# Interdisciplinary Applied Mathematics

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Other assumptions and simplifications used in this simplified formulation are (Ermakov et al., 1999): 10

Conductivity    of    the    solution    (a)    is    uniform    throughout    the    liquid

volume.

Concentration of the buffer solution is large enough so that the EDL thickness on channel walls is negligible, compared to the channel dimensions.

The temperature of the solution is uniform, and Joule heating is insignificant (for details on Joule heating see Section 7.4.6).

Thermophysical parameters, such as the diffusion coefficients, fluid viscosity, electrokinetic mobilities, and dielectric properties are constant.

Despite its limitations, the simplified model is employed by most research groups for modeling the electrophoretic transport (Palusinski et al., 1986; Ermakov et al., 1992; Grateful and Lightfoot, 1992; Ermakov et al., 1994; Ermakov et al., 1998; Ermakov et al., 2000; Giridharan and Krish-nan, 1998; Krishnamoorthy and Giridharan, 2000). However, this model requires revisions for finite EDL effects, observed in low ionic concentrations in nanoscale channels. Such revisions should incorporate local charge distribution effects on electrophoretic transport; see Chapter 12. In addition, isoelectric focusing (IEF), which utilizes pH gradients, cannot be modeled using the current formulation. Numerical modeling of isoelectric focusing can be found in (Baygents et al., 1997; Mosher and Thormann, 2002).

###### 7.5.2 Classification

Electrophoresis is one of the most extensively utilized techniques for separation and/or characterization of charged particles, as well as biological molecules (Tseng and Chang, 2001; Kleparnik et al., 2001; Saur et al., 2001). For example, proteins, amino acids, peptides, nucleotides, and polynucleotides can be separated using electrophoretic techniques. Electrophoresis can be divided into three major categories. These are the moving-boundary, steady-state, and zone electrophoresis (Melvin, 1987).

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