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 accomplished 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 example, the design of separation processes as well as environmental applications such as soil reclamation and wastewater treatment. An illustration of how a secondary electrical field can aid in reducing the optimal separation time is included.

Design criteria for soil cleaning operations in electrokinetic remediation: hydrodynamic aspects in a cylindrical geometry.

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 semiquantitative 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.

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 analytical hydrodynamic velocity profile. Numerical illustrations, demonstrating the effect of the cross-sectional area of the annular region on the velocity field, have been included. 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 understanding of the role of the soil geometry in potential soil cleaning field operations.

Avoiding pitfalls in electrokinetic remediation: robust design and operation criteria based on first principles for maximizing performance in a rectangular geometry.

The role of the symmetrical conditions on the temperature field is studied in a capillary of rectangular geometry. By using the generalized flux, i.e., Robin-type of boundary conditions for the heat transfer in such a capillary domain, it is possible to identify clearly conditions under which the velocity field will depend crucially on the basic parameters and, therefore, what types of flow regimes may arise in the capillary channel. In addition, it is possible to conclude under what conditions the velocity field will not at all depend on some of these. The behavior is intimately tied to the symmetrical conditions associated with the temperature field in the system. A "skew" or asymmetrical parameter, W infinity, has been identified in the temperature profiles; this parameter is useful for studying the role of the symmetrical conditions on the hydrodynamics field and in determining a set of a priori design criteria that limits the range of values of the parameters. Several numerical examples are presented to show the flow situations found in the system.