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Research Papers

Formulation of Generalized Mass Transfer Correlations for Blood Oxygenator Design

[+] Author and Article Information
Kenny W. Q. Low

Advanced Sustainable Manufacturing
Technologies (ASTUTE 2020) Operation,
College of Engineering,
Swansea University,
Bay Campus, Fabian Way,
Swansea SA1 8EN, UK
e-mail: k.w.q.low@swansea.ac.uk

Raoul Van Loon

Advanced Sustainable Manufacturing
Technologies (ASTUTE 2020) Operation,
College of Engineering,
Swansea University,
Bay Campus, Fabian Way,
Swansea SA1 8EN, UK
e-mail: r.vanloon@swansea.ac.uk

Samuel A. Rolland

Advanced Sustainable Manufacturing
Technologies (ASTUTE 2020) Operation,
College of Engineering,
Swansea University,
Bay Campus, Fabian Way,
Swansea SA1 8EN, UK
e-mail: s.rolland@swansea.ac.uk

Johann Sienz

Advanced Sustainable Manufacturing
Technologies (ASTUTE 2020) Operation,
College of Engineering,
Swansea University,
Bay Campus, Fabian Way,
Swansea SA1 8EN, UK
e-mail: j.sienz@swansea.ac.uk

1Corresponding author.

Manuscript received June 20, 2016; final manuscript received December 12, 2016; published online January 23, 2017. Assoc. Editor: Ram Devireddy.

J Biomech Eng 139(3), 031007 (Jan 23, 2017) (16 pages) Paper No: BIO-16-1262; doi: 10.1115/1.4035535 History: Received June 20, 2016; Revised December 12, 2016

This paper numerically investigates non-Newtonian blood flow with oxygen and carbon dioxide transport across and along an array of uniformly square and staggered arranged fibers at various porosity (ε) levels, focussing on a low Reynolds number regime (Re < 10). The objective is to establish suitable mass transfer correlations, expressed in the form of Sherwood number (Sh = f(ε, Re, Sc)), that identifies the link from local mass transfer investigations to full-device analyses. The development of a concentration field is initially investigated and expressions are established covering the range from a typical deoxygenated condition up to a full oxygenated condition. An important step is identified where a cut-off point in those expressions is required to avoid any under- or over-estimation on the Sherwood number. Geometrical features of a typical commercial blood oxygenator is adopted and results in general show that a balance in pressure drop, shear stress, and mass transfer is required to avoid potential blood trauma or clotting formation. Different definitions of mass transfer correlations are found for oxygen/carbon dioxide, parallel/transverse flow, and square/staggered configurations, respectively. From this set of correlations, it is found that transverse flow has better gas transfer than parallel flow which is consistent with reported literature. The mass transfer dependency on fiber configuration is observed to be pronounced at low porosity. This approach provides an initial platform when one is looking to improve the mass transfer performance in a blood oxygenator without the need to conduct any numerical simulations or experiments.

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Figures

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Fig. 1

Fiber bundles in the oxygenators which can be represented by a unit cell of ordered (a) square and (b) staggered arrays of cylinders. Illustration adopted from Ref. [31]. The annotations d and Sp. are the fiber diameter and spacing, respectively.

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Fig. 2

Comparison of nondimensional permeability for square and staggered configurations due to (a) transverse and (b) parallel flows against analytical results based on Re = 0.5 (△) and Re = 10 (□). Numerical results are indicated as solid and dash lines for square and staggered configurations, respectively. Analytical expression abbreviations are indicated as (Sq) and (St) for square and staggered configurations, respectively.

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Fig. 3

The development of Sh¯O2 and Sh¯CO2 for square configurations of (a) transverse and (b) parallel flows based on ε = 0.7 at Re = 10. The solid lines represent fitted data via least squares with R2 correlations of 0.95 and above. The dash lines refer to their respective C*.

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Fig. 4

Normalized velocity magnitude with streamlines superimposed (top half) and shear stress contours (bottom half) of porosity 0.7 and 0.3 for transverse flow past square (Sq) and staggered (St) configurations at (a)–(d) Re = 0.5 and (e)–(h) Re = 10. Contour legend in the top and bottom depicts the normalized velocity magnitude and shear stress, respectively. (i)–(l) Circumferential wall shear stress along one fiber of porosity 0.7 and 0.3 at (a) Re = 0.5 and (b)–(c) 10 transverse flow past square (Sq) and staggered (St) configurations. (a) Sq; ε = 0.7; Re = 0.5, (b) Sq; ε = 0.3; Re = 0.5, (c) St; ε = 0.7; Re = 0.5, (d) St; ε = 0.3; Re = 0.5, (e) Sq; ε = 0.7; Re = 10, (f) Sq; ε = 0.3; Re = 10, (g) St; ε = 0.7; Re = 10, (h) St; ε = 0.3; Re = 10, (i) Sq; ε = 0.7, (j) Sq; ε = 0.3, (k) St; ε = 0.7, and (l) St; ε = 0.3.

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Fig. 5

(a)–(h) Normalized partial pressure of O2 (top half) and CO2 (bottom half) of porosity 0.7 and 0.3 for transverse flow past square (Sq) and staggered (St) configurations at Re = 0.5 and Re = 10. (i)–(l) Local ShO2 and ShCO2 along one fiber of porosity 0.7 and 0.3 at Re = 0.5, 1, 5, and 10 transverse flow past square (Sq) and staggered (St) configurations. (a) Sq. ε = 0.7; Re = 0.5, (b) Sq. ε = 0.3; Re = 0.5, (c) St. ε = 0.7; Re = 0.5, (d) St. ε = 0.3; Re = 0.5, (e) Sq. ε = 0.7; Re = 10, (f) Sq. ε = 0.3; Re = 10, (g) St. ε = 0.7; Re = 10, (h) St. ε = 0.3; Re = 10, (i) Sq. ε = 0.7, (j) Sq. ε = 0.3, (k) St. ε = 0.7, and (l) St. ε = 0.3.

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Fig. 6

Mass transfer correlations comparison of (a) O2 and (b) CO2 for transverse flow at porosities 0.7 (◊), 0.6 (▷), 0.5 (△), 0.4 (×) and 0.3 (). Mass transfer parameters a (◁) and b (○) fittings of (c) O2 and (d) CO2 for transverse flow. Solid line represents square arrangement and dashed line represents staggered arrangements. Data are fitted via least squares and expressed in lines with the mass transfer and R2 correlations. The R2 correlations represent the actual fittings without the  log10 terms. (a) Transv. flow O2 mass transfer correlation, (b) Transv. flow CO2 mass transfer correlation, (c) Transv. flow O2 mass transfer parameters, and (d) Transv. flow CO2 mass transfer parameters.

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Fig. 7

(a)–(d) Normalized velocity magnitude with streamlines superimposed (top half) and shear stress contours (bottom half) of porosity 0.7 and 0.3 for parallel flow past square (Sq) and staggered (St) configurations at Re = 10. Contour legend in the top and bottom depicts the normalized velocity and shear stress, respectively. (e)–(h) Wall shear stress along one fiber of porosity 0.7 and 0.3 at Re = 0.5, 1, 5, and 10 transverse flow past square (Sq) and staggered (St) configurations. (a) Sq; ε = 0.7; Re = 10, (b) Sq; ε = 0.3; Re = 10, (c) St; ε = 0.7; Re = 10, (d) St; ε = 0.3; Re = 10, (e) Sq; ε = 0.7, (f) Sq; ε = 0.3, (g) St; ε = 0.7, and (h) St; ε = 0.3.

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Fig. 8

(a)–(h) Normalized partial pressure of O2 (top half) and CO2 (bottom half) of porosity 0.7 and 0.3 for parallel flow past square (Sq) and staggered (St) configurations at Re = 0.5 and Re = 10. (i)–(l) Local ShO2 and ShCO2 along one fiber of porosity 0.7 and 0.3 at Re = 0.5, 1, 5, and 10 parallel flow past square (Sq) and staggered (St) configurations. (a) Sq. ε = 0.7; Re = 0.5, (b) Sq. ε = 0.3; Re = 0.5, (c) St. ε = 0.7; Re = 0.5, (d) St. ε = 0.3; Re = 0.5, (e) Sq. ε = 0.7; Re = 10, (f) Sq. ε = 0.3; Re = 10, (g) St. ε = 0.7; Re = 10, (h) St. ε = 0.3; Re = 10, (i) Sq. ε = 0.7, (j) Sq. ε = 0.3, (k) St. ε = 0.7, and (l) St. ε = 0.3.

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Fig. 9

Mass transfer correlations comparison of (a) O2 and (b) CO2 for parallel flow at porosities 0.7 (◊), 0.6 (▷), 0.5 (△), 0.4 (×) and 0.3 (). Mass transfer parameters a (◁) and b (○) fittings of (c) O2 and (d) CO2 for parallel flow. Solid line represents square arrangement and dashed line represents staggered arrangements. Data are fitted via least squares and expressed in lines with the mass transfer and R2 correlations. The R2 correlations represent the actual fittings without the  log10 terms. (a) Parallel flow O2 mass transfer correlation, (b) parallel flow CO2 mass transfer correlation, (c) parallel flow O2 mass transfer parameters, and (d) parallel flow CO2 mass transfer parameters.

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Fig. 10

Mass transfer coefficients comparison between fiber configurations and flow directions at various ε levels for (a) O2 and (b) CO2. The notation Sq. refers to square and St. refers to staggered fiber configuration. The notation Transv. represents transverse flow and Paral. represents parallel flow.

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