n is equal to 0.5. In this case, Eq. 2.2 becomes the Sieverts-Fick law [36] ... 

As a consequence, when Sieverts-Fick law is valid, the hydrogen flux is written in terms of the so-called Richardson s equation ... 

The exponent n, instead, varies in the range 0.5—1, and it allows recognition of the limiting step if it is 0.5 the Eqn (4.7) becomes the Sieverts-Fick law, so the diffusion is the limiting step if it is bigger than 0.5, the reactions of dissociation or recombination are slower than the bulk diffusion. The dependency from temperature is expressed as an Arrhenius law for the permeabihty, which can be substituted inside the Sieverts-Fick law for obtaining the so-caUed Richardson s equation, reported below. 

As is well known, for dense Pd-membranes with thickness >5 pm, the hydrogen transport Eqn (6.1) can be expressed by the Sieverts-Fick law (6.1) ... 

In case of relatively low pressure, the rate-limiting step of the hydrogen permeation through the membrane is assumed to be the diffusion (Dolan, Dave, Ilyushechkin, Morpeth, McLennan, 2006). When the membrane thickness is greater than 5 pm, Eqn (8.1) becomes the Sieverts-Fick s law (2) ... 

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