Fickian kinetic expression

The complete kinetic expression for the metal-promoted hydrolysis of PVA-QA in the solid state requires the inclusion of terms for the rates of diffusion of the metal ion into the film and diffusion of the cleaved metal chelate out of the film into external buffer. The limited case of metal influx coupled to hydrolysis may be solved by assuming the diffusion is Fickian and the reaction rate is proportional to the average concentration of the metal in the film. Then, combining the kinetic expression for sorption from a fixed volume by a film with that of metal promoted hydrolysis, and integrating, leads to Equation 1, which is only valid if the rate of egress of the metal-chelate is rapid relative to its formation. ... 

Rate equations There are two basic types of kinetic rate expressions. The first and simpler is the case of linear diffusion equations or linear driving forces (LDF) and the second and more rigorous is the case of classic Fickian differential equations. 

The models mentioned so far are limited in their application as they represent only first order reaction kinetics with Fickian diffusion, therefore do not allow for multicomponent diffusion, surface diffusion or convection. Wood et al. [16] applied the algorithms developed by Rieckmann and Keil [12,44] to simulate diffusion using the dusty gas model, reaction with any general types of reaction rate expression such as Langmuir-Hinshelwood kinetics and simultaneous capillary condensation. The model describes the pore structure as a cubic network of cylindrical pores with a random distribution of pore radii. Transport in the single pores of the network was expressed according to the dusty gas model as... 

In the case of non-swelling tablets, drug release is generally expressed by Fickian diffusion, for which n = 0.5. For most erodible matrices, the drug release follows zero order kinetics, for which n = 1. In the case of swelling tablets, the drug release is due to a combination of swelling and erosion. They follow non-Fickian release behavior. For them, the value of n lies between 0.5 and 1.0 [78]. The value of n was calculated from the slopes of the log(M/M ) vs log t plot in acidic and neutral pH. 

For dilute gases, the generalized multicomponent Fickian diffusion coefficients are strongly composition dependent. It follows that these diffusion coefficients do not correspond to the approximately concentration independent binary difffisivities, Dsr, which are available from binary diffusion experiments or kinetic theory since Dgr Dsr. In response to this Fickian model limitation it has been proposed to transform the Fickian diffusion flux model, in which the mass-flux vector, jj, is expressed in terms of the driving force, dj, into the corresponding Maxwell-Stefan form [95, 97, 142, 143] where d is given as a linear function of jj. The key idea is to rewrite the Fickian diffusion flux in terms of an alternative set of difffisivities (i.e., preferably the known binary difffisivities) which are less concentration dependent than the Fickian difffisivities. 

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