Hindrance Factors for Diffusion and Convection in Pores

It is well-known that solutes in liquid-filled pores of molecular dimensions have reduced diffusivities and are sieved during filtration. For solute molecules that are large enough to act as hydrodynamic particles, these phenomena can be explained by a combination of particle-wall hydrodynamic interactions and steric restrictions. Theoretical expressions that include those effects have been available for many years, but, even for spheres in pores of constant cross-section, certain hydrodynamic information has been lacking until recently. In particular, the local enhanced drag and local lag coefficient for off-axis positions had not been fully characterized, requiring that results for symmetrically positioned particles ("centerline approximations") be employed in predicting diffusional and convective hindrances. In this paper the current status of hindered transport theory is reviewed for neutral spheres in long cylindrical pores or slits, and it is shown that such approximations are no longer necessary. New expressions are presented for diffusive and convective hindrance factors that are properly averaged over the pore cross-section. The root-mean-square errors in the centerline approximations are 20% and 6%, respectively, for diffusive and convective hindrance factors in cylindrical pores; for slit pores the corresponding errors are 16% and 10%. Comparisons are made between the predictions and recent data obtained by tracking particle positions in microchannels.