amplitude is approaching to the channel width (a/h "-1), the gap between the top and bottom
walls diminishes and the flow rate drops close to zero.
4.4.3 Similarity between Flow Velocity and Electric Field
The similarity between the flow velocity and the electric field is examined and shown in
Figure 4-8. The data suggests a high similarity between the plot of the electric field and the
streamline pattern. This similarity also exists between the electric field vectors and the velocity
vectors.
The similarity between the electric field and the EOF velocity field of arbitrary channel
geometry has been mathematically and experimentally verified.80'100 The following assumptions
are made for verification, including (1) the channel walls possess a constant uniform zeta
potential; (2) no singularity exists at channel wall profile; and (3) there is a negligible applied
pressure gradient in EOF.
Since E = -Vq, Poisson equation (Equation 4-9) is rewritten as
VE= 0. (4-47)
According to Faraday's law of induction, the curl of an electric field equals to the vector
rate of decrease of magnetic flux density with time, which is typically negligible in EOF. Hence,
the curl of the electric field is zero,
Vx =0 (4-48)
For channels with uniform zeta potential, the boundary conditions in Equations 4-16 and 4-
18 become
walls walls (4-49)
and
0(4-50)
waiws (4-50)