Biomedical Engineering Reference
In-Depth Information
Problems
4.1
A bioengineer is given the task of making a larger scale model of flow through
an arteriole, with instructions to duplicate arteriolar
N
Re
in a 0.25-mm diam-
eter tube using a fluid with a 5-cP viscosity and 3.0 g/cm
3
density. For the ar-
teriole fluid, assume viscosity to be 3.25 cP, density to be 1.05 g/cm
3
, diameter
as 0.005 cm, and mean velocity to be 0.75 cm/s. What
U
mean
should be used
for the model?
4.2
Microfluidic devices (see Chapter 10) have attracted a great deal of attention
because of their applications in biology and biotechnology. The prevalence of
laminar flow in microfluidics enables new technologies. For a cross-sectional
rectangular channel that is 100 mm wide and 50 mm deep, and water flowing
at 1 mL/s, confirm whether a laminar flow exists in the device. The density of
the fluid is 1,060 kg/m
3
and viscosity is 10.23 g/m.s.
4.3
A parallel plate flow chamber (56
0.28 mm) is a common device used
to test the effect of shear stress on various cells. For this system and for New-
×
24
×
Q
bh
6
tonian fluids, show that
where
Q
is the volumetric flow rate,
b
is
τ
=
μ
w
2
the width of the chamber, and
h
is the height of the chamber. What is the flow
rate required to expose the cells to 15 dyne/cm
2
? Viscosity is 1.6 times water.
If cells are seeded and their average height is 15 mm, then what is the actual
shear stress on the cells?
4.4
A group of bioengineers are evaluating the adhesive strength of cells on a ma-
terial using a parallel flow chamber of 7.6
0.02 cm
3
. What is the shear
stress expressed on the wall, if the volumetric flow rate is 2 mL/min? Viscosity
of the flow fluid is 0.007g/cm/s at 37°C.
×
3.8
×
4.5
Cordeiro et al. [9] built a flow chamber to study the behavior of adhering
microcapsules exposed to wall shear stresses. The device consists of a poly-
methylmethacrylate (PMMA) block (120
8 mm) in which a groove in
the bottom part forms a channel of a 5-mm width, a 18-mm length, and a 0.4-
mm depth. The bottom of the channel is closed with a thin microscope glass
slide (thickness
×
60
×
24 mm
and an optical quality
surface. The device also had a slowly diverging area at the entrance and con-
verging area at the exit to facilitate the development of the flow. Since in vivo
shear stress values range up to 10-20 N/m
2
, they want to know the fluid flow
rate. Calculate the fluid flow rates needed to obtain the shear stresses.
=
170
μ
m) with dimensions 24
×
4.6
Ujiie [10] performed
pulsatile flow studies using pulse cycles of 5 seconds in
3-mm circular tubes. For the pulsatile condition, the mean
flow velocity varied
from 0.4 to 0.9 m/s. The solution density is 1.044 g/cm
3
and viscosity is 1.14
×
10
−2
g/cm.s.
(a) Calculate the range of Reynolds numbers for the pulsatile flow. Comment
on the type of flow
(b) Calculate the Woomersly number. Comment on the type of flow (10
points).
