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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