(776c) Linear Driving Force for Shaped Adsorbents

The well-known Linear Driving Force mass transfer model represents a quasi-steady approximation of transient diffusion in which mass flux is proportional to the departure from saturation with transfer coefficient K.  In the original derivation, K was determined for a spherical particle from an integral of the transient response to a step change in external concentration [1].  This elaborate approach can only be used to derive formulae for K in other shapes if an explicit representation of the transient exists.  Although the value of K in a particular particle may be determined by numerical simulation and subsequent integration of the transient, repeated computations are necessary to indicate the effects of shape parameters.  Consequently, ad-hoc shortcut methods have been applied to generate approximate formulae for K in terms of shape parameters based on assuming a spatial concentration profile within the particle (often quadratic).

Here we present a new route to the LDF model based on asymptotic analysis of the diffusion equation that does not require construction of the full transient solution and thereby facilitates mass transfer analysis and computation.  We correct errors in mass transfer coefficients derived by shortcut methods and present exact solutions for a variety of simple shapes such as ellipsoids, cuboids, hollow cylinders and filled spheres as well as fast computations of K for complex shapes that are not amenable to analytical solution.  The new formulation readily incorporates external mass transfer resistance, thermal coupling and multi-component sorption.

[1] Glueckauf, E., Theory of chromatography Part 10 – formulae for diffusion into spheres and their application to chromatography, Trans. Farad. Soc. 51, 1540-1551 (1955).