First International Conference on
Microchannels and Minichannels
April 24-25, 2003, Rochester, New York, USA
ICMM2003-1124
EXAMPLES OF MICROCHANNEL MASS TRANSFER PROCESSES IN BIOLOGICAL SYSTEMS
Satish G. Kandlikar, [email protected]
Mark E. Steinke, [email protected]
Mechanical Engineering and Microsystems Engineering Department
Rochester Institute of Technology
Rochester, NY 14623
ABSTRACT
Heat and mass transfer processes become highly efficient
as the channel hydraulic diameter is reduced in size. Biological
systems, such as human body, rely on the extremely efficient
transport processes occurring at microscale in the functioning
of its vital organs. In this paper, the transfer processes in lungs
and kidneys will be reviewed. Although the flow in the
microchannels present in these organs is laminar, it yields very
high mass transfer coefficients due to the coupling of small
channel diameters. Furthermore, the molecular transport
mechanisms occurring across the membranes at nanoscales
through diffusion controlled processes also become extremely
important. Understanding these transport processes will enable
us to develop more efficient artificial organs and processes that
closely mimic the performance of the natural systems. These
ideas can be extended to other microscale system designs in
different technologies, such as IC cooling and MEMS micro
fuel cells.
R
Re
T
Sh
V
−
V
z
Greek
φ
µ
ν
ρ
Gas Constant ( = 8.31434 J/molK )
Reynolds number ( = GDh / µ )
Temperature ( °C )
Sherwood number ( = hmDh / DAB )
Velocity ( m/s )
Partial molar volume ( = RT/P )
z-axis
Electrical potential ( V )
Viscosity ( Ns / m2 )
valence
Density ( kg/m3 )
Subscript
A Species A
i
Species i
s Surface
∞ Bulk fluid
NOMENCLATURE
A Area ( m2 )
C Concentration ( kg/L )
Co Poiselle number
d Diameter ( m )
DAB Diffusion coefficient of species B in species A ( m2/s )
Dh Hydraulic diameter ( m )
Do Diffusion coefficient at infinite dilution ( m2/s )
E Potential ( V )
E0 Standard reduction potential ( V )
f Friction factor
F Faraday constant ( = 9.648531 x 104 C/mol )
G Mass flux ( kg/m2s )
h Heat transfer coefficient ( W/m2K )
hm Mass transfer coefficient ( m/s )
k Thermal conductivity, W/mK
l, L Length ( m )
m& Mass flow rate ( kg/s )
n Number of electrons
N'' Molar flux ( kgmol/m2s )
Nu Nusselt number ( = hDh/k )
P Pressure ( Pa )
INTRODUCTION
The advancement in our understanding of transport
processes in microchannels and its integration with the
Integrated Circuits (IC) and Microelectromechanical Systems
(MEMS) fabrication technology is opening new frontiers in
many fields, including bioengineering. Although the heat,
mass and momentum transfer processes have fundamental
similarities, their effective utilization occurs in different ranges
of channel hydraulic diameters. As an example, for effective
transfer of natural gas over long distances, the most economic
pipe diameter is found to be on the order of one or two meters.
For heat exchangers, the channel size is approaching a few mm
in compact. Applications such as automotive, aviation, and
spacecraft, or in applications where extremely high efficiencies
are desired from process considerations, such as air
liquefaction and separation processes are realized. On the other
hand, in biological mass transfer systems, such as lungs,
kidneys, brain and liver, we find channels with only tens of
micrometers in hydraulic diameter. Figure 1 shows the range
933
Copyright © 2003 by ASME
diameters of 3 – 25 µm in biological mass transfer systems.
Figure 3 shows the effect of diameter upon the pressure drop,
for a given velocity and blood flow.
of channel dimensions found in different systems. In biological
systems shown, the main mass transfer process occurs in
channels in 3 -100 µm range.
I
Aorta
Refrigeration
Evaporators/
condensers
2.5 mm
Henle’s
loop
Tubules
II
Alveolar Alveolar
sacs
ducts
Large veins
and arteries
25 mm
m
Electronics
Cooling
250 µm
Mass Convection Coefficient, h
Power
Condensers
( m/s )
Compact Heat
Exchangers
Boilers
III
Capillaries
25 µm
2.5 µm
Figure 1: Ranges of channel diameters employed in various
applications.
1E-06
1E-07
1E-06
1E-05
1E-04
1E-03
(1)
1E-02
V = 0.0001
V = 0.001
1E+04
( kPa/m )
V = 0.01
1E+02
1E-02
1E+00
1E-04
1E-06
1E-06
2d
1E-05
1E-04
1E-03
1E-02
Diameter ( m )
where ρ is the density of the fluid, V is the mean velocity, d is
the channel diameter, and f is the friction factor given by the
flowing equation for laminar flow:
Co
f =
Re
1E-05
Figure 2: Variation of the mass transfer coefficient for
Potassium as a function of channel dimensions; laminar
flow with D012 = 1.96 x 10-9 m2/s, Sh = 3.66 in standard
blood.
where hm is the mass transfer coefficient in m/s , d is the
channel diameter in meters, and D12 is the mass diffusivity of
species 1 in a mixture of species 2. For the transfer of
potassium ions at infinite dilution, the variation of hm with d is
shown in Figure 2. It can be seen that the mass transfer
coefficient increases rapidly with the decrease in the channel
diameter d. Extremely high mass transfer coefficients are
obtained for channels in the range of 3-25 µm.
However, the pressure drop increases significantly with the
reduction in channel dimension. The pressure drop relation is
given by the following equation:
dp 4 fρV 2
=
(2)
dL
1E-04
∆P / L
3.66 D12
d
1E-03
Diam eter ( m )
The flows in microchannels, channels smaller than 200
µm, are generally laminar; see the channel size classification as
defined by Kandlikar and Grande [1]. The Sherwood number
for the mass transfer process with a constant wall concentration
can be considered as constant at 3.66, Bronzino [2]. The mass
transfer coefficient variation with the channel diameter is given
by the following equation:
hm =
1E-02
Figure 3: Pressure Gradient dP/dz as a function of
diameter, for a given mass flux for three velocities, for
blood flow in capillaries and arteries. Co = 16, V = 0.0001,
0.001, and 0.01 m/s.
(3)
As the channel dimension decreases, the pressure gradient
increases considerably. At the same time, the flow rate
decreases in square proportion to the diameter for the same
velocity. As a result, the passage lengths have to be quite
small, and the flow velocity also is quite low for the channel
934
Copyright © 2003 by ASME
typically 7 µm in diameter. The respiratory membrane is
composed of several layers. They include a surfactant layer
that reduces the surface tension. Another layer is a thin film of
fluid to coat the surface. The next layer is the alveolar
epithelium cell layer. Next, there is a layer of interstitial fluid.
The blood capillary wall is comprised of a layer referred to as
the basement and a layer of endothelial cells. The respiratory
membrane layers can be seen in Figure 4.
The flow rates and volumes for the lung will be considered
at rest conditions. The concentration of different gasses within
the lung is determined using Henry’s law and the partial
pressure within the lung. The pulmonary flow rate is 5.0 L/min
with a head pressure of 1.6 kPa. The blood capillary length is
100 µm and the blood volume is 1.0 L, with a transient time of
0.3 seconds. Finally, the blood film thickness varies between 5
to 10 µm.
There has been a great deal of work and publication in the
area of transport in the lung. These publications go into much
greater detail with regards to the transport properties, structure,
and mechanisms that appear in respiratory physiology. An
excellent reference used for many introduction courses on this
topic is West [4].
OBJECTIVES OF THE PRESENT WORK
The present work is aimed at exploring opportunities and
challenges in applying microchannel theory to biological
applications. Some of the issues involved in making the
artificial organs are addressed. The present work provides the
basic information related to the biological systems and
compares it with those in the artificial organs. Specific
opportunities available in integrating the technological
developments in IC technology and MEMS are discussed in an
attempt at providing a roadmap for future development in this
area.
TRANSPORT IN THE LUNG
The primary functions of the lung can be generalized as the
transport of oxygen into the blood steam, and the removal of
carbon dioxide.
The different regions of the lung, the
bronchiole, alveolar duct, atrium, and alveolar sacs all have gas
flows that could be considered as minichannel flow ( 3 mm ≥
dh >200 µm), or microchannel flows (200 µm ≥ dh > 10 µm).
Below 10 µm diameters, the compressibility effects become
important in gas flows, but liquid flow remain unaffected. For
the purposes of this paper, only the transport within the alveolar
sacs will be considered.
1
3
5
RESEARCH OPPORTUNITIES
The single-phase gas flow in the lung structure is quite
complex. The flow of the gas into daughter branches is
accomplished to provide uniform flow of gas to each of the
alveolar sacs. This is an extremely difficult feat to achieve
through the design of manmade systems. Considering the flow
in a natural system, the flow is always in a transient mode, with
flow reversal occurring at each cycle. The flow uniformity is
maintained within a tight band over the wide range of flow
rates encountered during different metabolic rates dependent on
the body activity levels. Design of the branching architecture
poses a major challenge in single and two-phase heat
exchangers and mass transfer devices. Simple branching in the
header of a heat exchanger under different flow conditions is
quite difficult to achieve. Understanding the lung structure
from flow standpoint, with the resiliency built in the flow
passage walls, provides a great learning opportunity from the
natural biological systems.
The lungs often encounter two-phase flows as in the case
of medicine transport through aerosol inhaling devices. The
liquid droplets containing medicine are desired to reach the
alveoli with a somewhat uniform distribution. Deposition of
droplets near the bronchiole and the alveolar duct is
undesirable. However, avoiding this deposition as the gas
flows under reversing conditions, through the branches and
passages is a major challenge. Several researchers have made
progress in fundamental understanding in the area of aerosols.
For example, Ferron and Edwards [5] have studied particle
transport in the conducting airways. Henry et al. [6] have
developed a new model for aerosol transport based upon acinar
flow.
7
Alveolus
Capillary
2
4
6
Figure 4: Respiratory Membrane. Comprised of: 1)
Surfactant Layer, 2) Fluid Layer, 3) Alveolar Epithelium, 4)
Alveolar Basement, 5) Interstitial Fluid, 6) Capillary
Basement, and 7) Capillary Endothelium.
The alveoli provides the means of gas exchange. There is
approximately 1 to 2.5 million of the alveoli sacs within the
lung. Each alveoli sac is approximately 100 µm in diameter.
The alveoli are surrounded by a thin membrane that varies in
thickness from 0.1 µm to 1.0 µm, depending upon its location.
The membrane is called the respiratory membrane and is an
interesting transport subject. The membrane controls the
transfer of oxygen from the alveolus to the blood capillary and
the transfer of carbon dioxide (CO2) from the blood capillary to
the alveolus. The membrane surface area totals approximately
70 m2. The capillaries that surround the alveolar sacs are
935
Copyright © 2003 by ASME
Another instance of two-phase flow occurs when direct
liquid dousing is utilized in the application of surfactant
delivery. This area of research also has a great deal of
researchers making progress. Cassidy et al [7] have modeled
the transport of surfactants while the air passages are closing.
Conversely, Ghadiali and Gaver [8] have modeled the transport
when the passages open. In each case, the modeling of the
transport in these capillary passages has been discussed. Many
other researchers have developed the transport fundamentals.
The glomerulus in the Bowman’s corpuscle is where the
bulk filtration of blood plasma occurs. Each of the corpuscles
experience a flow rate that is comparable to the total blood flow
rate of 125 mL/min. The pressure within the corpuscle is
around 9.33 kPa. The outlet pressure is around 1.87 kPa. The
osmotic pressure governs the diffusion at this location. In
addition, the glomerulus is around 25 times more permeable
than other membranes. There are a number of species that are
transported across the membrane; sodium, chlorine, and
potassium are mentioned in the following discussion just as
examples.
The proximal tubule is the next section in the nephron.
The pressure in this section is generally 1.87 kPa. The total
flow rate begins at 125 mL/min and falls to around 20 mL/min.
Each proximal tubule has a length of 14 mm and a diameter of
30 µm. The resulting proximal Reynolds number is 0.76. The
three main mass transport mechanisms at work in this section
are active diffusion, passive diffusion, and osmosis. Sodium
ions are actively diffused in this section. The passive diffusion
can be seen in the transport of chlorine ions. The third
transport is osmosis and is used by water.
The Loop of Henle is the section where the majority of the
dialysis is performed. The loop is made of a tube that is
significantly smaller in diameter than the preceding proximal.
The loop continues at the smaller diameter and then enlarges as
it exits into the next section. The total flow rate slows to 20
mL/min while in the loop. The thinner sections of the loop
have a diameter of 12 µm. The other section of the loop has a
diameter of 20 µm. In the descending limb, the sodium ions
are moved with passive diffusion. The medullar region in the
descending limb is hyperosmotic, which causes water to flow
out. In the ascending limb, sodium is transported out via active
diffusion. Water does not pass through this membrane because
the membrane is impermeable to water.
The distal tubule is the next section of the nephron. The
distal has a diameter of 20 µm. The pressure in this section is
0.80 kPa. The flow rate in this section drops from 20 mL/min
to approximately 5 mL/min.
The collecting duct is the final section of the nephron. It is
also referred to as the Bellini duct. The collecting duct is
common for all of the individual nephrons. The diameter of the
collecting duct is 100 µm. The pressure in the tube is 0.267
kPa. The flow rate slows to 1 mL/min.
The nephron shows a common trend. The majority of
transport that takes place in this functional unit is mass
transport by means of diffusion and osmosis. Using very small
microchannels maximizes the dialysis process. The sections of
the nephron are summarized for length, diameter, flow rate, and
Reynolds number in Table 1, as compiled from Cooney [3] and
Brenner and Rector [9]. The surface area in each nephron is
quite large at 9.86 x 10-6. The total surface area made from all
of the nephrons is between 9.86 m2 to 24.7 m2, depending upon
the number of nephrons that are present in a kidney.
TRANSPORT PROCESSES IN THE KIDNEY
The function of the kidney can be divided into three main
processes. The first process is the ultra-filtration of the blood
plasma to remove major byproducts and contaminates. The
second process is the reabsorbing of ions and water. The third
process is the secretion of ions. The nephron is the main
functional unit of the kidney. All three of these processes take
place in this unit. There is approximately 1 to 2.5 million
nephrons in a typical kidney. The two types of nephrons are
the juxtamedullary and the cortical. The nephron is made up of
the Bowman’s corpuscle, Loop of Henle, and collecting duct.
The nephron can be further broken down into elements that will
describe the channel size and transport processes. Figure 5
shows the six portions of the nephron, as adapted from Cooney
[3]. The components are the Bowman’s corpuscle, Proximal,
Loop of Henle, Distal, and Collecting Duct. The peritubular
capillaries are also shown in Figure 5. The peritubular
capillaries constitute the other side of the membrane transport.
From
Artery
To
Renal
Vein
Renal
Filtration Process
1
4
5
2
3
6
Dialysis Process
(reabsorption and secretion)
Figure 5: Nephron of the Kidney. Components include; 1)
Bowman’s corpuscle, 2) Proximal, 3) Loop of Henle, 4)
Distal, 5) Collecting Duct, and 6) Peritubular Capillaries.
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Copyright © 2003 by ASME
Table 1: Hydraulic Properties of the Nephron; [3, 9].
P
(kPa)
Q
(cc/min)
Ac
( m2 )
G
(kg/m2s)
L/D
As
( m2 )
Proximal Tubule
Loop of Henle
Descending Limb
Ascending Thin Limb
Ascending Thick Limb
Distal Tubule
Collection Tubule
0.014
0.02
0.010
0.004
0.006
0.012
0.022
30
12
12
20
20
100
30
1.870
1.25E-04
7.07E-10
3.02
0.76
467
1.32E-06
1.537
1.203
0.870
0.800
0.267
1.25E-04
2.00E-05
2.00E-05
5.00E-06
1.0
1.13E-10
1.13E-10
3.14E-10
3.14E-10
7.85E-09
18.86
3.02
1.09
0.27
2173
1.89
0.30
0.18
0.045
1811
833
333
300
600
220
3.77E-07
1.51E-07
3.77E-07
7.54E-07
6.91E-06
Mass Convection Coefficient ( m/s )
d
(µm)
Re
Location in Nephron
L
(m)
3.0E-03
Hydrogen Ion
a)
Table 2: Ions of Interest - Diffusion Coefficients at Infinite
Dilution and Ionic Diameters; [3, 6].
Sodium Ion
2.5E-03
Potassium Ion
Calcium Ion
2.0E-03
Ion
D0
Substance ( cm2/s )
Magnesium Ion
Chlorine ion
1.5E-03
H+
Na+
K+
Ca2+
Mg2+
ClHCO3HPO42PO43SO42O2Glucose
Sucrose
Urea
Water
Bicarbonate Ion
1.0E-03
5.0E-04
0.0E+00
0
20
40
60
80
Location Along Nephron ( mm )
Hydrogen
Phosphate Ion
Phosphate Ion
7.0E-04
Mass Convection Coefficient (m/s)
b)
6.0E-04
Sulfate Ion
5.0E-04
Oxygen Ion
4.0E-04
Pore
Glucose
Urea
2.0E-04
(
1.0E-04
20
40
60
Location Along Nephron ( mm )
8.00
)
where NA” is the molar flux, hm is the mass convection
coefficient, CA,s is the concentration of species A at the surface,
and CA,∞ is the concentration of species A in the bulk fluid.
The previous equation can be multiplied by the molecular
weight of species A to get the mass flux, Equation 5.
G A = hm ρ A, s − ρ A,∞
(5)
0.0E+00
0
-
2.48
3.28
1.98
1.44
3.62
4.15
4.73
3.80
4.00
2.72
7.20
8.80
3.20
3.00
The mass transfer coefficients can be computed for the
blood flow in the nephron. Several ions of interest are used to
determine their mass transfer coefficients. Equation 4 governs
the diffusion of the ions in the nephron.
N A " = hm C A, s − C A,∞
(4)
Sucrose
3.0E-04
9.31E-05
1.33E-05
1.96E-05
1.58E-05
1.41E-05
2.03E-05
1.19E-05
8.78E-06
1.84E-05
2.13E-05
1.50E-05
9.00E-06
7.00E-06
1.67E-05
-
Diameter
(Å)
80
(
Figure 6: Mass transfer coefficient verses Location in
Nephron. For ions: 6a) Hydrogen, Sodium, Potassium,
Calcium, Magnesium, Chlorine, and Bicarbonate; 6b)
Hydrogen Phosphate, Phosphate, Sulfate, Oxygen, Glucose,
Sucrose, and Urea; [10].
)
where G is the mass flux and ρ is the density. Using 3.66 as
the constant Sherwood number for laminar flow with constant
wall concentration, the mass transfer coefficients can be
calculated for the geometries in the nephron. Table 2 shows the
diffusion coefficients at infinite dilution for some ions of
937
Copyright © 2003 by ASME
interest, as compiled from Conney [3] and Lide [10]. Figures 6
shows the resulting mass transfer coefficient. As expected, the
highest mass transfer occurs at the smallest diameter in the
Loop of Henle.
where Di is the diffusion coefficient for species i, C is the
species concentration, νι is the valence, F is the Faraday
constant, p is the electrical potential, R is the gas constant, T is
−
the temperature, V is the partial molar volume, and P is the
pressure.
The first term represents the flux due to the
concentration gradient across the membrane. The second term
is the electrical potential of the membrane. The third term is
the pressure gradient across the membrane. All three of these
forces act to provide selection and control of the diffusion
process in the natural membrane.
Once again, there are several references available that
will give much greater detail to the transport through a
membrane and the transport of ions. Some examples of the indepth analysis that has already been performed can be seen in
Schultz [12], Yagi and Pullman [13], Keeling and Benham [14],
and Lodish et al [15].
TRANSPORT IN MEMBRANE
The processes described above occur at the microscale
level. However, the transport across the membrane occurs at a
nanoscale level. The membrane allows the control and
selection of ions and substances as they pass through the
membrane. In the natural systems, the membrane is the key in
providing the overriding control of the ions and other species in
solution. The membrane structure is made from a layer of polar
phospholipids. The lipid has a polar head and a non-polar tail.
They line up head to tail and form an inner layer and an outer
layer. The polar head repels the ions. Proteins allow an ion to
pass through the membrane. The protein forms a channel for
the ion to pass through the lipid layer. Amino acids help in the
selectivity of the ion by binding on them. The ions will be
released upon receiving a signal, such as a conformational
change in the protein. Many ions are close in physical size and
electrical charge. The amino acid is used to distinguish
between the different ions. Figure 7 shows a schematic
representation of the membrane and a protein channel used to
allow passage of an ion, as adapted from Johnson [11].
Polar
Head
TRANSPORT IN ARTIFICIAL KIDNEY
The use of artificial kidneys in the form of a dialysis
machine has become a common treatment for some types of
renal failure. Several companies have developed dialyzers to
meet these needs. The basic function and structure of the
dialyzer is shown in Figure 8. The blood flows through a
cavity designated only for blood flow. Likewise, the dialysate
flows in its own channels. The dialyzer membrane separates
the two flow streams. The electrolytes and waste products flow
from the blood through the membrane and into the dialysate
channel. The control of this process is only by the dialysate.
Protein
Channel
Dialyzer
Membrane
K+
Ion
Ion &
Flow
Waste
Non-Polar
Tail
Figure 7: Membrane Structure with Protein Channel.
The transport through the membrane can be described
using Equation 7.
−


 dC i C iν i F dφ C i Vi dP 
+
+
N i = − Di 
RT dz
RT dz 
 dz


Dialysate
Flow
(7)
Blood
Flow
Figure 8: Dialyzer Structure and Process.
938
Copyright © 2003 by ASME
The desired concentration of the substances in the blood is
achieved only through the control of the composition of the
dialysate. Therefore, diffusion will occur to create equilibrium
between the blood side and the dialysate side. The membrane
itself does not provide any control or selection of material. The
membrane provides only a mechanical sort based upon the pore
diameter. Typically, a glucose membrane is used in the
dialyzer. The structure of the glucose membrane has an
effective pore size of 8.6 Å. This is close to the nominal pore
size of 8.0 Å in a natural membrane. Recently, several new
types of dialyzer membrane, such as polysulfone, have entered
into commercial dialyzers. In addition, several coatings and
manipulations are used to improve the performance and
efficiency of the membrane. Despite all of the improvements,
the main functionality of the dialyzer has not changed. There
still is no feedback and control associated with the dialyzer
unit. The level of dialysis accomplished at the end of a
treatment remains unknown until a Renal Function Test or a
specific serum test is performed.
Table 3: Typical Dialyzer Properties.
companies replaced with numbers.
mL/min and above. The dialysate flow rate is typically 500 to
800 mL/min. If both the flow rate of the blood and dialysate
are considered, the pumping power required for the dialyzer is
up to 10 times that of a natural kidney. Therefore, the
efficiency of the dialyzer is far below that of the natural system.
It is obvious that the only way to achieve higher efficiency is to
allow the channel dimensions to approach the capillary size on
both the blood and dialysate sides.
CONCENTRATION SENSOR DEVELOPMENT
The measurement of electrolytes in solution has been an
area for research for long time. This ability has been critical in
the development of fundamental theory in electrochemistry. It
is a key component that will provide an online feedback and
control possibility in a dialyzer. Early works used electrodes.
The standard electrode can vary in size ranging from 30 to 3
mm2. The area of the electrode can be reduced to create
microelectrodes that have areas less than 3 mm2. The electrode
is typically made from a material that is inert in the solution.
Platinum, silver, and mercury are the dominating materials used
for this purpose. The need to increase sensitivity and
resolution has developed microelectrodes.
These
microelectrodes range in size from 2 mm to 0.1 mm. The small
surface area has allowed analytical chemists to push the
detection range down into a few parts per billion (ppb) range.
A recent development in concentration measurement is the use
of implanted electrodes. These electrodes range from 0.1 mm
to 0.01 mm in size. The electrodes are made using IC and
micromachining techniques. A new invention in concentration
measurement developed in the 1970s. A new sensor called an
ion selective field effect transistor (ISFET) was developed for
concentration measurement. This sensor gained popularity in
the 1990s. The ISFET is a field effect transistor that is similar
to the metal oxide silicon field effect transistor (MOSFET)
developed for use in the IC industry. A MOSFET has two
highly doped wells embedded into a silicon substrate. The
wells are separated by a small space called the channel. An
insulating layer of silicon dioxide separates the wells from a
metal gate. A voltage is applied to the gate, and the gate
develops a conducting pathway in the channel. Current now
flows from the source well to the drain well. The IC industry
uses this device as a switch to turn on and off the current
pathway, thus creating computations. The ISFET is similar to
the MOSFET in structure. However, the ISFET is used in a
different manner. Instead of a switch, the ISFET is used to
measure the current flowing between the source and the drain.
The gate is modified to sense a particular ion in solution. The
gate is then exposed to the solution. The concentration of the
ion in the solution will vary the potential of the gate and thus
control the amount of current that passes through the transistor.
The typical size of an ISFET varies from 1 to 0.1 mm. Figure 9
shows the structure of an ISFET.
Actual dialyzer
Prime Overall Overall
ID
Dialyzer (µm)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
180
180
180
180
180
180
180
180
180
200
200
200
200
200
200
200
Thick
As
Vol.
Length
Width Weight
(µm) ( m ) (mL)
( mm )
( mm )
(g)
263
304
304
304
263
304
304
304
330
304
304
330
330
-
35
35
38
42
35
35
35
38
42
35
38
42
44
-
287
330
390
504
142
148
148
177
218
318
375
485
506
-
2
10
10
10
10
10
10
10
10
10
45
45
45
45
40
40
40
1.0
1.3
1.5
2.0
1.0
1.3
1.3
1.5
2.0
1.1
1.3
1.8
2.1
1.3
1.6
1.8
63
78
94
123
63
78
78
94
123
66
80
105
114
81
102
116
It would be useful to compare the performance of dialyzers
to the nephrons in the kidney. Table 3 shows some important
parameters of some commercial dialyzers. The surface area
available in the natural kidney for transport ranges from 10 to
24 m2. The surface area in the dialyzer ranges from 1.0 to 2.5
m2. It is clear that the natural system has a greater area. In
addition, the blood flow rate through a kidney is typically 125
mL/min. The blood flow rate in the dialyzer is typically 200
939
Copyright © 2003 by ASME
Ionic
Solution
+
+
+
+
+
+
+
Gate
p+
Source
specialized to react with a specific ion. This specialized
coupling provides a very high selectivity even in the presence
of interfering ions that are similar in size and charge to the ion
of interest. Moschou and Chaniotakis [20] used a CHEMFET
to measure potassium ions in blood plasma. The gate was
modified using two ionophores, one for the ion of interest and
another that detected hydrogen.
Another modification is to coat the gate with an enzyme.
The enzyme digest a protein of interest and the reaction is
generates the change in gate potential. The previous gate
manipulations have dealt with the measurement of ion
concentration. The ENFET modification can measure protein
concentration. Poghossian et al. [21] used an ENFET to detect
penicillin.
The gate was modified with penicillinase.
Hydrogen ions are generated from the catalyzed hydrolysis of
the penicillin. That affects the potential of the gate.
A recent development in the ISFET technology is called a
reference FET (REFET). The previous ISFETs measured ion
or protein concentration. However, they measure the absolute
potential of the solution. This is not the preferred analytical
chemical method. It is desired to use a reference electrode that
provides a reference potential in the solution to make a
comparison with the measured value. This method provides
improved accuracy and sensitivity to the concentration of the
ion of interest. The REFET is a reference electrode FET.
Previous ISFET had to have a separate external reference
electrode in the solution to perform standard analytical
techniques. A REFET coupled with an ISFET would provide
all of the necessary components on one chip.
The concentration sensors described in this section all
behave according to the Nerst equation. Assume that the
+
+
Field
Oxide
p+
Gate
Oxide
n-type
Si
Drain
Figure 9 Structure of an Ion Selective Field Effect
Transistor (ISFET).
Several different types of ISFETs have been developed.
They all behave as described earlier. The main difference
between the ISFETs is the manipulation of the gate material
and how they achieve the ion selectivity. A common gate
modification is to use silicon nitride (Si3N4) as the gate
material. The silicon nitride gate will directly respond to the
ion concentration. Yin et al. [16] used a gate modified with
silicon nitride to measure pH of an electrolyte.
Another common gate modification is to coat the gate with
a polyvinyl chloride (PVC). The PVC coating can easily be
manipulated to be selective for many ions of interest.
However, there is a major drawback with current gate
modifications. The adhesion between the gate and the coating
becomes problematic. Currently, the life span of the ISFET is
only a few days. Typically, the functional life is limited to 40
days. Sanchez et al. [17] used a PVC ISFET to provide
titration end point detection.
The gate can also be modified using a photocurable
polymer.
The photocurable polymer is similar to the
Photoresist used in the IC industry. The polymer can be
processed with the well-established photolithography
techniques. This modification has an advantage over the PVC
and other methods to be discussed because of its easy
integration into existing IC processes. Abramova et al. [18]
used a photocurable polymer to create an ISFET that measured
potassium ions in blood plasma. Bratov et al. [19] also used a
photocurable polymer ISFET to measure the calcium
concentration in milk.
In each case, the response to
concentration was linear. The linear behavior is the preferred
response for analysis. In addition, the ISFET was exposed to a
flow of milk and still provided a linear response.
A chemical formulation applied to the gate is another way
to provide selectivity. This manipulation is referred to as a
CHEMFET. An ionophore is typically used to provide the
chemical modification. An ionophore is a substance that is
−
reaction takes the form: aA + bB + ne = cC + dD
The general Nerst equation is shown in Equation 7.
c
d
RT  [C ] [D ]
E=E +
ln
nF  [A]a [B ]b
0




(7)
where E is the potential, E0 is the standard potential for the
reference electrode, R is the gas constant equal to 8.3147
J/moleK, T is the temperature in Kelvin, n is the number of
electrons used in the reaction, F is the Faraday constant equal
to 9.64846 x 104 C/mol. Typically, the temperature is assumed
to be 25 ºC and Equation 6 can be manipulated to give
Equation 8.
E = E0 +
c
d
0.059  [C ] [D ]
log
a
b
n
 [A] [B ]




(8)
The Nerst equation in this form is commonly used for analytic
techniques. It basically states that a decade change in
concentration will generate a 59 mV change in electric
potential for the half-cell.
940
Copyright © 2003 by ASME
RESEARCH OPPORTUNITIES
The currently available dialysis machines are able to
sustain the renal filtration function in patients to a limited
extent, but the control of the filtrate is practically absent. In
addition, the quality of life of the patients is adversely affected
due to the prolonged and cumbersome procedures in operating
these units. The artificial dialyzers employ channels that are
considerably larger than the capillaries and nephrons by almost
one or two orders of magnitudes. Employing smaller channels
poses two major difficulties: a) the pressure drop increases
significantly as the channel size is reduced, and b) the channels
are prone to clogging due to blood coagulation if the proper
flow rates and surface and flow structure are not maintained.
The pressure drop issue can be handled by providing large
number of parallel paths using the small diameter channels with
short lengths. Such arrangement is needed on both sides of the
membrane. This leads to a very complex system that is
prohibitively expensive and maintain to manufacture using
conventional technologies.
The filtration process employed does not replicate the
natural processes in its ability to maintain the concentration
levels of various blood constituents. For example, potassium
will be transferred effectively because of the large
concentration gradient available for the transfer. On the other
hand, species such as calcium and magnesium have limited
concentration differences available to cause the effective
transfer in the available surface area.
In addition to the filtration process, kidneys provide
control mechanisms for regulating proper balance of critical
components in the blood, including its pH. Even the filtration
process proceeds unregulated, except for the control through
the changes in the dialysate composition. The other functions,
hemostatic, regulatory, metabolic and endocrine are not
addressed by the dialysis machines to any degree of satisfactory
performance. The major hurdle being the deployment of
suitable sensors and the control mechanism to enable the
control on the transport processes. As a first step, we need to
develop sensors that can measure the concentrations of various
solutes in the dialysate and the blood streams. Control of the
transport processes in the membrane and release of proper
control fluids, say for endocrine function, pose further
challenges.
The IC chip technology and the MEMS fabrication
technology have a number of features that allow some of the
control features to be fabricated and installed at microscale.
Firstly, the MEMS fabrication technology allows for the
manufacture of large number of passages in either silicon chips
or in the glycol film deposited on the chips. The desired
membrane thickness and passage flow configurations can be
obtained using these technologies, which offer significant cost
reduction possibilities at high manufacturing volumes. Further,
the IC technology can provide the necessary electric field and
the control mechanisms to sense and regulate the diffusion rates
of various species. The electric driving force on the fluid can
be utilized not only for causing the motion to effectively reduce
the external pumping requirements, but it also can be used to
reduce the clogging conditions by sensing the channel size
reduction and making appropriate corrections in the driving
field.
The availability of large surface area using the small
channels has another advantage in reducing the overall volume
of the dialyzer. The small dialyzer volume, with its ability to
control the filtration process with respect to various
constituents, are steps that will eventually lead to small devices
that can be implanted within the bloodstream or large
circulatory ducts. A conceptual system incorporating some of
the elements discussed in this paper is shown schematically in
Figure 10.
Electric Field Generators for
Fluid Transport in
Microchannels
Electric Field
Generators for
Controlling
Diffusion Through
the Membrane
Microchannel for
Blood Flow
Microchannel for
Dialysate Flow
Diffusion
Membrane
Solute Specific
Concentration Sensors
Figure 10:
Conceptual mass transfer device with
regulatory function incorporating microchannels, fluid flow
field, concentration sensors, and electric field to control the
transport process through the membrane.
Blood and dialysate flow in adjoining microchannels. The
microchannels are rectangular with a membrane embedded
between their wide sides. The header configurations pose
another challenge where the MEMS fabrication technology
could be implemented to provide relatively short passages to
reduce the pressure drop. The dialysate itself may be produced
through an ultrafiltration step incorporating similar MEMS
devices. The flow of the fluids is accomplished through
electrokinetic forces induced through the passage of electric
current in the conductor elements shown in the figure (although
these field may be applied before the branching into individual
main ducts). The microchannels are separated by a suitable
membrane, made of a suitable polymer that is compatible with
the fluids, and that has pores of proper diameter and lengths.
The transport of solutes through the membrane is controlled
941
Copyright © 2003 by ASME
through another set of field effect conductors that are
incorporated within the membrane.
Placements of the
conductors creating the electric fields is in symbolic terms in
the figure; their placement will be at appropriate locations to
create the desired effect.
Figure 11 shows a schematic of a novel microdialyzer that
implements the ideas presented in this paper while integrating
the IC chip and MEMS technology. The electric field B is used
to cause the liquid motion. In the membrane the effect of an
electric field on the diffusion process is utilized to control the
rate of diffusion of a specific species in response to the sensor
signal. Separate sections would handle and control the
diffusion of different constituents in the dialysis process.
Membrane
Coil
Flow
Coil
Membrane
Dialysate
Flow
_
B
Concentration
Sensors
ACKNOWLEDGEMENT
All of the work was conducted in the Thermal Analysis
Laboratory at RIT. The support provided by Rochester
Institute of Technology is gratefully acknowledged.
_
B
_
B
Blood
Flow
volume) that is one to two orders of magnitudes above the
currently available artificial systems. Further improvements
can occur with the implementation of coupled microchannel
passages while integrating IC chip and MEMS fabrication
technology.
3. The lack of sensing and control mechanism in artificial
dialyzers is a serious limiting condition. Research in the
sensor development and integration is extremely important
to provide an increase in quality and functionality.
4. The ability to control the transfer process across a
membrane through electric field effects has attractive
possibilities. It needs to be explored further.
5. Sensing and controlling the dialysis process to achieve the
desired level of blood constituent concentration levels will
greatly enhance the quality of life of the patients with
certain kinds of renal failure.
REFERENCES
[1]
Kandlikar, S.G., and W.J. Grande. "Evolution of
Microchannel Flow Passages - Thermohydraulic
Performance and Fabrication Technology." Proceedings
of International Mechanical Engineering Congress and
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IMECE02-32043. ASME Publications.
[2]
Bronzino, J.D. ed. The Biomedical Engineering
Handbook. New York: CRC Press and IEEE Press, 2000.
[3]
Cooney, D.O. Biomedical Engineering Principles: An
Introduction to Fluid, Heat, and Mass Transport
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[4]
West, J.B. Respiratory Physiology: The Essentials, Sixth
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[5]
Ferron, G.A., and D.A. Edwards. "Numerical Simulation
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[6]
Henry, F.S., Butler, J.P., and A. Tsuda. "Kinematically
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[7]
Cassidy, K.J., Halpern, D., Ressler, B.G., and J.B.
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Flow
Coil
Figure 11: Schematic of a novel MEMS mass transfer
device
with
regulatory
function
incorporating
microchannels, fluid flow field, concentration sensors, and
electric field to control the transport process through the
membrane.
Although some of the ideas presented in this paper seem
rather far-fetched at this time, they nevertheless provide a
viable research path utilizing technological developments in
various fields. Some of the immediate areas that could be
addressed are: development of IC based concentration sensors
for various constituents in the bloodstream, manufacturing
techniques for microchannel passages in a mass transfer
devices with built in electric field for driving the flow,
development of membranes utilizing the electric field
controllers for regulating the transfer of specific constituents at
the desired levels, and IC chip and MEMS material
development for compatibility with the biological systems.
CONCLUSIONS
1. The recent focus on microchannels in heat transfer
applications indicates the high mass transfer efficiencies
possible with the use of microchannels in artificial
biological systems.
2. The natural systems reviewed here, the lung and the kidney,
have an extremely high surface area density (area per unit
942
Copyright © 2003 by ASME
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
[24]
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Yin, L.-T., Chou, J.-C., Chung, W.-Y., Sun, T.-P.,
Hsiung, S.-K. "Characteristics of Silicon Nitride after O2
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IEEE Transactions on Biomedical Engineering 48, no 3
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Sanchez, J., Beltran, A., Alonso, J., Jimenez, C., del
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Abramova, N., Borisov, Y., Bratov, A., Gavrilenko, P.,
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Bratov, A., Abramova, N., Dominguez, C., Baldi, A.
"Ion-selective field effect transistor (ISFET)-based
calcium ion sensor with photocured polyurethane
membrane suitable for ionized calcium determination in
milk." Analytica Chimica Acta 408 (2000): 57-64.
Moschou, E.A., and N.A. Chaniotakis. "Potassium
selective CHEMFET based on an ion-partitioning
membrane." Analytica Chimica Acta 445 (2001): 183190.
Poghossian, A., Yoshinobu, T., Simonis, A., Ecken, H.,
Luth, H., Schoning, M.J. "Penicillin detection by means
of field-effect based sensors: ENFET, capacitive EIS
sensor or LAPS." Sensors and Actuators B 78 (2001):
237-242.
Kays, W.M. and M.E. Crawford. Convective Heat and
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Transfer. New York: John Wiley & Sons, 1993.
943
Copyright © 2003 by ASME