. khe zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Chemical Engineering Journal, 36 (1987) B29 - B37 B29 c zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA M ass Tksfer to a Sphere With a Non-uniform Boundary Layer: Implications in Chromatographic Analysis S. J. GIBBS, S. J. KARRILA and E. N. LIGHTFOOT Department of Chemical Engineering, Univereity of Wieconein - Mad.ieon, WI 53706 (U.S.A.) (Received April 24,1987) ABSTRACT The effects of non-uniform boundary- layer resistance on transient mass transfer between a solid sphere and a surrounding fluid are investigated theoretically via a model which employs a distribution of external mass-transfer resistance typical for creeping flow at high Schmidt number, and a constant m te of increase in solute concentration in the approaching fluid. The resulting analysis predicts that errors in estimating solute diffusivities inside the sphere and in the surrounding fluid from experimental measurements of the overall mass-transfer resistance and the assumption of a uniform boundary-layer resistance can ‘be substantial, as large as 3396, even in the absence of experimental data scatter. Errors in simulating system behavior from separately determined diffusivities and average boundary- layer resistances are much less. This analysis, though approximate, suggests caution in estimating solute diffusivities from chromatographic effluent curves. 1. INTRODUCTION - Chromatographic separations are playing an ‘U&f \Ueff increasingly important role in the downstream processing of biological products. Crucial in where /3 is the mean distance traveled by entering solute from the sphere surface to the the successful design of large-scale chromato- interior, and (z> eft is the effective diffusion graphic processors are reasonable estimates of coefficient of the solute in the sorbent phase. governing physical parameters. Normally, For a uniform external boundary layer, p will these estimates are made via analysis of pulse have an average value of l/5 the sphere radius experiments in a laboratory-scale packed bed, [ 11. For a non-uniform boundary layer, a dis- However, because of uncertainties in the na- proportionate part of the entering solute will ture of the physical processes occurring in the enter where the boundary layer is thinnest, packed bed, this technique is not optimal for and the average interior transport distance estimation of the solute diffusivities in the must increase. This effect will clearly be sorbent phase and the boundary-layer mass- greatest when the external resistance is large 0300-9467/87/$3.50 @ ElsevierSequoia/Printedin The Netherlands transfer coefficients, key parameters for pro- cess design. Here, we show how one such uncertainty, the nature of the variation of the boundary-layer convective mass-transfer resis- tance around the surface of a packing particle, may lead to errors in the estimation of the governing physical parameters from packed- column experiments. We also show, however, that these errors may be avoided by carefully chocsing experimental operating conditions. Present models of chromatography [l- 71 usually assume that the convective mass- transfer resistance around the surface of a packing particle can be considered as uniform, and employ an ill-defined mean value. How- ever, if the convective mass-transfer resistance is non-uniform and significant compared with the internal resistance of the particle, then the replacement of a position-dependent convec- tive resistance by a uniform resistance can lead to errors in the description of the inter- nal rate processes of the sorbent phase. The physical basis for this effect is quite simple qualitatively. The time response of a spherical packing particle to any long-continued exter- nal concentration perturbation at the solid- fluid interface is of the order