Flow in a three-dimensional channel with a sinusoidally-wavy, vertical
wall is examined for the case of applied down- and cross-channel velo
city components. An important parameter for the analysis of the nature
of laminar mixing in the flow field occurs when the changes in the do
wnstream direction can be decoupled from the changes in the cross-chan
nel direction, thereby allowing for a two-dimensional solution of the
system of equations. This paper shows the effect on the nature of lami
nar mixing when the decoupling of the momentum equations from a fully
three-dimensional case to one where a two-dimensional solution can be
performed. Experiments are performed on a channel with sinusoidally va
rying vertical walls that cover the range of decoupling criteria. Sili
cone pigmented either white or black was run in the apparatus, cured,
and cross-sectioned. The cross sections embody a local, detailed histo
ry of the state of mixing as it proceeds down the mixer. The amount of
mixing is presented as a function of position at each cross section f
or the different channel configurations. The nature of mixing changes
from a linear growth rate in the amount of interfacial area to an expo
nential rate as the amplitude of the wave is increased. Results demons
trate the existence of chaos, islands, and the factors affecting the m
ixing behavior.