Eleonora Erdmann 1 Mario A. Oyanader 2 Pedro Arce 3 1 Instituto de Investigaciones para Industria Química, INIQUI-CONICET, Facultad de Ingeniería, Consejo de Investigaciones, CIUNSA, Universidad Nacional de Salta, Buenos Aires, Argentina 2 Department of Chemical Engineering, Universidad Católica del Norte, Antofagasta, Chile 3 Department of Chemical Engineering, Tennessee Technological University, Cookeville, TN, USA Effect of the Joule heating and of the material voids on free-convective transport in porous or fibrous media with applied electrical fields The effect of the geometry of the soil in electrokinetic application has been studied by using capillary models of annular geometry. The Joule heating generation has been included as a primary effect of temperature development leading to buoyancy flows. The heat transfer model has been formulated for conduction-dominated regime. The results of this model have been coupled with the motion equation to obtain the ana- lytical hydrodynamic velocity profile. Numerical illustrations, demonstrating the effect of the cross-sectional area of the annular region on the velocity field, have been inclu- ded. It is observed that a substantial effect on the magnitude of such velocity field for different parameters of the system. The results are useful to obtain better under- standing of the role of the soil geometry in potential soil cleaning field operations. Keywords: Annular capillary / Electrohydrodynamics / Joule heating / Soil cleaning DOI 10.1002/elps.200500111 1 Introduction The use of an applied electrical field to move solutes (i.e., macromolecules, small particles, and drops) in a given medium (i.e., gas, liquid, and/or a porous matrix) has been practiced for quite some time [1–3]. Several aspects, however, have kept the technology development from reaching its full potential. Among these aspects one could include, for example, the lack of proper electrode mate- rial, the lack of a complete understanding of the various transport and physicochemical mechanisms involved in the process, and the absence of a priori design criteria of several of the applications seems to be missing. Further- more, the analysis of the role of the thermal effects that always appear in the presence of an electrical field (i.e., the Joule heating effect) seems to have received less attention than other aspects. In addition, the role played by the morphology of the material (i.e., separation media or soil) in the heat transfer process is not well understood. Recent advances in the development of new and more corrosion-resistant materials, the need for more efficient strategies in the cleaning of contaminated soils [4–6], and the urgency of having separation techniques that show a high separation efficiency have prompted a new and vig- orous interest in the research and development related to applied field technologies. Examples of current field-sen- sitive particle processes in a variety of applications (that involved a porous or a fibrous medium) may be identified, in a broad sense, in environmental control process [7, 8], separation of biomacromolecules, material processing applications, and biomedical pharmaceutical engineering processes [9]. One of the goals of this contribution is to study the role of the Joule heating effect on the hydrodynamics of the system. Another closely related aim is to determine the effect of the porosity of the soil or separation material on the hydrodynamic velocity field. This analysis would help in gaining understanding of model predictions for a pos- sible design of a cleaning up procedure or a separation strategy. The method developed in this contribution is useful for determining the effect of both porosity and Joule heating on the dispersive mixing of a solute in a fibrous or porous media when an applied electrical field is present. This can be achieved following a procedure published by Bosse and Arce [10] that has been reported elsewhere. The analysis of the transport of energy, momentum, and mass in the presence of Joule heating generation in a porous or fibrous media is a complex task. In general, the equations are fully coupled since the velocity profile depends upon the temperature profile of the system and Correspondence: Dr. Pedro Arce, Department of Chemical Engineering, Tennessee Technological University, Cookeville, TN, USA 38505 E-mail: Parce@tntech.edu. Fax: 1931-372-6352 Electrophoresis 2005, 26, 2867–2877 2867  2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim General