Abstract
A CO2-electrode system consisting of a membrane covered pH electrode, an electronic antilog modul and a special electronic analog circuit is described. Since the electrode output signal is a logarithmic function of the CO2 partial pressure the output signal of the antilog module is proportional to the CO2 partial pressure. The time course of the electrode signal has been analyzed after a step change of\(p_{{\text{CO}}_{\text{2}} }\). This step response may be approximated by a sum of three exponential functions. Knowing the dynamic behaviour, the transfer function is formulated mathematically and a special analog circuit is constructed with a frequency response inverse to the frequency response of the electrode. Using this device the response time (T 95) of the electrode system is diminished from 11,5 s to 750 ms after a step change of\(p_{{\text{CO}}_{\text{2}} }\) in gas (Luttmann, et al., 1974). If the time for the hydration of CO2 is decreased by the addition of carbonic anhydrase the response time of the electrode is diminished to 6.5 s. Using the analog circuit yields a response time of 200 ms.
Further studies were made to analyze the transient response in fluids at various flow velocities and various mountings. In order to analyze the influence of the fluid boundary layer on the surface of the electrode a photometric method has been developed (Luttmann and Mückenhoff, 1975), which allows to estimate the time course of the CO2 partial pressure independently of and simultaneously with the electrode measurement.
The experimental data are compared with a theory based on theoretical considerations of Schuler and Kreuzer (1967) and Crank (1956).
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Abbreviations
- A i :
-
gain factor of thei-th compartment
- A′ i :
-
gain factor of the simulation network
- C i :
-
capacity
- D :
-
diffusion coefficient
- d :
-
electrode diameter
- \(F_{{\text{CO}}_{\text{2}} }\) :
-
fraction of CO2
- F c (jω) :
-
frequency response of the linearizing network
- F g (jω) :
-
frequency response of the boundary layer
- F M (jω) :
-
frequency response of the measuring system
- F′ M :
-
frequency response of the simulation network
- I i :
-
impedance transformer
- j :
-
Gauss number (j 2=−1)
- \(P_{{\text{CO}}_{\text{2}} }\)(jω):
-
frequency function of the CO2 partial pressure
- \(p_{{\text{CO}}_{\text{2}} }\)(t):
-
time function of the CO2 partial pressure
- R i :
-
electrical resistance
- T i :
-
time constant of the electrode
- T′ i :
-
time constant of the simulation network
- T 95 :
-
time for reaching 95% of the total difference
- V :
-
voltage gain factor
- v :
-
velocity of the streaming fluid
- x :
-
coordinate
- x(t) :
-
time function
- X(jω) :
-
corresponding frequency function
- α:
-
dilution factor
- β:
-
inverse time constant
- \(\bar \varepsilon\) :
-
thickness of boundary layer
- μ* :
-
kinematic viscosity
- ξ:
-
thickness of diffusion layer
- ω:
-
radian frequency
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Supported by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 114 (Bionach)
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Luttmann, A., Mückenhoff, K. & Loeschcke, H.H. Fast measurement of the CO2 partial pressure in gases and fluids. Pflugers Arch. 375, 279–288 (1978). https://doi.org/10.1007/BF00582442
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DOI: https://doi.org/10.1007/BF00582442