Kinetic expressions derived for diffusion limited reactions

3 KINETIC EXPRESSIONS DERIVED FOR DIFFUSION-LIMITED REACTIONS 

Since the interposition of a barrier layer diminishes the effective contact between reactants, the nucleation step in solid + solid reactions is Usually completed very rapidly at temperatures conveniently used in studies of the bulk reaction and, accordingly, the rate processes are often deceleratory throughout. In addition to the progressive diminution in rate 

The simplest kinetic law obeyed, when the surface area is constant and the diminution of reaction rate is a consequence of increasing thickness of the barrier layer, is 

This expression, the parabolic law [38,77,468], has been shown to be obeyed in the oxidation of metals, where the reactant is in the form of a thin sheet. Variations in behaviour are apparent when diffusion in the barrier layer is inhomogeneous as a consequence of cracking or due to the development of more than a single product layer. Alternative rate relations may be applicable, e.g. 

The rate expression for reaction of a cylindrical particle (radius r) is [469] 

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