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Blood oxygenation in coiled silicone-rubber tubes of complex geometry

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Abstract

Oxygen transfer to blood and water was investigated experimentally for steady flow in a ‘complex coil’, a silicone-rubber tube formed into a sequence of helical coil sections of alternating orientation. The series of reorientations caused the secondary flow induced by the helical motion to be continually re-established, so that mixing of the liquid was enhanced. Complex coils of various configurations were tested in an oxygen atmosphere and a significant improvement of the oxygen-transfer to the liquids was measured while the pressure drop increased moderately. The case of ideal oxygen transfer, i.e. a perfectly mixed fluid, was treated theoretically and a comparison of these results with the experimental data demonstrated how much the fluid-side resistance was reduced by complex coiling.

Sommaire

Le passage de l’oxygène dans le sang et dans l’eau fut étudié de façon expérimentale pour un débit constant dans une ‘spirale complexe’, tube en caoutchouc de silicone constitué d’une série de sections hélicoìdales à orientation alternée. La série de réorientations provoquait le rétablissement continu du flux secondaire induit par le mouvement hélicoìdal, de manière à accroître le mélange du liquide. Des spirales complexes de diverses configurations furent soumises à des essais dans une atmosphère d’oxygène et une amélioration significative du passage de l’oxygène dans les liquides fut mesurée alors que la chute de pression s’intensifiait modérément. Le cas d’un transfert idéal d’oxygène—par example dans un liquide parfaitement mélangé—fut traité de façon théorique et une comparaison de ces résultats avec les données expérimentales a demontré à quel point la résistance latérale du liquide était réduite par le système de spirales complexes.

Zusammenfassung

Sauerstoffübertragung an Blut und Wasser wurde experimentell für stetige Strömung in einer ‘komplexen Spule’ untersucht, einem Silikonkautschukrohr, das in eine Folge von Wendelspulen alternativer Orientierung geformt wurde. Die Reihe von Wieder-Orientierungen verursachte die fortgesetzte Wiederherstellung des von der Spiralbewegung induzierten Sekundärstromes, so daß die Mischung der Flüssigkeit gefördert wurde. Komplexe Spulen verschiedener Konfiguration wurden in einer Sauerstoffatmophäre geprüft und es wurde eine beträchtliche Verbesserung der Sauerstoffübertragung an die Flüssigkeiten gemessen, während der Druckanfall ein wenig anstieg. Der Fall der idealen Sauerstoffübertragung-d.h. an eine vollkommen gemischte Flüssigkeit- wurde theoretisch behandelt und ein Vergleich dieser Resultate mit den experimentellen Daten zeigte, um wieviel der Widerstand von Seiten der Flüssigkeit durch komplexe Spulung verringert wurde.

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Abbreviations

a :

internal tube radius, cm

a 1,a 2,a 3 :

coefficients of the modified Hill equation (eqn. 5)

c :

concentration, mole/cm3

c s :

amount of oxygen per unit blood volume bound to haemoglobin at full saturation (s=1), cm3 (s.t.p.)/100 ml blood or mole/cm3

d :

internal tube diameter, cm

d h :

hydraulic diameter = (4-times area)/circumference), cm

D :

coil diameter, cm

De :

Re√(d/D), Dean number

D m :

oxygen diffusivity in the membrane, cm2/s

f :

Δp(d/L)/(v 2 g/2), friction factor

f s :

64/Re, friction factor for laminar flow in straight tubes

G :

4(αD) m /(αD) wb , dimensionless membrane permeability

Hb :

total haemoglobin concentration of the blood = (g haemoglobin)/(100 ml blood),g%

L :

tube length, cm

P :

(p−p 0)/(p g −p 0), dimensionless partial pressure of oxygen

P f :

dimensionless partial pressureP in the ideally mixed fluid

p :

partial pressure (of oxygen), mmHg

p co 2 :

partial pressure of carbon dioxide mmHg

p o2 :

partial pressure of oxygen, mmHg

p g :

gas-side partial pressure of oxygen, mmHg

p o :

inlet oxygen partial pressure of the fluid, mmHg

p 1 :

outlet oxygen partial pressure of the fluid, mmHg

Δp :

static pressure drop along the tube axis, mmHg

pH:

standard measure for the concentration of free hydrogen ions

Q :

flow rate, ml/min

R :

r/a, dimensionless radial co-ordinate

r :

radial co-ordinate, cm

Re :

vd/v=2a v/v, Reynolds number

s :

degree of oxygen saturation of blood haemoglobin (0≤s≤1)

Sc :

(v/D o2) wb , Schmidt number for oxygen diffusion in whole blood (=wb)

T :

temperature, deg C

v :

mean velocity, cm/s

W :

w/a, dimensionless wall thickness

w :

wall thickness, cm

Z :

(z/a) G/(Re Sc), dimensionless axial co-ordinate

z :

axial co-ordinate, cm

(αD) m :

membrane oxygen-permeability, mole/(s cm mmHg)

α f :

effective oxygen-solubility of the fluid, for blood, α f is defined by eqn. 4, mole/(cm3 mmHg)

α f *:

α f /α wb , dimensionless effective oxygen solubility for whole blood

α m :

membrane oxygen solubility, mole/(cm3 mmHg)

α wb :

oxygen solubility of the whole blood, including plasma and red cells, mole/(cm3 mmHg)

ν:

kinematic viscosity, cm2/s

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Authors and Affiliations

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

    U. Baurmeister, D. F. James & W. Zingg

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  1. U. Baurmeister
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  2. D. F. James
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  3. W. Zingg
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Baurmeister, U., James, D.F. & Zingg, W. Blood oxygenation in coiled silicone-rubber tubes of complex geometry. Med. Biol. Eng. Comput. 15, 106–117 (1977). https://doi.org/10.1007/BF02442953

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