physically possible in terms of the channel geometry. The curve with circles splits entire
parameter space into two zones: a recirculation zone below the curve and a recirculation-free
zone between the curve and the solid line. The circles represent the data obtained from the
solution. The curve starts from (a = 0, h = 2) and approaches to the physical boundary as h
increases. The wavy channel of a = 0.45 and h = 2.84 described in Figures 4-9e and 4-9f does
fall in the recirculation zone, consistent with the result shown in Figure 4-13a.
Note that the intercept (h0 value when a = 0) of the curve corresponds to a channel of
constant cross sectional area, in which the flow velocity at the centerline is zero due to the fact
that the maximum velocity of a pressure flow (Umax = PH2/(8k/L)) is equal to the EOF velocity
(Ueo = ro/L ). Equating umax to ueo results in h0 = f/K This equation can be used as the
starting point of the calculation for the K curves, which separates the recirculation zone from the
recirculation-free zone for the given K value.
The exploded view of the K curve near the intercept is shown in the inset of Figure 4-13a.
The solid line is based on the calculated velocity profile at the neck, while the dashed line is
based on the velocity profile at the trough of the wavy channel. They coincide at h = 2, but the
onset conditions of recirculation are slightly different, depending on the location and geometry of
the channel. As shown in Figure 4-1 Ic, flow recirculation is observed only at the neck, but not
at the trough of the channel when a = 0.015, h = 2 with K = 2. As a result, the diagrams in
Figure 4-13 are generated by using flow reversal at the neck as the criteria of flow recirculation.
Figure 4-13b shows the dependence of the onset of flow recirculation on the applied forces
represented by the dimensionless parameter K. When K is small, EOF dominates and it is
difficult to have recirculation in the flow. When K is large, pressure flow dominates,
recirculation easily occurs. The plot provides a means to determine the geometry and external