Porous solid, steady-state flux

In the Wicke-Kallenbach cell, diffusion occurs in one dimension through the porous solid as a result of a concentration, Co, at one of the two faces (z=0) of the solid the other, at distance (x=L), being maintained at a value approaching zero, while keeping the total pressure at each face constant. For a two component mixture of A and B the steady state flux of A is given by ... 

For porous solids having a pore size distribution f(r), where f(r)dr is the fraction of pore volume having pore radii between r and r+dr, and if all the pores are cylindrical in shape and oriented along the direction of flow, the steady state flux based on total cross sectional area of the component 1 can be calculated from ... 

Unsteady state diffusion in monodisperse porous solids using a Wicke-Kallenbach cell have shown that non-equimolal diffusion fluxes can induce total pressure gradients which require a non-isobaric model to interpret the data. The values obtained from this analysis are then suitable for use in predicting effectiveness factors. There is evidence that adsorption of the non-tracer component can have a considerable influence on the diffusional flux of the tracer and hence on the estimation of the effective diffusion coefficient. For the simple porous structures used in these tests, it is shown that a consistent definition of the effective diffusion coefficient can be obtained which applies to both the steady and unsteady state and so can be used as a basis of examining the more complex bimodal pore size distributions found in many catalysts. 

The situation in a zeolite is different from the situation in a macro-porous catalyst with respect to the condition at the boundary a = 0. In the case of a macroporous solid, the gas phase extends into the pore volume in the small pores of a zeolite, a sorbate particle will always be under the influence of a significant force field from the solid, and the plane at a = 0 has to be considered as a phase boundary. At this phase boundary, the concentration (Ca)o in the zeolite must not necessarily be proportional to the partial pressure ( a)o in the gas. Although the local rate of reaction in the solid may be strictly proportional to (first order), the dependence of the observed rate on the concentration in the gas, that is, the order with respect to Pa will be determined by the relation between Pa and (Ca)o This relation results from the requirement that at steady state the fluxes of A or B on both sides of the boundary must be equal. Under the assumption that the rates of transfer through the phase boundary (expressed in moles/cm sec) are linear in the degrees of saturation (0j)o. we have the continuity conditions at a = 0 ... 

Characterization of the average pore size in a porous solid can be performed using a technique described by Yasuda and Tsai. The expression for the steady-state mass or molar flux of a gas through a porous... 

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