# Interdisciplinary Applied Mathematics

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The main simplifying assumptions and approximations are as follows:

1. The fluid viscosity is independent of the shear rate; i.e., Newtonian fluid is assumed.

2. The fluid viscosity is independent of the local electric field strength. This condition is an approximation. Since the ion concentration and the electric field strength within the EDL are increased, the viscosity of the fluid may be affected. However, such effects are neglected in the current analysis, which considers only dilute solutions; in Chapter 12 we consider such effects for nanochannels.

3. The Poisson-Boltzmann equation (7.4) is valid. Hence the ion convection effects are negligible.

4. The solvent is continuous, and its permittivity is not affected by the overall and local electric field strength.

5. The ions are point charges.

###### 7.4.1 Channel Flows

In this section mixed electroosmotic/pressure-driven flows in straight microchannels are analyzed for channel heights (h) much smaller than the channel width (W). Therefore, the flow can be treated as two-dimensional,

y*=1

FIGURE 7.6. Schematic view of a mixed electroosmotic/pressure-driven flow channel. The inlet and exit portions of the channel have negligible electroosmotic effects.

as shown in Figure 7.6. For simplicity, fully developed steady flow with noslip boundary conditions is assumed. The streamwise momentum equation is

‘£=^d^+peEx    (722)

where u is the streamwise velocity and Ex = —йф/dx. Using equation (7.7) and (7.4) for pe we obtain

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