Typically, an asymptotic behavior, 91 int u( ~ a2 /2 +a / + ., is clearly
established for 1 > 10ff. For |1 > 100;, the asymptotic approximation becomes a very accurate
representation of the integrand. Hence, to ensure sufficient overall accuracy, L,,t = 1,0247n is
1 a+
used and 91 -i int u()d 2--. The constant a2 depends on {, K, a, h} but can be
i Lint
4nt nt
reliably determined for each set of position, flow condition, and geometric parameters via a
simple polynomial fit for large values of || using 1/ II as a variable. The leading order
asymptotic error of the integration is estimated to be which is close to 108 for a < 0.8 (as
is the case in the present study) and L,nt = 1,0247t.
The detailed solution procedures for 0, in Equation 4-45 are provided in the Appendix C.
4.4 Results and Discussion
4.4.1 Electric Potential
The electric potential distribution in a wavy channel depends on the scaled channel width
(h) and the scaled wave amplitude (a) as illustrated by the plot of equipotential lines (Figures 4-
3 and 4-4). The plots are based on the assumption that a fluid with uniform properties is filled in
the channel, a uniform zeta potential exists on the channel walls.
Figure 4-3 shows the variation in the electric potential distribution as a function of a
while the h is fixed at 2.5. The baseline is in Figure 4-3a when the wave amplitude is zero (i.e.,
the bottom wall is also flat). The exact solution gives a series of equidistant parallel lines normal
to the channel walls. Therefore, the electric field strength is uniform with the same magnitude
along walls, as shown in Figures 4-3e (top wall) and 4-3f (bottom wall) when a = 0. When the