region expands (Figure 4-1 e), then shrinks (Figures 4-1 f and 4-1 g), and finally diminishes to
the channel walls when the flow is completely dominated by the pressure-driven flow.
Since the combination of the pressure gradient and the electrokinetic force in the opposite
direction will always produce a local maximum, umax, in the u-profile at the neck, the condition
for which umax = 0 at x = -r is taken as the onset of the recirculation flow. To compute umax
for a given set of(K, a, h), the velocity profile at x = -r is computed at 10 locations in they-
direction. A polynomial fit for u(y) is then obtained based on those 10 data. A preliminary
location, y', of the maximum u is identified. The velocities at five location near y' are
computed using very small interval size and a much more refined polynomial fit is obtained for
the velocity profile near y'. Subsequent determination of the true maximum velocity, umax, and
its location, ymx contain very small interpolation error.
Figure 4-12 shows the velocity profiles at the neck as a function ofK used in Figure 4-11.
The data supports the conclusion that the onset of the recirculation bubbles starts when a flow
opposite to EOF appears at the neck.
By keeping K constant, we also examine the effects of the channel geometry represented
by the scaled wave amplitude (a) and the scaled channel width (h). When the gap between the
top wall and the neck of the wavy bottom wall becomes small, i.e. either a becomes large or h
becomes small, EOF dominates. Hence there is no backflow, and no recirculation exists in the
flow. In contrast, when a becomes small or h becomes large the pressure flow dominates and
recirculation occurs in the flow.
Figure 4-13a shows the geometric relationship between ( and h required for the onset of
recirculation at K = 2. The solid black line represents the physical boundary when the neck of
the wavy bottom wall touches the top wall, a = h. As a result, only the region below this line is