Biomedical Engineering Reference
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FIGURE 3.10
Vortex structure of the secondary flow generated by the waviness of the pore
and helicity of the perfusion flow. The higher the Dean number is, the stronger
the vortex is. As the fluid spins in the curved channel, a control mass of
fluid travels in the transverse direction, eventually reaching the outer wall,
where it must change direction toward a return path. Such a transverse mass
transfer produced by this secondary flow, from the axis of the pore toward
the wall where the cells are localized, is likely to highly supplement diffusion
effects.
These results, calculated for the same reference values of the parameters,
are significantly different from those obtained with a one-dimensional ana-
lytical approach (equation 3.22) where higher amplitudes and more uniform
distribution in downstream direction of the oxygen concentration were found.
Indeed, the presence of stagnation zones in the flow field within such a crenel-
lated duct leads to a drastic decrease in local concentration in the stream wise
direction, as revealed by the waviness of the profile given in Figure 3.12.
Moreover, such a flow generates in the vicinity of the fiber surface a non-
unidirectional and nonhomogeneous repartition of viscous stresses, the mag-
nitude of which is of the order of 10 3 -10 2
Pa on the major part of the
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