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5-100 44 STOCKHOLMThe importance of separating chemical components by fluidsolid operations has created a need for predicting the performance of adsorption equipment. A central problem in the design of fixed-bed adsorbers is the prediction of the concentrationtime relationship, or breakthrough curve, of t h e effluent stream. Apart from the influence of axial dispersion, a mathematical model of adsorption from the flowing stream should take into account:Diffusion of the component from the main body of the flowing phase to the external surface of the adsorbent particle (external diffusion) Diffusion through the porous network of the particle (internal diffusion)The adsorption process itselfIn the general case, all three steps can contribute to the overall rate of adsorption.Mathematical solutions for the breakthrough curve have been presented for special cases where one of the three processes controls the rate. These results have supposed that the effect of longitudinal dispersion in the flowing phase in the bed is insignificant. It is also supposed that the equilibrium adsorption curve on the solid surface is linear. The boundary conditions used are:The boundary condition (Eq. 8) is the link between the Eqs. 1 and 2. It states mathematically that the mass entering or leaving the particles must equal the flow of mass transported across a stagnant fluid film at the external surface.The Laplace transform of C , e, with the slightly different inlet condition: C(0, t ) = C" C(0, t ) = 0 0 5 t 5 t,, t > t,, has been derived by Kubin (1965), and was used to obtain up to the third central moment of the chromatographic curve C(z, t). Using the properties of the Laplace-transform, the transform for the present inlet condition (Eq. 4) is simply obtained by dividing Kubin's result by (1 -e-'e) (or letting t,? * a). In the present notation we obtain: