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Simulation of Electrokinetic Flow and Analyte Transport in Nano Channels

J.J. Feng, S. Krishnamoorthy, G.W. Wang and S. Sundaram
CFD Research Corporation, US

nanochannel, electrokinetics, transport, separation by valence

This paper demonstrates the electrokinetic flow and transport of charged and neutral analytes in nanochannels by solving full system of governing Poisson-Nernst-Planck equations without any assumptions. The issues related to the spatial and time scales are resolved using first-order perturbation approach1. The simulations are used to demonstrate charge-based separation of analytes in nano-channels. The transport at nano-channels is markedly different from that occur in microchannels. The most notable feature at the nanoscale is the dominance of the electric field transverse to the flow direction, which could significantly affect the EOF and analyte transport. This field arises due to the surface zeta (z) potential. When the z potential is strong or the background electrolyte is weak, the electric double layer may be considerably thick and overlap. In addition, the conductance of nanochannels is regulated by surface charge at low ionic strength, and by the geometry and bulk ionic concentration at high ionic strength2. When double layer occupies significant portion of the channel, the velocity profile will be no longer plug shaped, and the local electrostatic force may potentially expel counterions (to the surface charge). In addition, modifying the surface charges or varying the applied electric field can also facilitate charged-based separation1, 3, 4. In this paper, we will demonstrate a valence based separation systems.
The electrokinetic fluid flow and analyte transport are described by continuum or molecular model. The continuum model assumes that the transport coefficients are independent of position and time, and that the macroscopic state variables do not vary appreciably in the system and can be derived from statistic models of molecular level. We will use continuum based model description since the length scales are larger than 5 nm and the time scale is greater than 1 ns. We assume that the surface charge or the z potential is arbitrary. Hence, instead of solving Poisson-Boltzmann equation, we use Poisson-Nernst-Planck equation to calculate ionic flux, which is general enough to describe extreme situations of overlapping double layer. The fluid flow is solved using incompressible Navier-Stokes equation, taking account of body forces that arise from charged ionic species subjected to an electric field. The finite volume method is used for solving the governing equations.
The numerical method is validated against the results obtained from a high order compact finite difference method (Figure 1) for an 1D electroosmotic flow with various z potentials and double layer thickness. The interacting double layer for two colloidal spheres is simulated and shown in Figure 2. To illustrate application in nano-electrophoresis, we investigated separation of neutral and negatively charged species injected into a nanochannel. Figure 3 shows the prototype device comprising of a nano channel array that connects two reservoirs. The axial flow is driven by external electric field. The EOF velocity and the overlapping of double layer are shown. The concentration field of species is shown for t=0 and 0.1s and the separation is observed even within a short period of time. The numerical simulation can be applied to study a variety of nano electrokinetics and species transport problems quantitatively.

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