Modeling the velocity field of the electroosmotic flow in charged capillaries and in capillary columns packed with charged particles: interstitial and intraparticle velocities in capillary electrochromatography systems

Mass transfer systems based on electrokinetic phenomena (i.e., capillary el ectrochromatography (CEC)) have shown practical potential in becoming power ful separation methods for the biotechnology and pharmaceutical industries. A mathematical model has been constructed and solved to describe quantitat ively the profiles of the electrostatic potential, pressure, and velocity o f the electroosmotic flow (EOF) in charged cylindrical capillaries and in c apillary columns packed with charged particles. The results obtained from m odel simulations (i) provide significant physical insight and understanding with regard to the velocity profile of the EOF in capillary columns packed with charged porous particles which represent systems employed in CEC, (ii ) provide the physical explanation for the experimental results which indic ate that the velocity of the EOF in capillary columns packed with charged p orous particles is a very weak function (it is almost independent) of the d iameter of the particles, and (iii) indicate that the intraparticle velocit y, v(p,i), of the EOF can be greater than zero. The intraparticle Peclet nu mber, Pe(int) (rap), for lysozyme was found to be greater than unity and th is intraparticle convective mass transfer mechanism could contribute signif icantly, if the appropriate chemistry is employed in the mobile Liquid phas e and in the charged porous particles, in (a) decreasing the intraparticle mass transfer resistance, (b) decreasing the dispersive mass transfer effec ts, and (c) increasing the intraparticle mass transfer rates so that high c olumn efficiency and resolution can be obtained. Furthermore, the results f rom model simulations indicate that for a given operationally permissible v alue of the applied electric potential difference per unit length, E-x, hig h values for the average velocity of the EOF can be obtained if (1) the zet a potential, zeta(p), at the surface of the particles packed in the column has a large negative magnitude, (2) the value of the viscosity, mu, of the mobile liquid phase is low, (3) the magnitude of the dielectric constant, e psilon, of the mobile liquid phase is reasonably large, and (4) the combina tion of the values of the concentration, C-infinity, of the electrolyte and of the dielectric constant, epsilon, provide a thin double layer. The theo retical results for the velocity of the EOF obtained from the solution of t he model presented in this work were compared with the experimental values of the velocity of the EOF obtained from a fused-silica column packed with charged porous silica C-8 particles. Systems with four different particle d iameters and three different concentrations of the electrolyte were conside red, and the magnitude of the electric field was varied widely. The agreeme nt between theory and experiment was found to be good. (C) 2000 Elsevier Sc ience B.V. All rights reserved.