Mathematical modelling of adsorption and transport processes in capillary electrochromatography: Open‐tubular geometry

Abstract

A mathematical modelling approach for open-tubular capillary electrochromatography is presented. The spatially one-dimensional model takes into account (i) a coupling of (non)linear adsorption of positively or negatively charged analyte molecules (at a negatively charged capillary inner surface) with the equilibrium electrokinetics at this solid-liquid interface, (ii) mobile phase transport by electroosmosis and pressure-driven flow, as well as (iii) transport of species by electrophoresis and molecular diffusion. Under these conditions the local zeta-potential and electroosmotic mobility become a function of the concentration of the charged analyte. The resulting inhomogeneity of electroosmotic flow through the capillary produces a compensating pore pressure as requirement for incompressible mobile phase flow (i.e., for constant volumetric flow along the capillary). The results of the simulations are discussed in view of the surface-to-volume ratio of the capillary lumen, the analyte concentration (in combination with a Langmuir isotherm for the adsorption process), and buffer effects.

Protein adsorption in static microsystems: effect of the surface to volume ratio

“…(4). The values are similar only for the higher Cu values, due to the depletion occurring in this microsystem (h 5 50 mm).…”

“…The theoretical C eq / C max values are calculated from eqn. (4). The experimental C eq /C max is obtained from simulations run with the geometry of Fig.…”

“…Adsorption and transport processes under the Langmuir isotherm assumptions have been modelled mathematically 3 to better understand the phenomena involved in capillary electrochromatography. 4,5 Several models exist for protein mass transfer, 6 for their adsorption on ion exchange particles [7][8][9][10] and on sorbent matrices. 11,12 Mathematical models have also been used to describe the adsorption kinetics of proteins 13 and polyelectrolytes 14 on planar surfaces.…”

Pharmaceutical and biomedical applications of chiral capillary electrophoresis and capillary electrochromatography: An update

“…Paces et al [127] developed a new mathematical modeling approach to describe adsorption and transport processes in open tubular CEC with porous adsorbents. The elution of charged analytes was shown to be a complex interplay of the z-potential, adsorption isotherm, surface to volume ratio, pH, analyte, and background electrolyte concentration.…”

Dynamic computer simulations of electrophoresis: A versatile research and teaching tool

“…In contrast to the dynamic models referred to above, this approach is based upon the modeling of the trajectories of each individual molecule, requires extremely powerful computers in order to compute the motion of a statistically significant number of molecules and is not further considered in this review. Other theoretical work absent from this review includes (i) a stochastic model describing the consequences of wall adsorption in CE [84], (ii) the temperature-dependent interconversion models of dynamic electrophoresis [85][86][87][88], (iii) the simulation model for electroinjection analysis and electrophoretically mediated microanalysis [89], (iv) the affinity electrophoresis models of Andreev et al [90] and Fang and Chen [91][92][93][94], which describe affinity interactions in CE under simplified electromigration conditions, (v) the models of Cann and coworkers describing interacting systems in ZE [95], MBE [96] and IEF [97][98][99], (vi) the models predicting analyte separation in CEC [100][101][102][103][104], (vii) all multi-dimensional models that describe electrokinetically driven mass transport and separations in microfabricated chip devices, such as those of Ermakov et al [105], Bianchi et al [106], Chatterjee [107], Sounart and Baygents [108], Datta and Ghosal [109] and Hirokawa et al [110], (viii) the model of electrokinetic sample injection for capillary CZE with consideration of the electrode configuration [111], (ix) the models that predict sample zone formation, distortion and solute separation in continuous flow electrophoresis [112,113] and recycling electrophoresis [114][115][116], (x) the models describing off-gel electrophores...…”