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Characteristics of a multicathode polarographic oxygen electrode

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Abstract

Recent work on Clark-type pO2 electrodes has shown that significant performance improvements can be achieved through the use of a multicathode arrangement. To provide a sound basis for the design of such electrodes, we present an analysis and discussion of their properties. The electrode is initially modelled by asuming the cathodes consist of noninteracting membrane-covered discs. Expressions are derived for the pO2 distribution and polarographic current. The influence of cathode diameter, membrane thickness and permeability are examined, particularly in relation to flow velocity dependence. An extension of the analysis to the situation where interaction between the cathodes becomes significant is also presented. The analysis and results provide a proper basis for the optimal design of multicathode p O2 electrodes.

Sommaire

Des travaux récents sur des électrodes du type ClarkpO2 ont démontré que des améliorations remarquables de performance peuvent être obtenues en faisant usage de dispositifs multicathodes. Afin de former une base solide pour la conception de telles électrodes, nous présentons une analyse et une discussion de leurs propriétés. L'électrode est tout d'abord modelée en présumant que les cathodes consistent de disques recouverts de membrane et sans action réciproque. Les expressions de distribution depO2 et du courant polarographique sont dérivées. L'effet du diamètre de la cathode, de l'épaisseur de la membrane et de sa perméabilité sont étudiés en relation particulière avec la dépendance de la vitesse d'écoulement. Une extension de l'analyse à une situation dans laquelle l'action réciproque entre les cathodes devient significative est aussi présentée. L'analyse et les résultats forment une bonne base pour la conception optimale d'électrodespO2 à multicathode.

Zusammenfassung

Kürzlich vorgenommene Arbeiten anpO2-Elektroden vom Clark-Typ haben gezeigt, daß man bedeutende Leistungsverbesserungen durch die Verwendung von Multikathoden-Anordnungen erzielen kann. Um eine angemessene Basis für die Konstruktion solcher Elektroden zu schaffen, stellen wir eine Analyse vor und besprechen ihre Merkmale. Die Elektrode wird anfänglich im Modell dargestellt, indem man annimmt, daß die Kathoden aus mit Membranen abgedeckten Scheiben ohne Wechselwirkung bestehen. Aus derpO2-Verteilung und dem polarographischen Strom werden Gleichungen abgeleitet. Der Einfluß des Kathodendurchmessers, der Membranstärke und der Durchlässigkeit werden untersucht, besonders in bezug auf die Abhängigkeit der Durchflußgeschwindigkeit. Eine Erweiterung der Analyse auf die Situation, wo eine Wechselwirkung zwischen den Kathoden bedeutend wird, wird ebenfalls dargestellt. Analyse und Ergebnisse bieten die richtige Grundlage für eine optimale Konstruktion von Multikathoden-pO2-Elektroden.

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Abbreviations

C :

constant

D m :

diffusion coefficient of oxygen in the membrane

D o :

diffusion coefficient of oxygen in the medium

F :

Farady's constant

J 0 :

zeroth-order Bessel function

K e :

oxygen permeability of electrolyte solution

K m :

oxygen permeability of membrane

K o :

oxygen permeability of medium

n :

number of electrons involved in the reduction of one molecule of oxygen (n=4)

P :

absolute partial pressure (oxygen tension)

P * :

oxygen tension of unperturbed medium

p :

oxygen tension normalised toP *

p o :

oxygen tension under zero-flow conditions normalised toP *

p ∞ :

oxygen tension under infinite-flow conditions normalised toP *

q o :

normalised flux of oxygen under zero-flow conditions, normalised toP *

q ∞ :

normalised flux of oxygen under infinite flow conditions, normalised toP *

R ex :

Reynolds number

r 0 :

radius of the cathode

U :

main-stream flow velocity of the medium

x :

distance from the leading edge where the diffusion layer is initiated

z 0 :

thickness of membrane normalised tor 0

α m :

oxygen solubility in the membrane

α o :

oxygen solubility in the medium

δ:

boundary-layer thickness

ɛ:

diffusion-layer thickness

ν:

kinematic viscosity of the medium

σ:

sensitivity of the cathode

\(\bar \sigma \) :

normalised sensitivity of the cathode

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Authors and Affiliations

  1. Institute of Biomedical Engineering, University of Toronto, M5S 1A4, Toronto, Canada

    W. Siu & R. S. C. Cobbold

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  1. W. Siu
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  2. R. S. C. Cobbold
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Siu, W., Cobbold, R.S.C. Characteristics of a multicathode polarographic oxygen electrode. Med. & biol. Engng. 14, 109–121 (1976). https://doi.org/10.1007/BF02478736

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  • DOI: https://doi.org/10.1007/BF02478736

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