Interdisciplinary Applied Mathematics

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complex microchannel geometries (Mitchell et al., 2000; Qiao and Aluru, 2002). They also investigated the validity of the Poisson-Boltzmann equation in nanochannels using molecular dynamics (MD) simulations and coupled these MD results with a modified hydrodynamic continuum model; see Chapter 12 and also (Qiao and Aluru, 2003b; Qiao and Aluru, 2003d), for details.

7.2 The Electric Double Layer (EDL)

Electrokinetic phenomena are present due to the electric double layer (EDL), which forms as a result of the interaction of ionized solution with static charges on dielectric surfaces (Hunter, 1981). For example, when silica is in contact with an aqueous solution, its surface hydrolyzes to form silanol surface groups. These groups may be positively charged as Si-OH+, neutral as Si-OH, or negatively charged as Si-O~, depending on the pH value of the electrolyte solution. If the channel surface is negatively charged (such as in    the    case    of    deionized    water),    the    positive    ions    are attracted    toward

the surface, and the negative ions are repelled from the surface, keeping the bulk of the liquid, far away from the wall, electrically neutral. A schematic of ion distribution in the buffer solution is shown in Figure 7.1. The ions of opposite charge cluster immediately near the wall, forming the Stern layer, a layer of typical thickness of one ionic diameter. The ions within the Stern layer are attracted to the wall with very strong electrostatic forces; hence they are immobilized near the charged surface, as demonstrated also by molecular dynamics studies (Lyklema et al., 1998). Immediately after the

Stern layer there forms the diffuse layer, where the ion density variation obeys the Boltzmann distribution, consistent with the derivation based on statistical-mechanical considerations (Feynman et al., 1977). Hence, the EDL consists of two distinct zones: Stern and diffuse layers. The extent of the EDL can be approximately predicted by the Debye length (Ad), which is defined as the distance from the wall, where the electrokinetic potential energy is equal to the thermal energy. The Debye length depends on the molar concentration of the ionized fluid, and its thickness Ad can be estimated using the Debye-Huckel parameter (w):

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