Fluid dynamic behavior in nanochannels is dominated by the interactions between the channel surface and the fluid. An example of a particularly significant surface-fluid interaction involves the electric double layer. The electric double layer is a region of high charge density close to the channel surfaces, where counter-ions are attracted to the surface charge and co-ions are repelled. Electric double layer thicknesses are on the order of nanometers and can therefore significantly affect fluid flow at the nanoscale.

In this work, we develop a continuum model for the transport of charged, finite-size particles in electroosmotically driven flow that includes the effects of finite-thickness electric double layers. In our model, we assume a dilute solution of particles and a DC electric field applied along the axis of the channel. Under these assumptions, previous work has shown that the combination of cross-channel gradients in velocity and electric potential allows for a separation mechanism, where higher counter-ion charged analytes have faster velocities [1]. The model we propose extends this previous analysis, incorporating Taylor-Aris dispersion theory. By theoretical means and direct numerical simulation, we show that differences in particle size, and therefore in diffusivities, can enhance, diminish, or even reverse the separation behavior compared to the case of particles that have the same size but different charge.

To validate our model, we performed separation experiments on simple-cross, isotropically-etched, 5μm wide by 1μm deep fluidic channels. We injected buffered flow (10mM borate buffer, pH 9.2) seeded with charged polystyrene spherical particles (50 and 100nm diameter, fluorescently labeled) into a channel, and measured fluorescence intensity 15mm downstream from the injection point. Preliminary results showed that separation of charged particles in the nanochannels qualitatively matches our theory.

[1] “Free-solution oligonucleotide separation in nanoscale channels”, Pennathur, S., Baldessari, F., Santiago, J., et al. Analytical Chemistry, 79, 8316-8322, (2007).