Hydrogels are widely used to produce biomolecular separations in electrophoretic applications, where gel morphology and charge effects combine to produce the separation. Nanocomposite gels are poised to revolutionize this field in both improved handling characteristics and improved separations. Gel morphology and charge effects have traditionally been manipulated by varying the copolymer composition, but recent reports show that novel morphological changes can also be induced in the gel using templating methods and nanoparticle addition. To aid realization of the potential for novel electrically driven separations arising from such novel morphologies, we review here advances in materials development alongside a review of the directions in biomolecule/hydrogel electrophoretic transport modeling. Models for polyelectrolyte transport that are potentially useful for understanding novel behaviors caused by gel morphology are analyzed first. With the perspective of theoretical guidance, we then survey nanocomposite hydrogel morphologies keyed by the nanoparticle and matrix. Finally, we survey as well reports of dramatic improvements in the mechanical properties that may be the key to the early adoption of these new materials in biomolecular separation applications. For modeling, we have identified the different scales involved in biomolecular transport in these materials and provided a taxonomy of transport models that emphasize the role of gel morphology in determining both polyelectrolyte mobility and diffusion. Three aspects for future work unique to nanocomposite gel materials are described: (a) descriptions of the distribution of nanoparticles within the gels; (b) descriptions of the motion of the buffer solution that may include electroosmotic effects for nanoparticles with surface charges; (c) descriptions of the motion of the polyelectrolyte molecule inside the new gel material for a given application. These aspects will help to uncover further quantitative details about the ability of these gels to be tunable for differential mass transport of a given type of molecule. Standard gels, currently, lack a broad flexibility to increase the separation of biomolecules and, in general, are not tunable.

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.

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.

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The prediction of optimal times of separation as a function of the applied electrical field and cation valence have been studied for the case of field flow fractionation [Martin M., Giddings J. C., J. Phys. Chem. 1981, 85, 727] with charged solutes. These predictions can be very useful to a priori design or identify optimal operating conditions for a Couette-based device for field flow fractionation when the orthogonal field is an electrical field. 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 assessed [Oyanader M. A., Arce P., Electrophoresis 2005; 26, 2857]. Moreover, explicit analytical expressions are derived for the effective parameters, i.e. diffusivity and convective velocity as functions of the applied (orthogonal) electrical field. These effective transport parameters are used to study the effect of the cation valence of the solutes and of the magnitude of the applied orthogonal electrical field on the values of the optimal time of separation. These parameters play a significant role in controlling the optimal separation time, leading to a family of minimum values, for particular magnitudes of the applied orthogonal electrical field.

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.

Within the last decade, novel gel materials with a modified internal morphology have been synthesized and are available for a wide range of applications including drug delivery, separation of biomolecules with relevance in clinical diagnostics, electrokinetic pumping, and sensors 1-3 . One way to achieve this internal modification is to embed nanoparticles into the polymer matrix, so that when an electrical field is applied to the system, the presence of these particles can change the biomacromolecule transport through the gel, possibly altering the separation 4 . As a result, gaining a very deep understanding of the role that these nanoparticles can have on the separation efficiency in terms of electrophoresis techniques becomes very important. To the best of our knowledge, this contribution is the first effort that examines the role of morphology (in the form of a axially-diverging microdomain) on the prediction of optimal separation times for two protein models when they are subjected to electrophoresis. The research conducted predicts that the optimal separation time of a short, straight pore yields the best resolution in this type of electrophoretic separation.

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