Electrophoretic motion of a charged porous sphere within micro- and nanochannels is investigated theoretically. The Brinkman model and the full non-linear Poisson-Boltzmann equation are adopted to model the system, with the charged porous sphere resembling polyelectrolytes like proteins and DNA. General electrokinetic equations are employed and solved with a pseudo-spectral method. Key parameters of electrokinetic interest are examined for their respective effect as well as overall impact on the particle motion. We found, among other things, that the confinement effect of the channel can be so drastic that 75% reduction of particle mobility is observed in some situations for a poorly permeable particle. However, only 15% for the corresponding highly permeable particle due to the allowance of fluid penetration which alleviates the retarding shear stress significantly. In particular, an intriguing phenomenon is observed for the highly permeable particle: the narrower the channel is, the faster the particle moves! This was experimentally observed as well in the literature on DNA electrophoresis within nanostructures. The reason behind it is thoroughly explained here. Moreover, charged channels can exert electroosmosis flow so dominant that sometimes it may even reverse the direction of the particle motion. Comparison with experimental data available in the literature for some polyelectrolytes is excellent, indicating the reliability of this analysis. The results of this study provide fundamental knowledge necessary to interpret experimental data correctly in various microfluidic and nanofluidic operations involving bio-macromolecules, such as in biosensors and Lab-on-a-chip devices.

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Electrophoretic behavior of a charged porous sphere normal to an air-water interface is investigated theoretically. The charged porous sphere is a very popular model of DNA and proteins, among other polyelectrolytes, based on the experimental observation of the DNA and protein conformations in a free solution. Two major motion-deterring effects are thoroughly investigated in particular: the boundary effect due to the presence of an air-water interface and the double layer polarization effect due to the convection-induced ion flux redistribution. The presence of the air-water interface is found to reduce the particle mobility in general, especially when the double layer is very thick or the particle is close to the interface. This boundary effect diminishes as the double layer gets very thin. However, an interesting phenomenon is observed that a particle closer to the interface may actually move faster than a farther one under some circumstances. The reason behind this phenomenon is attributed to the interaction between the boundary and polarization effects. This is demonstrated with evidence of corresponding contour plots. Convenient charts of correction factors are provided to facilitate the usage by interested experimental researchers.