Biomedical Engineering Reference
In-Depth Information
Exercise A.3.11.
he dielectrophoretic force on a dielectric sphere in a dielectric medium
given in
Equation 3.34
can be written as
3
2
F
=
2
π ε
r
Re{
K E
}
rms
m
where
K
is the complex Clausius-Mossotti function given by
ε
*
−
+
ε
*
p
m
K
=
ε
*
2
ε
*
p
m
where
ε
*
and
ε
*
are the complex dielectric constants of the medium and the particle, respec-
tively. he complex dielectric constants can be expressed as ε
σ
ω
* = −
i
(a) List two parameters that can be used in the design or operation of a device to increase
the DEP force for a target cell of a given size in a given medium.
(b) Write a computer script to calculate and plot the real part of the normalized Clausius-
Mossotti function as a function of frequency from DC to 1 GHz for the following
cases:
ε
(i) ε = σ, ε
m
= 2ε
p
(ii) ε = σ, 2ε
m
=ε
p
(iii) ε = 2σ, ε
m
=2ε
p
(iv) 2ε=σ,ε
m
=2ε
p
Exercise A.3.12.
(a) For a microchannel with dimensions
w
= 100 μm,
h
= 20 μm,
l
= 2 mm,
calculate the microluidic resistance. (b) What would be the resistance of four identical channels
with these dimensions in parallel?
Exercise A.3.13.
You would like to design a binary branching tree to distribute low evenly
across a large area. You would like to maintain equivalent low velocity at each level of the tree
while the width of channels is larger by a factor of 2 relative to the next level. By what factor
would you scale the length of the channels relative to the previous level?
Exercise A.3.14.
here are two rectangular PDMS microchannels which are fabricated by
sot lithography. he irst microchannel is 3.5 mm in length, 50 μm in width, and 75 μm in
height. he second microchannel is 4 mm in length and 60 μm in height. What should the width
of the second microchannel be to have an equal luidic resistance as the irst microchannel?
Exercise A.3.15.
Using
Equation 3.14
, calculate the radius of a circular-cross-section micro-
channel that has a length of 2 mm and a resistance of 7.0 × 10
11
N·s·m
−1
when illed with water
(η = 8.90 × 10
−4
Pa·s).
A.4 Suggested Exercises for Chapter 4
Exercise A.4.1.
Enumerate three advantages and three disadvantages of Afymetrix's oligonu-
cleotide microarrays. Repeat the exercise with Pat Brown's DNA microarrays.
Exercise A.4.2.
Sketch three diferent designs of PCR chips.
Exercise A.4.3.
Explain the basis of the ELISA-based microluidic pregnancy test.
Exercise A.4.4.
Assume a solid crystal-silicon cantilever (length = 100 μm, thickness = 1 μm,
width = 10 μm) vibrating in vacuum. What is the expected frequency shit when an average-
sized (dry) bacterium is deposited near the tip?
