Numerical simulation is used to calculate the electrophoretic mobility of a charged spherical nanoparticle confined in a nanochannel, under a weakly applied electric field. Classic models for electrophoretic mobility are valid only in the linear regime of small particle zeta potential, and for an unbounded fluid domain. However, these models fail to predict the electrophoretic mobility measured experimentally in bounded nanochannels. We adopt asymptotically-expanded formulations and solve the fully-coupled equations on a 3D finite element domain. Factors affecting particle mobility include electrolyte concentration, channel size, and zeta potentials on both the particle surface and channel walls. Specifically, spherical particles are examined with diameters 2 a = 10 and 50 nm, in a 100 nm high channel. The non-dimensional electric double layers were varied between 0.1 < ka < 100. The results indicate that the mobility of a particle located at the nanochannel centerline agrees to within 1% of the average mobility of a particle distributed transversely throughout the nanochannel. Furthermore, confinement by the nanochannel walls was found to affect greatly nanoparticle mobility. As a result, it is feasible to use nanochannels to separate two different size nanoparticles, even when the particles have equal zeta potentials. Finally, a new method is proposed to estimate accurately particle and wall zeta potentials by contrasting the observed differences in mobility in two different height channels.

Next, two-dimensional nanorods are simulated numerically to study the electromigration within nanoscale fluidic channels. We improved on an existing steady-state model to include fluid-structure interaction and capture dynamics of moving nanorods. Specifically, we investigate the motion of a 2 nm x 3.4 nm two-dimensional rod-like particle (representative of 10 bp DNA) in a 100 nm two-dimensional channel under an applied external electric field. The results show that due to the interaction between the electric double layers (EDLs) of the particle and the channel walls, the particle is confined to the centerline of a channel with thick EDLs. In contrast, an oscillatory motion is observed for thin EDLs, which can be explained by examining the electrophoretic and hydrodynamic forces and moments on the particle. Although thermal fluctuations are not modeled, and could negate the effects of the oscillatory motion in practical systems, the effect is still of value to understand. We calculate the electrophoretic mobility of these confined nanorods and compare the results with the approximated mobility from our steady-state model. Although the thick EDL systems match well, the results show an up to 10% difference in mobility of the two models for the 50 mM electrolyte concentration, which indicates that the fluid-structure interaction is important for mobility of non-spherical particles, in thin double-layer systems.

Finally, we use our model to estimate particle zeta potential by measured mobility from several experiments. The results show that our model is required to capture double layer polarization and double layer interaction. In addition, the composition of electrolyte solution is important in determining the particle mobility as well as the zeta potential.