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A mathematical model with finite-element analysis of recessed dissolved-oxygen cathode array
Sensors and Actuators B, IO (1993) 223-228
223
A mathematical model with finite-element analysis of recessed dissolved-oxygen cathode array* Chen Yu-Quan and Li Guang Department of Scientific Instrumentation,
Zhejiang University, Hangzhou 310027 (China)
(Received October 7, 1991; in revised form July 21, 1992;accepted August 13, 1992)
Abstract
A mathematical model of recessed dissolved-oxygen cathode array sensors is described. A three-dimensional cylindrical coordinate (R, 0, Z) finite-element analysis with a trigonal ring element has been developed for analysing the complex geometry of the recessed cathode plain array. Some priorities to estimate sensitivity, response time, stability, diffusion cross-talk and flow independence concurrently are provided. It is found that a microhole with a vertical wall is more effective in limiting the diffusion field than those with different wall slope, given the same depth/diameter (H/D) ratio. In order to avoid cross-talk between the diffusion fields of two microholes, their centres must be more than 1.9D apart. A new microhole cathode array three-electrode oxygen sensor has been developed using the result of the model.
Introduction
The electrochemical dissolved-oxygen sensor has been a powerful tool in medical, biological, environmental and clinical settings. The three-electrode mode of operation, in which a working electrode, a counter electrode and a reference electrode are used, can be a means to increase the stability and durability of the sensor. Electrochemical oxygen measurement is a kind of amperometric measurement. The sensors are based on the electrocatalytic reduction of oxygen on a noblemetal working electrode surface. When the electrode is appropriately polarized, the reaction that most likely occurs on the working electrode surface is:
HzO, + 2H+ + 2e- --*2H,O In amperometric measurement, the current output is directly proportional to the surface area of the working electrode (the cathode, in the case of oxygen reduction). Thus, when a large current output is desired for ease of signal processing, a large cathodic surface area is required. Yet, the cathode of the oxygen sensor should have a small surface area in order to have a minimum flow effect and a relatively fast response. The flow effect can be minimized by using an oxygen-permeable membrane, but this also reduces the response speed. Several
*Paperpresentedat the 6th International Conference on SolidState Sensors and Actuators (Transducers ‘91), San Francisco, CA, USA, June 24-28, 1991.
0925-4005/93/$6,00
types of recessed dissolved-oxygen cathode array sensors have been developed because of the recent progress in microelectronic technology [ 1,2]. In this configuration each cathode is small, and the cathodes are interconnected. These sensors showed several advantages over a conventional Clark-type sensor, such as long durability and relatively minor flow effects and faster response. Obviously, only when a microcathode array is properly designed can it be expected to have good performance. Various mathematical models of electrodes have been suggested and analysed in an attempt to provide design guidelines for the oxygen sensor [3,4]. Silver [4] utilized considerable geometric simplifications of the electrode to facilitate their analyses. Schneiderman utilized the finite-element method with Mushrooming Maxwellian coordinates to analyse a recessed microelectrode [ 31.However, because of the complex geometry of the recessed electrode array, some aspects of the electrode array design could not be studied. The recessed cathode array is a noble-metal thin film covered with an insulating slice which has a microhole array. Because of the tight contact between the insulator and the metal film, the available cathode area is only the bottom area of the microholes. Different methods of forming the recessed cathode array cause different slopes of the microholes. The present work attempts to provide a realistic simulation of the recessed array geometry. A finite-element analysis was made on a steady-state recessed dissolved-oxygen cathode. It indicates that the recessed cathode array has the advantage of flow independence and fast response while maintaining adequate output. Some basis was provided to esti-
@ 1993- ElsevierSequoia.All rights reserved
mate sensitivity, response time, stability, diffusion crosstalk between two microcathodes and flow dependence concurrently. A new microhole cathode array threeelectrode oxygen sensor has been developed using the result of the model [S].
Mathematical model and finite-elementanalysis When properly polarized with respect to a given reference, an oxygen cathode reduces the O2 at its surface completely and therefore induces a disturbance in the ~0, field in the vicinity of the cathode. Because of the fast reduction of the 0,, the current is determined by the rate of O2 diffusion to the cathode. If the distance between two adjacent microholes is large enough, each cathode can be considered as being unaffected by the others. The steady-state oxygen profiles and gradients around an oxygen cathode operating in an unstirred homogeneous medium of initially uniform p02 can be derived by obtaining the solution of the equations composed of Laplace’s equation (V’P = 0) and boundary conditions appropriate for the geometry of the electrode. A three-dimensional cylindrical coordinate (R, 42) finite-element method analysis with a trigonal ring element has been developed for a recessed cathode (Fig. 1) and the complex geometry of the recessed cathode plain array. The form of Laplace’s equation in cylindrical coordinates is
a*p iap
For an individual recessed cathode, the boundary conditions are given by P=O
Z=O,r
(2)
P=P,
z=co
(3)
ap 5'0
O
(4)
ap s=O
Z=H,r>r,
where P is the concentration of dissolved oxygen and P, is the initial concentration of dissolved oxygen. A linear interpolation with a trigonal ring element may reach a higher level of conciseness, accuracy and operation speed: P(r, Z) = N, Pi + N, P, + N3P,,, = [N] {P}’
(6)
where i, j, m are three vertices of a trigonal ring element.
(7)
INI = IN,> Nz>N,}
(8)
N, = fA(ai + b,r + c,Z)
(9)
N2 = $A& + b,r + c,Z)
(10)
p+;y$+p,,z+,,2=0
N,=fA(a,+b,,r+c,Z)
(11)
Because of the axial symmetry, Laplace’s equation can be simplified as follows:
where A is the section area of a trigonal ring element. a,, bi, c,, Us,b,, cj, a,, b,, c,, are the algebraic cofunctions of the matrix
i a*8 a*p
+$=O
(1)
ring
respectively. According to the oxygen concentration gradient, the size of the element away from the mouth of a recessed electrode increases gradually through the program to reduce the operation time. The oxygen concentration equation will be shown as - j[N]T[~~(r~)+$]=O
Fig.
1. Three-dimensional cylindrical coordinatesystem.
(12)
where [NIT is a linear interpolation function about the point coordinate of the trigonal ring element, [PI’ is a vector of element concentration and V, is the volume of the trigonal ring element.
225
With partial integration, we have from eqn. (12):
(13) A
where A is the surface area of a trigonal ring element. n,, nz are the fractions of A at the coordinates R and Z respectively. Equation ( 13) is fuither simplified as {r}e+ [Kk]{P}e = 0
(15)
where
A
b,*
[KJ = 2
I
+ ci2
bibj + c,cj
b,,,b, + c,q
(16) b,b, + CiCj bib, + C,C, bj2 + cj2
bib, + cjcm
b,b, + c,,,cj
b,* f cm2 I (17)
? is the average of the R coordinate of the element.
Equation (15) is just the finite-element equation of the simplified Laplace equation. It is easy to solve
the equation by the finite-element method using a computer. The oxygen diffusion fields are calculated and analysed. Figures 2 and 3 are cross sections of ~0, contour planes induced by the operation of recessed electrodes in an infinite homogeneous medium. The p02 contour planes are labelled with the percentage of the ~0, of an infinite distance from the cathode. At the cathode surface p02 is zero and, for increasing distances from the cathode, p02 increases asymptotically to lOO%,which corresponds to the initially uniform p02 of the external medium. Figure 2(a)-(d) shows the cross sections of the p02 contour planes with the same depth (H/D = 2.0) and different wall slope of the microholes. Figure 3(a)-(d) shows the cross sections of the pOz contour planes with a vertical wall and different depths of the microholes. According to Fig. 2(a)-(d), we can get Fig. 4. It shows that the vertical wall of the microhole is most effective for limiting the diffusion fields. For a vertical wall, as shown in Fig. 5, which is derived from Fig. 3(a)-(b), when H/D > 2.0, the slope of the P-H/D curve becomes very small. When H/D = 10, the oxygen concentration in the mouth is P, > 0.98P,. When H/D is 1.6-2.0, the change of the slope of the P-H/D curve is highest, P,/Po > 85%. This is an important part of the electrode design.
4s 72 30
H/D=0.5
H/D=2.0
(4
(a)
H/D=2.0
wall slope ia 20*'
(b)
wall
slope
95
-Q88
30
W
is 0.
H/D=1.8 98
95
95
--I?88
88 30
30
--I?-
H/D=2.0
tc)
wall slope
is
-5'
30
H/D=2.0
1 H/D= 2.0
Cd) wall slope
is
-10'
Fig. 2. Cross sections of the ~0, contour planes induced by the operation of recessed electrodes in an infinite homogeneous medium.
(c)
Cd)
H/D=I.O
Fig. 3. Cross sections of the ~0, contour planes induced by the operation of recessed electrodes in an infinite homogeneous medium.
and the current sensitivity u is nFD, PO
H 3 2.00
’ x H exp(0.2D/H)
(19)
where f(Z, t) is the oxygen flux, A is the area of a section and D,, is the diffusion constant. His the depth of the hole. According to Fick’s theorem
0.90
WT t) =
D
af
0.90
I 0.75 -10
I I
I
I
0
10
20
Wall
I 30
slopetdegree)
Fig. 4. When H/D is a constant, fH changes with the wall slope of the recessed microhole
a2fv, 4 0 a22
where P(Z, t) is the oxygen concentration at time t and coordinate Z and Do is the diffusion coefficient of oxygen. By Laplace’s conversion, we can get
wz, 4 az
PO z=o
(21)
(wDot)“2
Thus, the transient current (I,)’ is H>2D
PII& 1.C
and the response time tw is Hz exp( 0.4D/H) t90 =
0.81nD,
H>2D
(23)
It is shown that when His large enough, CJdecreases with the increase of H. This is in accordance with Morita and Shimisu’s experimental result [2].
Experiment and conclusions
3
H/O
Fig. 5. The concentration of oxygen at the mouth of the recessed electrode, P,, changes with H/D. For complex geometry of the recessed cathode plain array, we can evaluate the cross-talk of the recessed cathodes in a similar way by changing the boundary conditions.
Current sensitivity and response time
In the microhole, the diffusion flux through every section is equivalent to the flux at the mouth. When H > 2.00, the pOz contour plane near the mouth of the microhole cathode can be approximately considered as PO. So the oxygen diffusion field in the mouth can be considered as being linear. Thus the static limited current (ZJ is
We designed several three-electrode oxygen sensors with a recessed cathode array. Their reference and counter electrodes have the same shape. Their cathodes have different H/D ratios but the sum of all the cathode areas is 0.37 mm*. Each sensor was put in the same place of a solution stirred by a magnetic bar covered with Teflon at various rotation speeds. The response time and flow dependence of the sensors were measured and compared. Table 1 shows that when H/D > 2.0 the stirred effect becomes very small and the response time depends on the depth of the microhole. The design of a minute dissolved-oxygen sensor must take into consideration the current sensitivity, response TABLE I. Sensor results for D = 100pm
HID 0.7 2.0 3.3
Sensitivity
f90
Flow error
(P&pm 0, mm*)
(s)
(“/)
4.65 2.48 1.52
30 55 180
8.8 3.1 1.9
.cmtour plUIs
Fig. 6. (a) The individual recessed cathode (H/D = 1.8) with 97% P0 contour plane. (b) The recessed cathode array (H/D = 1.8, centre separation 2.60) with 97% PO contour plane. (c) The recessed cathode array (H/D = 1.8, centrc separation 2.OD) with 97% PO contour plane.
time, stability, stirring effect, etc. concurrently. From this analysis, it is found that a microhole with a vertical wall is more effective for limiting the diffusion field than those with the same H/D ratio but different wall slope. When H/D < 1.6, PH < 85% P0 and the sensors are flow sensitive. When HID > 2.0, PH > 90% PO and the sensors become flow independent, but the increase of response time and decrease of current sensitivity become considerable with high HID ratio. When 1.6
Acknowledgement This project is supported by the National Science Foundation of China.
References 1 V. Karagounis, L. Lun and C. C. Liu, A thick-film multiple component cathode three-electrode oxygen sensor, IEEE Trww. Biomed. Eng., BME-33 (1986) 108-112. 2 K. Morita and Y. Shimisu, Microhole array for oxygen electrode, Anal. Chem., 61 (1989) 159-162. 3 G. Schneiderman and T. K. Goldstick, Oxygen electrode design criteria and performance characteristics: recessed cathode, J. A$. Physiol., 45 (1978) 145-154. 4 C. Silver, Problems in the investigation of tissue oxygen microenvironment, in D. Reneau (ed.), Chemical Engineering in Medicine, Am. Chem. Sot., Washington, DC, 1973, pp. 343351. 5 Y.-Q. Chen and G. Li, An auto-calibrated miniature microhole cathode array for measuring dissolved oxygen, Sensors and Actuators E, IO (1993) 219-222.
228
Biographies Chen Yu-Quun was born in Hangzhou, China, on Sept. 7, 1944. He received B.S. and MS. degrees from Zhejiang University, and has been associate professor in the Scientific Instrument Department of Zhejiang University since 1985. He worked in the Electronic Design Center and Biomedical Engineering Department of Case Western Reserve University, USA, as a visiting scholar from 1985 to 1987. He currently works at the National Transducer Key Laboratory of China, Zhejiang University. His
research interests include microsensors and biomedical instruments. Li Guang was born in Wuxi, China, on April 20, 1965. He received B.S. and M.S. degrees in biomedical engineering from Zhejiang University in 1987 and 1991, respectively. From 1987 to 1989, he was an assistant professor in the Department of Scientific Instrumentation at Zhejiang University. He is currently working at the National Biomedical Transducers Key Laboratory in China. His research interests include biomedical sensors and instruments.
223
A mathematical model with finite-element analysis of recessed dissolved-oxygen cathode array* Chen Yu-Quan and Li Guang Department of Scientific Instrumentation,
Zhejiang University, Hangzhou 310027 (China)
(Received October 7, 1991; in revised form July 21, 1992;accepted August 13, 1992)
Abstract
A mathematical model of recessed dissolved-oxygen cathode array sensors is described. A three-dimensional cylindrical coordinate (R, 0, Z) finite-element analysis with a trigonal ring element has been developed for analysing the complex geometry of the recessed cathode plain array. Some priorities to estimate sensitivity, response time, stability, diffusion cross-talk and flow independence concurrently are provided. It is found that a microhole with a vertical wall is more effective in limiting the diffusion field than those with different wall slope, given the same depth/diameter (H/D) ratio. In order to avoid cross-talk between the diffusion fields of two microholes, their centres must be more than 1.9D apart. A new microhole cathode array three-electrode oxygen sensor has been developed using the result of the model.
Introduction
The electrochemical dissolved-oxygen sensor has been a powerful tool in medical, biological, environmental and clinical settings. The three-electrode mode of operation, in which a working electrode, a counter electrode and a reference electrode are used, can be a means to increase the stability and durability of the sensor. Electrochemical oxygen measurement is a kind of amperometric measurement. The sensors are based on the electrocatalytic reduction of oxygen on a noblemetal working electrode surface. When the electrode is appropriately polarized, the reaction that most likely occurs on the working electrode surface is:
HzO, + 2H+ + 2e- --*2H,O In amperometric measurement, the current output is directly proportional to the surface area of the working electrode (the cathode, in the case of oxygen reduction). Thus, when a large current output is desired for ease of signal processing, a large cathodic surface area is required. Yet, the cathode of the oxygen sensor should have a small surface area in order to have a minimum flow effect and a relatively fast response. The flow effect can be minimized by using an oxygen-permeable membrane, but this also reduces the response speed. Several
*Paperpresentedat the 6th International Conference on SolidState Sensors and Actuators (Transducers ‘91), San Francisco, CA, USA, June 24-28, 1991.
0925-4005/93/$6,00
types of recessed dissolved-oxygen cathode array sensors have been developed because of the recent progress in microelectronic technology [ 1,2]. In this configuration each cathode is small, and the cathodes are interconnected. These sensors showed several advantages over a conventional Clark-type sensor, such as long durability and relatively minor flow effects and faster response. Obviously, only when a microcathode array is properly designed can it be expected to have good performance. Various mathematical models of electrodes have been suggested and analysed in an attempt to provide design guidelines for the oxygen sensor [3,4]. Silver [4] utilized considerable geometric simplifications of the electrode to facilitate their analyses. Schneiderman utilized the finite-element method with Mushrooming Maxwellian coordinates to analyse a recessed microelectrode [ 31.However, because of the complex geometry of the recessed electrode array, some aspects of the electrode array design could not be studied. The recessed cathode array is a noble-metal thin film covered with an insulating slice which has a microhole array. Because of the tight contact between the insulator and the metal film, the available cathode area is only the bottom area of the microholes. Different methods of forming the recessed cathode array cause different slopes of the microholes. The present work attempts to provide a realistic simulation of the recessed array geometry. A finite-element analysis was made on a steady-state recessed dissolved-oxygen cathode. It indicates that the recessed cathode array has the advantage of flow independence and fast response while maintaining adequate output. Some basis was provided to esti-
@ 1993- ElsevierSequoia.All rights reserved
mate sensitivity, response time, stability, diffusion crosstalk between two microcathodes and flow dependence concurrently. A new microhole cathode array threeelectrode oxygen sensor has been developed using the result of the model [S].
Mathematical model and finite-elementanalysis When properly polarized with respect to a given reference, an oxygen cathode reduces the O2 at its surface completely and therefore induces a disturbance in the ~0, field in the vicinity of the cathode. Because of the fast reduction of the 0,, the current is determined by the rate of O2 diffusion to the cathode. If the distance between two adjacent microholes is large enough, each cathode can be considered as being unaffected by the others. The steady-state oxygen profiles and gradients around an oxygen cathode operating in an unstirred homogeneous medium of initially uniform p02 can be derived by obtaining the solution of the equations composed of Laplace’s equation (V’P = 0) and boundary conditions appropriate for the geometry of the electrode. A three-dimensional cylindrical coordinate (R, 42) finite-element method analysis with a trigonal ring element has been developed for a recessed cathode (Fig. 1) and the complex geometry of the recessed cathode plain array. The form of Laplace’s equation in cylindrical coordinates is
a*p iap
For an individual recessed cathode, the boundary conditions are given by P=O
Z=O,r
(2)
P=P,
z=co
(3)
ap 5'0
O
(4)
ap s=O
Z=H,r>r,
where P is the concentration of dissolved oxygen and P, is the initial concentration of dissolved oxygen. A linear interpolation with a trigonal ring element may reach a higher level of conciseness, accuracy and operation speed: P(r, Z) = N, Pi + N, P, + N3P,,, = [N] {P}’
(6)
where i, j, m are three vertices of a trigonal ring element.
(7)
INI = IN,> Nz>N,}
(8)
N, = fA(ai + b,r + c,Z)
(9)
N2 = $A& + b,r + c,Z)
(10)
p+;y$+p,,z+,,2=0
N,=fA(a,+b,,r+c,Z)
(11)
Because of the axial symmetry, Laplace’s equation can be simplified as follows:
where A is the section area of a trigonal ring element. a,, bi, c,, Us,b,, cj, a,, b,, c,, are the algebraic cofunctions of the matrix
i a*8 a*p
+$=O
(1)
ring
respectively. According to the oxygen concentration gradient, the size of the element away from the mouth of a recessed electrode increases gradually through the program to reduce the operation time. The oxygen concentration equation will be shown as - j[N]T[~~(r~)+$]=O
Fig.
1. Three-dimensional cylindrical coordinatesystem.
(12)
where [NIT is a linear interpolation function about the point coordinate of the trigonal ring element, [PI’ is a vector of element concentration and V, is the volume of the trigonal ring element.
225
With partial integration, we have from eqn. (12):
(13) A
where A is the surface area of a trigonal ring element. n,, nz are the fractions of A at the coordinates R and Z respectively. Equation ( 13) is fuither simplified as {r}e+ [Kk]{P}e = 0
(15)
where
A
b,*
[KJ = 2
I
+ ci2
bibj + c,cj
b,,,b, + c,q
(16) b,b, + CiCj bib, + C,C, bj2 + cj2
bib, + cjcm
b,b, + c,,,cj
b,* f cm2 I (17)
? is the average of the R coordinate of the element.
Equation (15) is just the finite-element equation of the simplified Laplace equation. It is easy to solve
the equation by the finite-element method using a computer. The oxygen diffusion fields are calculated and analysed. Figures 2 and 3 are cross sections of ~0, contour planes induced by the operation of recessed electrodes in an infinite homogeneous medium. The p02 contour planes are labelled with the percentage of the ~0, of an infinite distance from the cathode. At the cathode surface p02 is zero and, for increasing distances from the cathode, p02 increases asymptotically to lOO%,which corresponds to the initially uniform p02 of the external medium. Figure 2(a)-(d) shows the cross sections of the p02 contour planes with the same depth (H/D = 2.0) and different wall slope of the microholes. Figure 3(a)-(d) shows the cross sections of the pOz contour planes with a vertical wall and different depths of the microholes. According to Fig. 2(a)-(d), we can get Fig. 4. It shows that the vertical wall of the microhole is most effective for limiting the diffusion fields. For a vertical wall, as shown in Fig. 5, which is derived from Fig. 3(a)-(b), when H/D > 2.0, the slope of the P-H/D curve becomes very small. When H/D = 10, the oxygen concentration in the mouth is P, > 0.98P,. When H/D is 1.6-2.0, the change of the slope of the P-H/D curve is highest, P,/Po > 85%. This is an important part of the electrode design.
4s 72 30
H/D=0.5
H/D=2.0
(4
(a)
H/D=2.0
wall slope ia 20*'
(b)
wall
slope
95
-Q88
30
W
is 0.
H/D=1.8 98
95
95
--I?88
88 30
30
--I?-
H/D=2.0
tc)
wall slope
is
-5'
30
H/D=2.0
1 H/D= 2.0
Cd) wall slope
is
-10'
Fig. 2. Cross sections of the ~0, contour planes induced by the operation of recessed electrodes in an infinite homogeneous medium.
(c)
Cd)
H/D=I.O
Fig. 3. Cross sections of the ~0, contour planes induced by the operation of recessed electrodes in an infinite homogeneous medium.
and the current sensitivity u is nFD, PO
H 3 2.00
’ x H exp(0.2D/H)
(19)
where f(Z, t) is the oxygen flux, A is the area of a section and D,, is the diffusion constant. His the depth of the hole. According to Fick’s theorem
0.90
WT t) =
D
af
0.90
I 0.75 -10
I I
I
I
0
10
20
Wall
I 30
slopetdegree)
Fig. 4. When H/D is a constant, fH changes with the wall slope of the recessed microhole
a2fv, 4 0 a22
where P(Z, t) is the oxygen concentration at time t and coordinate Z and Do is the diffusion coefficient of oxygen. By Laplace’s conversion, we can get
wz, 4 az
PO z=o
(21)
(wDot)“2
Thus, the transient current (I,)’ is H>2D
PII& 1.C
and the response time tw is Hz exp( 0.4D/H) t90 =
0.81nD,
H>2D
(23)
It is shown that when His large enough, CJdecreases with the increase of H. This is in accordance with Morita and Shimisu’s experimental result [2].
Experiment and conclusions
3
H/O
Fig. 5. The concentration of oxygen at the mouth of the recessed electrode, P,, changes with H/D. For complex geometry of the recessed cathode plain array, we can evaluate the cross-talk of the recessed cathodes in a similar way by changing the boundary conditions.
Current sensitivity and response time
In the microhole, the diffusion flux through every section is equivalent to the flux at the mouth. When H > 2.00, the pOz contour plane near the mouth of the microhole cathode can be approximately considered as PO. So the oxygen diffusion field in the mouth can be considered as being linear. Thus the static limited current (ZJ is
We designed several three-electrode oxygen sensors with a recessed cathode array. Their reference and counter electrodes have the same shape. Their cathodes have different H/D ratios but the sum of all the cathode areas is 0.37 mm*. Each sensor was put in the same place of a solution stirred by a magnetic bar covered with Teflon at various rotation speeds. The response time and flow dependence of the sensors were measured and compared. Table 1 shows that when H/D > 2.0 the stirred effect becomes very small and the response time depends on the depth of the microhole. The design of a minute dissolved-oxygen sensor must take into consideration the current sensitivity, response TABLE I. Sensor results for D = 100pm
HID 0.7 2.0 3.3
Sensitivity
f90
Flow error
(P&pm 0, mm*)
(s)
(“/)
4.65 2.48 1.52
30 55 180
8.8 3.1 1.9
.cmtour plUIs
Fig. 6. (a) The individual recessed cathode (H/D = 1.8) with 97% P0 contour plane. (b) The recessed cathode array (H/D = 1.8, centre separation 2.60) with 97% PO contour plane. (c) The recessed cathode array (H/D = 1.8, centrc separation 2.OD) with 97% PO contour plane.
time, stability, stirring effect, etc. concurrently. From this analysis, it is found that a microhole with a vertical wall is more effective for limiting the diffusion field than those with the same H/D ratio but different wall slope. When H/D < 1.6, PH < 85% P0 and the sensors are flow sensitive. When HID > 2.0, PH > 90% PO and the sensors become flow independent, but the increase of response time and decrease of current sensitivity become considerable with high HID ratio. When 1.6
Acknowledgement This project is supported by the National Science Foundation of China.
References 1 V. Karagounis, L. Lun and C. C. Liu, A thick-film multiple component cathode three-electrode oxygen sensor, IEEE Trww. Biomed. Eng., BME-33 (1986) 108-112. 2 K. Morita and Y. Shimisu, Microhole array for oxygen electrode, Anal. Chem., 61 (1989) 159-162. 3 G. Schneiderman and T. K. Goldstick, Oxygen electrode design criteria and performance characteristics: recessed cathode, J. A$. Physiol., 45 (1978) 145-154. 4 C. Silver, Problems in the investigation of tissue oxygen microenvironment, in D. Reneau (ed.), Chemical Engineering in Medicine, Am. Chem. Sot., Washington, DC, 1973, pp. 343351. 5 Y.-Q. Chen and G. Li, An auto-calibrated miniature microhole cathode array for measuring dissolved oxygen, Sensors and Actuators E, IO (1993) 219-222.
228
Biographies Chen Yu-Quun was born in Hangzhou, China, on Sept. 7, 1944. He received B.S. and MS. degrees from Zhejiang University, and has been associate professor in the Scientific Instrument Department of Zhejiang University since 1985. He worked in the Electronic Design Center and Biomedical Engineering Department of Case Western Reserve University, USA, as a visiting scholar from 1985 to 1987. He currently works at the National Transducer Key Laboratory of China, Zhejiang University. His
research interests include microsensors and biomedical instruments. Li Guang was born in Wuxi, China, on April 20, 1965. He received B.S. and M.S. degrees in biomedical engineering from Zhejiang University in 1987 and 1991, respectively. From 1987 to 1989, he was an assistant professor in the Department of Scientific Instrumentation at Zhejiang University. He is currently working at the National Biomedical Transducers Key Laboratory in China. His research interests include biomedical sensors and instruments.