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Journal of Biomechanical Engineering | Volume 128 | Issue 1 | TECHNICAL PAPERS
TECHNICAL PAPERS: Fluids/Heat/Transport

Pulsatile Flow and Mass Transport Over an Array of Cylinders: Gas Transfer in a Cardiac-Driven Artificial Lung

[+] Author and Article Information
Kit Yan Chan, Hideki Fujioka, James B. Grotberg

Department of Biomedical Engineering, The University of Michigan, Ann Arbor, Michigan 48109

Robert H. Bartlett, Ronald B. Hirschl

Department of Surgery, The University of Michigan Medical School, Ann Arbor, Michigan 48109

J Biomech Eng 128(1), 85-96 (Sep 14, 2005) (12 pages) doi:10.1115/1.2133761 History: Received May 04, 2005; Revised September 14, 2005
Article
References
Figures
Tables
Citing Articles

The pulsatile flow and gas transport of a Newtonian passive fluid across an array of cylindrical microfibers are numerically investigated. It is related to an implantable, artificial lung where the blood flow is driven by the right heart. The fibers are modeled as either squared or staggered arrays. The pulsatile flow inputs considered in this study are a steady flow with a sinusoidal perturbation and a cardiac flow. The aims of this study are twofold: identifying favorable array geometry/spacing and system conditions that enhance gas transport; and providing pressure drop data that indicate the degree of flow resistance or the demand on the right heart in driving the flow through the fiber bundle. The results show that pulsatile flow improves the gas transfer to the fluid compared to steady flow. The degree of enhancement is found to be significant when the oscillation frequency is large, when the void fraction of the fiber bundle is decreased, and when the Reynolds number is increased; the use of a cardiac flow input can also improve gas transfer. In terms of array geometry, the staggered array gives both a better gas transfer per fiber (for relatively large void fraction) and a smaller pressure drop (for all cases). For most cases shown, an increase in gas transfer is accompanied by a higher pressure drop required to power the flow through the device.
Copyright © 2006 by American Society of Mechanical Engineers
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References

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Fazzalari, F. L., Bartlett, R. H., 1994, “An Intrapleural Lung Prothesis-Rationale, Design, and Testing,” Artif. Organs, 18 (11), pp. 801–805.
2
Lynch, W. R., Montoya, J. P., 2000, “Hemodynamic Effect of a Low-Resistance Artificial Lung in Series With the Native Lungs of Sheep,” Ann. Thorac. Surg., 69 (2), pp. 351–356.
3
Zwischenberger, J. B., and Alpard, S. K., 2002, “Artificial Lungs: A New Inspiration,” Perfusion, 17 (4), pp. 253–268.
4
Ichinose, K., Okamoto, T., 2004, “Comparison of a New Heparin-Coated Dense Membrane Lung With Nonheparin-Coated Dense Membrane Lung for Prolonged Extracorporeal Lung Assist in Goats,” Artif. Organs, 28 (11), pp. 993–1001.
5
Haft, J. W., Griffith, B. P., 2002, “Results of an Artificial-Lung Survey to Lung Transplant Program Directors,” J. Heart Lung Transplant, 21 (4), pp. 467–472.
6
Vaslef, S. N., Mockros, L. F., 1994, “Use of a Mathematical Model to Predict Oxygen Transfer Rates in Hollow Fiber Membrane Oxygenators,” ASAIO J., 40 , pp. 990–996.
7
Vaslef, S. N., Mockros, L. F., 1994, “Computer-Assisted Design of an Implantable, Intrathoracic Artificial Lung,” Artif. Organs, 18 (11), pp. 813–817.
8
Hewitt, T. J., Hattler, B. G., 1998, “A Mathematical Model of Gas Exchange in an Intravenous Membrane Oxygenator,” Ann. Biomed. Eng.  [CrossRef], 26 (1), pp. 166–178.
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Dierickx, P. W., De Somer, F., 2000, “Hydrodynamic Characteristics of Artificial Lungs,” ASAIO J.  [CrossRef], 46 (5), pp. 532–535.
10
Kanamori, T., Niwa, M., 2000, “Estimate of Gas Transfer Rates of Intravascular Membrane Oxygenator,” ASAIO J.  [CrossRef], 46 (5), pp612–619.
11
Dierickx, P. W., De Wachter, D. S., 2001, “Mass Transfer Characteristics of Artificial Lungs,” ASAIO J.  [CrossRef], 47 (6), pp. 628–633.
12
Weissman, M. H., and Mockros, L. F., 1968, “Oxygen and Carbon Dioxide Transfer in Membrane Oxygenators,” Med. Biol. Eng., 7 , pp. 169–184.
13
Smeby, L., and Grimsrud, L., 1974, “Theoretical Investigation of Mass Transfer in Membrane Oxygenators,” Med. Biol. Eng., 12 (5), pp. 698–706.
14
Dorson, W. J., Larsen, K. G., 1971, “Oxygen Transfer to Blood: Data and Theory,” Trans. Am. Soc. Artif. Intern. Organs, 17 , pp. 309–316.
15
Baker, D. A., Holte, J. E., 1991, “Computationally Two-Dimensional Finite-Difference Model for Hollow-Fiber Blood-Gas Exchange Device,” Med. Biol. Eng. Comput., 29 , pp. 482–488.
16
Wang, N. H., and Keller, N. H., 1979, “Solute Transport Induced by Erythrocyte Motions in Shear-Flow,” Trans. Am. Soc. Artif. Intern. Organs, 25 , pp. 14–18.
17
Wang, N. H., and Keller, N. H., 1985, “Augmented Transport of Extracellular Solutes in Concentrated Erythrocyte Suspensions in Couette-Flow,” J. Colloid Interface Sci.  [CrossRef], 103 (1), pp. 210–225.
18
Dierickx, P. W. T., De Wachter, D., 2000, “Blood Flow Around Hollow Fibers,” Int. J. Artif. Organs, 23 (9), pp. 610–617.
19
Dierickx, P. W., De Wachter, D. S., 2001, “Two-Dimensional Finite Element Model for Oxygen Transfer in Cross-Flow Hollow Fiber Membrane Artificial Lungs,” Int. J. Artif. Organs, 24 (9), pp. 628–635.
20
Mockros, L. F., and Gaylor, J. D. S., 1975, “Artificial Lung Design—Tubular Membrane Units,” Med. Biol. Eng., 13 (2), pp. 171–181.
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Gage, K. L., Gartner, M. J., 2002, “Predicting Membrane Oxygenator Pressure Drop Using Computational Fluid Dynamics,” Artif. Organs  [CrossRef], 26 (7), pp. 600–607.
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Boschetti, F., Cook, K. E., 2003, “Blood Flow Pulsatility Effects Upon Oxygen Transfer in Artificial Lungs,” ASAIO J.  [CrossRef], 49 (6), pp. 678–686.
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Pennati, G., Fiore, G. B., 1998, “Mass Transfer Efficiency of a Commercial Hollow Fiber Oxygenator During Six-Hour in vitro Perfusion With Steady and Pulsatile Blood Flow,” Int. J. Artif. Organs, 21 (2), pp. 97–106.
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Haft, J. W., Bull, J. L., 2003, “Design of an Artificial Lung Compliance Chamber for Pulmonary Replacement,” ASAIO J.  [CrossRef], 49 (1), pp. 35–40.
25
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Patankar, S. V., 1980, "Numerical Heat Transfer and Fluid Flow", Hemisphere Pub. Corp., McGraw-Hill, New York, Washington.
27
Edwards, D. A., Shapiro, M., 1990, “The Influence of Reynolds Number Upon the Apparent Permeability of Spatially Periodic Arrays of Cylinders,” Phys. Fluids A  [CrossRef], 2 (1), pp. 45–55.
28
Ghaddar, C. K., 1995, “On the Permeability of Unidirectional Fibrous Media: A Parallel Computational Approach,” Phys. Fluids  [CrossRef], 7 (11), pp. 2563–2585.

Figures

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+Artificial lung device (reproduced with permission from Michigan Critical Care Consultant Inc., Ann Arbor, MI)
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Artificial lung device (reproduced with permission from Michigan Critical Care Consultant Inc., Ann Arbor, MI)
Figure 1

Artificial lung device (reproduced with permission from Michigan Critical Care Consultant Inc., Ann Arbor, MI)

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+Fiber arrangement. The unit cell is marked by the dashed lines
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Fiber arrangement. The unit cell is marked by the dashed lines
Figure 2

Fiber arrangement. The unit cell is marked by the dashed lines

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+Example of unit cells
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Example of unit cells
Figure 3

Example of unit cells

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+Two functional forms of pulsatile input U(t)
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Two functional forms of pulsatile input U(t)
Figure 4

Two functional forms of pulsatile input U(t)

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+Gas concentration computational domain and boundary conditions. Dash rectangle represents the computational domain.
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Gas concentration computational domain and boundary conditions. Dash rectangle represents the computational domain.
Figure 5

Gas concentration computational domain and boundary conditions. Dash rectangle represents the computational domain.

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+Sample grid
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Sample grid
Figure 6

Sample grid

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+Plot of time-averaged Sherwood number and gas concentration vs fiber layer number. (Square array: α=1; Re=10; A=0.5; ε=0.8036.)
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Plot of time-averaged Sherwood number and gas concentration vs fiber layer number. (Square array: α=1; Re=10; A=0.5; ε=0.8036.)
Figure 7

Plot of time-averaged Sherwood number and gas concentration vs fiber layer number. (Square array: α=1; Re=10; A=0.5; ε=0.8036.)

Grahic Jump Location
+Concentration profile and instantaneous streamlines: squared array. The upper plot indicates the concentration contours lines and the lower plot shows the instantaneous streamlines pattern. (a) t=14cycle; (b) t=34cycle; (c) U(t) (α=1; Re=10; A=0.5; ε=0.8036).
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Concentration profile and instantaneous streamlines: squared array. The upper plot indicates the concentration contours lines and the lower plot shows the instantaneous streamlines pattern. (a) t=14cycle; (b) t=34cycle; (c) U(t) (α=1; Re=10; A=0.5; ε=0.8036).
Figure 8

Concentration profile and instantaneous streamlines: squared array. The upper plot indicates the concentration contours lines and the lower plot shows the instantaneous streamlines pattern. (a) t=14cycle; (b) t=34cycle; (c) U(t) (α=1; Re=10; A=0.5; ε=0.8036).

Grahic Jump Location
+Concentration profile and instantaneous streamlines: staggered array. The upper plot indicates the concentration contours lines and the lower plot shows the instantaneous streamlines pattern. (a) t=14cycle; (b) t=34cycle; (c) U(t) (α=1; Re=10; A=0.5; ε=0.8036).
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Concentration profile and instantaneous streamlines: staggered array. The upper plot indicates the concentration contours lines and the lower plot shows the instantaneous streamlines pattern. (a) t=14cycle; (b) t=34cycle; (c) U(t) (α=1; Re=10; A=0.5; ε=0.8036).
Figure 9

Concentration profile and instantaneous streamlines: staggered array. The upper plot indicates the concentration contours lines and the lower plot shows the instantaneous streamlines pattern. (a) t=14cycle; (b) t=34cycle; (c) U(t) (α=1; Re=10; A=0.5; ε=0.8036).

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+(a) α influence on the surface-average Sherwood number time cycle. (b) α influence on ΔP∕L time cycle (Re=10; A=0.5; ε=0.8036).
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(a) α influence on the surface-average Sherwood number time cycle. (b) α influence on ΔP∕L time cycle (Re=10; A=0.5; ε=0.8036).
Figure 10

(a) α influence on the surface-average Sherwood number time cycle. (b) α influence on ΔP∕L time cycle (Re=10; A=0.5; ε=0.8036).

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+Concentration profile and instantaneous streamlines. The upper plot indicates the concentration contours lines and the lower plot shows the instantaneous stream lines pattern. (a) t=0cycle; (b) t=12cycle; (c) U(t) (α=2; Re=10; A=0.5; ε=0.8036).
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Concentration profile and instantaneous streamlines. The upper plot indicates the concentration contours lines and the lower plot shows the instantaneous stream lines pattern. (a) t=0cycle; (b) t=12cycle; (c) U(t) (α=2; Re=10; A=0.5; ε=0.8036).
Figure 11

Concentration profile and instantaneous streamlines. The upper plot indicates the concentration contours lines and the lower plot shows the instantaneous stream lines pattern. (a) t=0cycle; (b) t=12cycle; (c) U(t) (α=2; Re=10; A=0.5; ε=0.8036).

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+(a) A influence on the surface-average Sherwood number time cycle. (b) A influence on the ΔP∕L time cycle (α=1; Re=10; ε=0.8036).
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(a) A influence on the surface-average Sherwood number time cycle. (b) A influence on the ΔP∕L time cycle (α=1; Re=10; ε=0.8036).
Figure 12

(a) A influence on the surface-average Sherwood number time cycle. (b) A influence on the ΔP∕L time cycle (α=1; Re=10; ε=0.8036).

Grahic Jump Location
+(a) Re influence on the surface-average Sherwood number time cycle. (b) Re influence on the ΔP∕L time cycle (α=1; A=0.5; ε=0.8036).
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(a) Re influence on the surface-average Sherwood number time cycle. (b) Re influence on the ΔP∕L time cycle (α=1; A=0.5; ε=0.8036).
Figure 13

(a) Re influence on the surface-average Sherwood number time cycle. (b) Re influence on the ΔP∕L time cycle (α=1; A=0.5; ε=0.8036).

Grahic Jump Location
+(a) ε influence on the surface-average Sherwood number time cycle. (b) ε influence on ΔP∕L time cycle (α=1; Re=10; A=0.5).
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(a) ε influence on the surface-average Sherwood number time cycle. (b) ε influence on ΔP∕L time cycle (α=1; Re=10; A=0.5).
Figure 14

(a) ε influence on the surface-average Sherwood number time cycle. (b) ε influence on ΔP∕L time cycle (α=1; Re=10; A=0.5).

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+Streamline patterns of staggered array with different ε(t=14cycle). (a) ε=0.4973; (b) ε=0.8036.
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Streamline patterns of staggered array with different ε(t=14cycle). (a) ε=0.4973; (b) ε=0.8036.
Figure 15

Streamline patterns of staggered array with different ε(t=14cycle). (a) ε=0.4973; (b) ε=0.8036.

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+Concentration profile and instantaneous stream lines with cardiac U(t): squared array. (a) t=14cycle; (b) t=11∕20cycle; (c) U(t).
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Concentration profile and instantaneous stream lines with cardiac U(t): squared array. (a) t=14cycle; (b) t=11∕20cycle; (c) U(t).
Figure 16

Concentration profile and instantaneous stream lines with cardiac U(t): squared array. (a) t=14cycle; (b) t=11∕20cycle; (c) U(t).

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+Concentration profile and instantaneous stream lines with cardiac U(t): staggered array. t=14cycle; (b) t=11∕20cycle; (c) U(t).
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Concentration profile and instantaneous stream lines with cardiac U(t): staggered array. t=14cycle; (b) t=11∕20cycle; (c) U(t).
Figure 17

Concentration profile and instantaneous stream lines with cardiac U(t): staggered array. t=14cycle; (b) t=11∕20cycle; (c) U(t).

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+The log-log plot of space-average Sherwood vs Reynolds number. The solid symbols represent actual data; the solid line is the least-square fit. (Re=10, ε=0.4986).
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The log-log plot of space-average Sherwood vs Reynolds number. The solid symbols represent actual data; the solid line is the least-square fit. (Re=10, ε=0.4986).
Figure 18

The log-log plot of space-average Sherwood vs Reynolds number. The solid symbols represent actual data; the solid line is the least-square fit. (Re=10, ε=0.4986).

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