Biomedical Engineering Reference
In-Depth Information
Figure1.14
Microflow at a sudden widening of a channel cross-section: (a) Newtonian, or slightly
non-Newtonian, behavior, and (b) non-Newtonian behavior at a viscoelastic Mach number larger
than .
Microflow in curved channel may have recirculating regions. These recir-
culations can be used to concentrate cells or particles [24], or to enhance the
mixing of solutes [25]. The Dean number characterizes the possibility of having
recirculations
De U R R R R R
(1.29)
where
R
is the dimension of the channel and
R
c
is the curvature radius. For a suf-
ficiently large Dean number, a pair of vortices forms in the cross-section, carrying
flow from the inside to the outside of the bend across the center and back around
the edges (Figure 1.13).
Recently, the viscoelastic Mach number was introduced in order to predict the
distortion of fluid streamlines in microsystems under the effect of viscoelasticity
[26]. This number is defined by
=
ν
= Re
c
c
Mv Wi V C V V
(1.30)
where
C
s
is the viscoelastic wave speed. Distortions of streamlines appear for
Mv
>
1-2. An illustration is shown in Figure 1.14.
Walls of microsystems very frequently have electric charges; these charges spon-
taneously create an electrical double layer (EDL) in the adjacent fluid. Electro-os-
mosis makes use of this EDL to motion the fluid. The Dukhin number characterizes
the surface conductivity and deformation of the electric field by the conductivity of
the double layer; the Dukhin number is the ratio of the conductivity of the double
layer to that of the bulk fluid [27]
=
Re
=
=
η ρτ
=
ν τ
s
0
(1.31)
Du
=
σ σ
EDL
bulk
