Mario A. Oyanader 1 * Pedro Arce 2 1 Department of Chemical Engineering, Universidad Católica del Norte, Antofagasta, Chile 2 Department of Chemical Engineering, Tennessee Technological University, Cookeville, TN, USA Role of geometrical dimensions in electrophoresis applications with orthogonal fields The role of geometrical dimensions in electrophoresis applications with axial and orthogonal (secondary) electric fields is investigated using a rectangular capillary channel. In particular, the role of the applied orthogonal electrical field in controlling key parameters involved in the effective diffusivity and effective (axial) velocity of the solute is identified. Such mathematically friendly relationships are obtained by applying the method of spatial averaging to the solute species continuity equation; this is accom- plished after the role of the capillary geometrical dimensions on the applied electrical field equations has been studied. Moreover, explicit analytical expressions are derived for the effective parameters, i.e., diffusivity and convective velocity as functions of the applied (orthogonal) electric field. Previous attempts (see Sauer et al., 1995) have only led to equations for these parameters that require numerical solution and, therefore, limited the use of such results to practical applications. These may include, for exam- ple, the design of separation processes as well as environmental applications such as soil reclamation and wastewater treatment. An illustration of how a secondary elec- trical field can aid in reducing the optimal separation time is included. Keywords: Bioseparation / Gel electrophoresis / Microchannels / Orthogonal fields DOI 10.1002/elps.200500112 1 Introduction Electrophoresis and electrokinetic applications in areas such as separation of biomacromolecules, elimination of contaminants from soils, and drug delivery have attracted the attention of numerous researchers (see, for example, Probstein [1]; Jaroszeski et al. [2]; Oyanader et al. [3]). In spite of this fact, as the interest continues to grow, a need for additional understanding and further research becomes evident. In particular, the role of the internal structure of the material in gel electrophoresis [4] and the role of operating parameters such as the nature of the applied electrical field [5] and the separation efficiency have been recently studied. Motivation for these efforts is rooted in new potential applications that have emerged, i.e., the electrophoretic separation of large macro- molecules, such as DNA and proteins [6, 7] and soil cleaning processes [1, 8]. Within the framework described above, particular atten- tion has been given to the analysis of (secondary) orthog- onal applied electric fields to potentially enhance separa- tion. Sauer et al. [5], for example, studied this effect on the transport of solute in a Poiseuille flow regime using a capillary channel of rectangular geometry. In this analysis, mathematical expressions for the effective transport pa- rameters, i.e., effective diffusivity and effective velocity, were obtained; the effort provided a new angle for the understanding of the effect of secondary fields on solute dispersion and velocity. These relationships are a key to understanding the role of operating parameters, i.e., orthogonal electrical fields, in controlling the effective dif- fusivity and effective mobility in capillary channels and, therefore, very useful in assessing the overall efficiency of processes such as electrophoretic separation and soil cleanup by using electrical fields. Before the work reported by Sauer et al. [5], only ad hoc expressions were known for dispersion under the effect of an electrical field [9–11] and the effect of a secondary field were only known experimentally [7, 12, 13]. Sauer and collaborators introduced a nontrivial modeling approach as a tool for the analysis of the system under study [5]. This effort was the first that systematically explained experi- mental trends [7] in enhancing separation efficiency when a secondary orthogonal field is applied. One limitation of the analysis is that the predicting formulae for the effective transport parameters are in terms of integrals that require numerical solution. Motivated by this approach and in an Correspondence: Dr. Pedro Arce, Department of Chemical Engineering, Tennessee Technological University, Prescott Hall 214, Cookeville, TN 38505, USA E-mail: parce@tntech.edu Fax: +931-372-6352 Electrophoresis 2005, 26, 2857–2866 2857 * Current address: Interchange Fulbright Scholar, Civil and Envi- ronmental Engineering Department, Florida State University, 2525 Pottsdamer Street, Tallahassee, FL 3231 0-6046, USA. E-mail: oyanader@ucn.cl  2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim General