The electrokinetic process of soil remediation is affected by different transport driving forces that are responsible for the motion of the bulk fluid and solute species. In particular, the electro-mechanisms, that is, electroosmosis, electrophoresis, and electromigration, may compete with buoyancy and advection promoting distinct flow regimes. The earlier applications of electrokinetic phenomena, that is, electro-assisted drug delivery, micro-electrophoretic separations, and material processing, just to name a few, mainly in the area of electrophoresis, neglected this competition and therefore the hydrodynamics of electrokinetic systems was considered simpler. Field test results demonstrate that this is not the case with soil cleanup processes. The unique characteristics of soil porous media call for a different approach and are in need of further analysis. In this contribution, the basic aspects of the behavior of such a system are captured by using an annular capillary model. Under the proposed geometry, a differential model is formulated using simplifying assumptions to maintain the mathematical aspects to a minimum level, and a solution is presented for the different fields, that is, the temperature and the velocity. Several numerical examples are shown to portray the flow situations found in the system for a selection of values of the parameter space. From the analysis of these graphic representations, a qualitative and semiquantitative description of the different flow regimes inside the annular channel is obtained. Particularly interesting in this study is the inclusion of the resistive heating effect in the core of the annular capillary channel as a force term. Temperature developments are explained and analyzed under different scenarios. This information is useful to identify further aspects for the investigation and delineate a systematic approach for a more rigorous description. Implications for design of devices and cleaning strategies are also included. The results obtained in this study are useful to promote a deeper understanding of the behavior of the system, to have a better idea about the experimental effort needed for validation of the different trends, and to lead to important guidelines for improving the separation or cleaning efficiency in a given application.