An Electrokinetic-Hydrodynamics-Ekhd Based Approach to Determine Effective Transport Parameters: Illustrative Results and Comparison

Jennifer Anne Pascal1, Mario Oyanader2, and Pedro E. Arce2. (1) Chemical Engineering, Tennessee Tech University, PH-214, Cookeville, TN 38505, (2) Chemical Engineering, Tennessee Technological University, Department of Chemical Engineering, P.O. Box 5013, Cookeville, TN 38505

A number of contributions have been made to the field of electrokinetics, i.e. electrophoresis, EOF, etc. as it relates to the behavior of diffusion and hydrodynamics in various systems. Many of these efforts have been influenced by the work conducted by the group of Giddings (see, for example, Martin and Giddings [1], [2]) who worked in the area of field flow fractionation (FFF). In this separation technique, an orthogonal applied field (i.e. gravitational, electrical, etc.) drives the motion of the charged molecules towards the channel walls; thus, the solute that is most susceptible to the influence of the field locates closest to the walls, and, depending on the solute properties, different species reach the wall at different locations.

Among illustrative contributions and without being thorough in the literature citations, Giddings ([1]), based on nonequilibrium theory, predicted retention times in various types of FFF devices. Brenner and Edwards ([3]), examined a Couette-based flow apparatus with cross flow in which equations governing the transport of Brownian solute particles (i.e. diffusivity and velocity) were developed. More recently, Horiuchi et. al. ([4]) have examined two dimensional flow in rectangular microchannels with non constant electrostatic potential on the walls. They obtained analytical solutions for the velocity profile and pressure as well as the effective diffusivity. These “effective” parameters control the quality of the separation in the device.

A powerful mathematical framework that is currently available ([5]) for these types of problems is the coupling of EKHD with the spatial averaging approach ([6], [7], [8], [9]). This mathematically efficient approach allows for up-scaling as well as systematization from the micro (molecular or continuum) scale to the macro (bulk) scale. One of the advantages of this combined approach is the prediction of optimal separations for a wide variety of cases with a minimum effort. Moreover, the analytical results are rather simple mathematical functions of the fundamental physical parameters of the system. In this presentation, the authors will present illustrative results for both the Poiseuille as well as the Couette hydrodynamic flows (i.e. optimal separation times). Furthermore, the authors will compare these predictions with results found in the literature related to these cases and draw conclusions about the possible more suitable description and general validity of such predictions.

[1] Giddings, J. C., Science, 1993, 260, 1456.

[2] Martin, Michel; Giddings, J.C. Journal of Physical Chemistry. 1981, 85, 727.

[3] Brenner, H.; Edwards, D.A. Macrotransport Processes. Butterworth-Heinemann Series in Chemical Engineering, 1993.

[4] Horiuchi, K. Dutta, P., Ivory, C. “Electroosmosis with Step Changes in

Zeta Potential in Microchannels.” AIChE Journal 53 (2007): 2521.

[5] Oyanader, M. A. and P. Arce, Electrophoresis, 26, 2857 (2005).

[6]Slattery, J. C., Momentum, Energy and Mass Transfer in Continua, Krieger, New York, 1981.

[7] Whitaker, S., Chem. Eng. Sci. 1985, 40, 1387.

[8] Cwirko, E. H.; Carbonell, R. G., . J. Colloid Interface Sci. 1989, 129, 513.

[9] Arce, P.; M. Oyanader, and J. Pascal, “Electrokinetic Hydrodynamics: An Introductory Graduate level Course.” To be submitted to Chemical Engineering Education.