afterwards. As K increases toward infinity, the bubble diminishes to the channel boundary and
their size approximates asymptotically to zero.
Figure 4-15A shows the effect of the scaled wave amplitude (a) on the size of
recirculation region in a wavy channel. The Kvalue is set at 2 while h is fixed at 2.84. The
result indicates that recirculation occurs when a <1.31, but flow becomes recirculation-free
beyond the value. This result agrees with the discussion above on the onset of recirculation:
recirculation occurs at small a values, but not at large a values. The maximum size of the
recirculation region takes place when a = 1.08. The streamline patterns corresponding to a =
0.31, 0.91, and 1.19 are shown in the insets of Figure 4-15A.
The effect of the scaled channel width (h) on the size of recirculation region is also studied
(Figure 4-15B). The K value is set at 2 while a is fixed at 0.45. The flow is recirculation-free
until h = 2.0. Bubbles rapidly enlarge as h increases, and reaches to the maximum size at h =
2.2. As h further increases, the size of recirculation region slowly decreases and drops
asymptotically to zero.
4.5 Summary
Using the complex function and boundary integral formulation, an accurate method for
obtaining 2D electroosmotic flow in a wavy channel is developed. Effective slipping boundary
conditions are employed to decouple the electrostatic and hydrodynamic effects. Because of the
flexibility of the boundary integral formulation, this method is shown to be an effective and more
accurate alternative to the lubrication theory and perturbation method. Compared to the
approximate solutions using the lubrication theory, the restriction of a slow change in the wall
charge or geometry is removed in the present formulation so that the effects of arbitrary values of
a and h can be investigated.