The applications of electrokinetics embrace a large family of important industrial, pharmaceutical, biomedical, and environmental applications. Processes such as separation, drug delivery, soil remediation, and others constitute alist of applications where electrical fields are used to induce the movement of solute species. Different transport driving forces participate in the motion of the solute. In the particular case of soil remediation, the electromechanisms may compete with buoyancy and advection, promoting distinct flow regimes. As a rule of thumb, some of the earlier applications of electrokinetic phenomena, mainly in the area of electrophoresis, neglected this competition, and therefore the hydrodynamics of the systems was considered simpler. The nature of the process in soil, a porous media, calls for a different approach and is in need of further analysis of the complete map of collaborating driving forces. The identification and analysis of the characteristic flow regimes may lead to important guidelines for improving the separation, avoiding the mixing, and more efficient cleaning in a given application. In this contribution, using a cylindrical capillary model, the basic aspects of the behavior of the system are captured. A differential model is formulated using simplifying assumptions, maintaining the mathematical aspects to a minimum level, and a solution is presented for the different fields, i.e., the temperature and the velocity. Based on the selection of values of the parameter space, several limiting cases and flow regimes are presented and discussed. Implications for the design of devices and cleaning strategies are also included. Needs for further research are identified. The main idea behind the study is to obtain a qualitative and semi-quantitative description of the different flow regimes inside the channel. This information is useful to identify further aspects of the investigation and delineate a systematic approach for a more rigorous description. More specifically, the authors believe that the results obtained in this study are useful to promote a deeper understanding of the behavior of the system and to have a better idea about the experimental effort needed for validation of the different trends.