Adsorption with axial diffusion in shallow beds

Approach to constant pattern behavior and breakthrough behavior are analyzed for adsorption in fixed beds with axial diffusion. Local equilibrium between fluid and solid phases is assumed, with concentrations related by favorable Langmuir and Freundlich isotherms. Results are presented as midheight slopes of internal and actual breakthrough curves and as breadths of actual breakthrough curves. The solutions merge smoothly with asymptotic limits appropriate for deep beds and results obtained here for very short beds. It is shown that breakthrough curves are sharper than corresponding internal breakthrough curves for beds of any length, with the difference being even more pronounced in shallow beds than in deep beds. The principal factor that determines whether or not a breakthrough curve differs significantly from the corresponding internal breakthrough curve, regardless of whether the bed is long or short or the isotherm very favorable or linear, is the breadth of the adsorption wave near the bed outlet.