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Effect of a soluble surfactant on a finite-sized bubble motion in a blood vessel

Published online by Cambridge University Press:  23 December 2009

T. N. SWAMINATHAN ,
K. MUKUNDAKRISHNAN ,
P. S. AYYASWAMY  and
D. M. ECKMANN
T. N. SWAMINATHAN
Affiliation:
Department of Anesthesiology and Critical Care, University of Pennsylvania, PA 19104, USA Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, PA 19104, USA
K. MUKUNDAKRISHNAN
Affiliation:
Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, PA 19104, USA
P. S. AYYASWAMY*
Affiliation:
Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, PA 19104, USA
D. M. ECKMANN
Affiliation:
Department of Anesthesiology and Critical Care, University of Pennsylvania, PA 19104, USA
*
†Email address for correspondence: ayya@seas.upenn.edu
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Abstract

We present detailed results for the motion of a finite-sized gas bubble in a blood vessel. The bubble (dispersed phase) size is taken to be such as to nearly occlude the vessel. The bulk medium is treated as a shear thinning Casson fluid and contains a soluble surfactant that adsorbs and desorbs from the interface. Three different vessel sizes, corresponding to a small artery, a large arteriole, and a small arteriole, in normal humans, are considered. The haematocrit (volume fraction of RBCs) has been taken to be 0.45. For arteriolar flow, where relevant, the Fahraeus–Lindqvist effect is taken into account. Bubble motion causes temporal and spatial gradients of shear stress at the cell surface lining the vessel wall as the bubble approaches the cell, moves over it and passes it by. Rapid reversals occur in the sign of the shear stress imparted to the cell surface during this motion. Shear stress gradients together with sign reversals are associated with a recirculation vortex at the rear of the moving bubble. The presence of the surfactant reduces the level of the shear stress gradients imparted to the cell surface as compared to an equivalent surfactant-free system. Our numerical results for bubble shapes and wall shear stresses may help explain phenomena observed in experimental studies related to gas embolism, a significant problem in cardiac surgery and decompression sickness.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 642 , 10 January 2010 , pp. 509 - 539
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Ayyaswamy, P. S. 2008 Introduction to biofluid mechanics. In Fluid Mechanics, 4th ed. (ed. Kundu, P. K. & Cohen, Ira M.), pp. 765–840. Academic Press.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Mechanics. Cambridge University Press.Google Scholar
Berger, S. A., Goldsmith, W. & Lewis, E. R. 1996 Introduction to Bioengineering. Oxford University Press.Google Scholar
Bond, W. N. & Newton, D. A. 1928 Bubbles, drops and stokes' law (paper 2). Phil. Mag. 5, 794–800.CrossRefGoogle Scholar
Branger, A. B. & Eckmann, D. M. 1999 Theoretical and experimental intravascular gas embolism absorption dynamics. J. Appl. Physiol. 87, 1287–1295.Google Scholar
Branger, A. B. & Eckmann, D. M. 2002 Accelerated arteriolar gas embolism reabsorption by an exogenous surfactant. Anesthesiology 96 (4), 971–979.Google Scholar
Butler, P. J., Tsou, T. C., Li, J. Y. S., Usami, S. & Chien, S. 2001 Rate sensitivity of shear-induced changes in the lateral diffusion of endothelial cell membrane lipids: a role for membrane perturbation in shear-induced mapk activation. Faseb J. 15, 216–218.Google Scholar
Cavanagh, D. P. & Eckmann, D. M. 1999 Interfacial dynamics of stationary gas bubbles in flows in inclined tubes. J. Fluid Mech. 398, 225–244.CrossRefGoogle Scholar
Chang, C.-H. & Franses, E. I. 1995 Adsorption dynamics of surfactants at the air/water interface: a critical review of mathematical models, data, and mechanisms. Colloids Surfaces A: Physicochem. Engng Aspects 100, 1–45.Google Scholar
Colella, P. 1990 A multidimensional second order Godunov scheme for conservation laws. J. Comput. Phys. 87, 171.Google Scholar
Das, B., Johnson, P. C. & Popel, A. S. 2000 Computational fluid dynamic studies of leukocyte adhesion effects on non-Newtonian blood flow through microvessels. Biorheology 37 (3), 239–258.Google Scholar
Eckmann, D. M. & Armstead, S. C. B. S. 2006 Influence of endothelial glycocalyx degradation and surfactants on air embolism adhesion. Anesthesiology 105 (6), 1220–1227.Google Scholar
Eckmann, D. M., Kobayashi, S. & Li, M. 2005 Microvascular embolization following polidocanol microfoam sclerosant administration. Dermatologic Surgery 31 (5), 636–643.Google Scholar
Eckmann, D. M. & Lomivorotov, V. N. 2003 Microvascular gas embolization clearance following perfluorocarbon administration. J. Appl. Physiol. 94, 860–868.Google Scholar
Eckmann, D. M., Zhang, J., Lampe, J. & Ayyaswamy, P. S. 2006 Gas embolism and surfactant-based intervention. Ann. New York Acad. Sci. 1077, 256–269.CrossRefGoogle ScholarPubMed
Eggleton, C. D., Pawar, Y. P. & Stebe, K. J. 1999 Insoluble surfactant on a drop in an extension flow: a generalization of the stagnated surface limit to deformable interfaces. J. Fluid Mech. 385, 79–99.Google Scholar
Eggleton, C. D., Tsai, T. M. & Stebe, K. J. 2001 Tip streaming from a drop in the presence of surfactants. Phys. Rev. Lett. 87 (4), 048302(1–4).CrossRefGoogle ScholarPubMed
Fung, Y. C. 1997 Biomechanics: Circulation. Springer.Google Scholar
Ghadiali, S. N. & Gaver, D. P. 2003 The influence of non-equilibrium surfactant dynamics on the flow of a semi-infinite bubble in a rigid cylindrical capillary tube. J. Fluid Mech. 478, 165–196.CrossRefGoogle Scholar
Griffith, B. E. & Peskin, C. S. 2005 On the order of accuracy of the immersed boundary method: higher-order convergence rates for sufficiently smooth problems. J. Comput. Phys. 208, 75–105.Google Scholar
Happel, J. & Brenner, H. 1983 Low Reynolds Number Hydrodynamics. Martinus Nijhoff.Google Scholar
Huang, H. D., Kamm, R. D. & Lee, R. T. 2004 Cell mechanics and mechanotransduction: pathways, probes, and physiology. Am. J. Physiol. Cell Physiol. 287, C1–C11.CrossRefGoogle ScholarPubMed
Jacqmin, D. 1999 Calculation of two-phase Navier–Stokes flows using phase-field modelling. J. Comput. Phys. 55, 96.Google Scholar
James, A. J. & Lowengrub, J. 2004 A surfactant-conserving volume-of-fluid method for interfacial flows within soluble surfactant. J. Comput. Phys. 201, 685–722.Google Scholar
Johnson, R. A. & Borhan, A. 2003 Pressure-driven motion of surfactant-laden drops through cylindrical capillaries: effect of surfactant solubility. J. Colloid Interface Sci. 261, 529–541.Google Scholar
Johnson, R. E. & Sadhal, S. S. 1983 Stokes flow past bubbles and drops partially coated with thin films. Part 2. Thin films with internal circulation – a perturbation solution. J. Fluid Mech. 132, 295–318.CrossRefGoogle Scholar
Lee, L. & Leveque, R. 2003 An immersed interface method for incompressible Navier–Stokes equations. SIAM J. Sci. Comput. 25, 832.Google Scholar
Levich, V. G. 1962 Physicochemical Hydrodynamics. Prentice Hall.Google Scholar
Li, X. F. & Pozrikidis, C. 1997 The effect of surfactant on drop deformation and on the rheology of dilute emulsion in stokes flow. J. Fluid Mech. 341, 165–194.Google Scholar
Liu, S. Q., Ruan, Y. Y., Tang, D., Li, Y. C., Goldman, J. & Zhong, L. 2002 A possible role of initial cell death due to mechanical stretch in the regulation of subsequent cell proliferation in experimental vein grafts. Biomech. Model. Mechanobiol. 1 (1), 17–27.Google Scholar
McKinney, J. S., Willoughby, K. A., Liang, S. & Ellis, E. F. 1996 Stretch-induced injury of cultured neuronal, glial, and endothelial cells: effect of polyethylene glycol–conjugated superoxide dismutase. Stroke 27 (5), 934–940.Google Scholar
McNeil, P. L. & Steinhardt, R. A. 1997 Loss, restoration, and maintenance of plasma membrane integrity. J. Cell Biol. 137, 1–4.Google Scholar
Mendez, J. L., Rickman, O. B. & Hubmayr, R. D. 2004 Plasma membrane stress failure in ventilator-injured lungs – a hypothesis about osmoregulation and the pharmacologic protection of the lungs against deformation. Biol. Neonate 85, 290–292.CrossRefGoogle ScholarPubMed
Milliken, W. J. & Leal, L. G. 1994 The influence of surfactant on the deformation and breakup of a viscous drop. J. Colloid Interface Sci. 166, 275–285.Google Scholar
Mukundakrishnan, K., Ayyaswamy, P. S. & Eckmann, D. M. 2008 a Finite-sized gas bubble motion in a blood vessel: non-newtonian effects. Phys. Rev. E 78, 036303(1–15).Google Scholar
Mukundakrishnan, K., Ayyaswamy, P. S. & Eckmann, D. M. 2009 Bubble motion in a blood vessel: shear stress induced endothelial cell injury. J. Biomech. Engng 131 (7), 074516.Google Scholar
Mukundakrishnan, K., Eckmann, D. M. & Ayyaswamy, P. S. 2008 b Bubble motion through a generalized power-law fluid flowing in a vertical tube. Ann. New York Acad. Sci. 1161, 256–267.Google Scholar
Mukundakrishnan, K., Quan, S., Eckmann, D. M. & Ayyaswamy, P. S. 2007 Numerical study of wall effects on buoyant gas-bubble rise in a liquid-filled finite cylinder. Phys. Rev. E 76, 036308(1–15).Google Scholar
Muradoglu, M. & Tryggvason, G. 2008 A front-tracking method for computation of interfacial flows with soluble surfactants. J. Comput. Phys. 227, 2238–2262.Google Scholar
Oguz, H. N. & Sadhal, S. S. 1988 Effects of soluble and insoluble surfactants on the motion of drops. J. Fluid Mech. 194, 563–579.Google Scholar
Oike, M., Droogmans, G. & Nilius, B. 1994 Mechanosensitive Ca2+ transients in endothelial cells from human umbilical vein. Proc. Natl Acad. Sci. USA 91 (8), 2940–2944.Google Scholar
Osher, S. & Fedkiw, R. 2001 Level set methods: an overview and some recent results. J. Comput. Phys. 169, 463.Google Scholar
Palaparthi, R., Papageorgiou, D. T. & Maldarelli, C. 2006 Theory and experiments on the stagnant cap regime in the motion of spherical surfactant-laden bubbles. J. Fluid Mech. 559, 1–44.Google Scholar
Papanastasiou, T. C. 1987 Flows of materials with yield. J. Rheol. 31 (5), 385–404.CrossRefGoogle Scholar
Park, C. W. 1992 Influence of soluble surfactant on the motion of a finite bubble in a capillary tube. Phys. Fluids A 4 (11), 2335–2347.Google Scholar
Quan, S. & Schmidt, D. P. 2007 A moving mesh interface tracking method for 3d incompressible two-phase flows. J. Comput. Phys. 221, 761–780.Google Scholar
Radl, S., Tryggvason, G. & Khinast, J. G. 2007 Flow and mass transfer of fully resolved bubbles in non-Newtonian fluids. AIChE J. 53, 1861–1878.Google Scholar
Rodrigue, D., De Kee, D. & Chan Man Fong, C. F. 1996 An experimental study of the effect of surfactants on the free rise velocity of gas bubbles. J. Non-Newt. Fluid Mech. 66 (3), 213–232.Google Scholar
Rodrigue, D., De Kee, D., Chan Man Fong, C. F. & Yao, J. 1999 The slow motion of a single gas bubble in a non-newtonian fluid containing surfactants. J. Non-Newt. Fluid Mech. 86, 211–227.Google Scholar
Sadhal, S. S., Ayyaswamy, P. S. & Chung, J. N. 1997 Transport Phenomena with Drops and Bubbles. Springer.Google Scholar
Sadhal, S. S. & Johnson, R. E. 1983 Stokes flow past bubbles and drops partially coated with thin films. Part 1. Stagnant cap of surfactant film - exact solution. J. Fluid Mech. 133, 65–81.CrossRefGoogle Scholar
Scardovelli, R. & Zaleski, S. 1999 Direct numerical simulation of free surface and interfacial flow. Ann. Rev. Fluid Mech. 31, 576.Google Scholar
Sharan, M. & Popel, A. S. 2001 A two-phase model for blood flow in narrow tubes with increased viscosity near the wall. Biorheology 38, 415–428.Google Scholar
Shin, S., Abdel-Khalik, S. I., Daru, V. & Juric, D. 2005 Accurate representation of surface tension using the level contour reconstruction method. J. Comput. Phys. 203, 493–516.Google Scholar
Shin, S. & Juric, D. 2002 Modelling three-dimensional multiphase flow using a level contour reconstruction method for front tracking without connectivity. J. Comput. Phys. 180, 427–470.Google Scholar
Sigurdson, W. J., Sachs, F. & Diamond, S. L. 1993 Mechanical perturbation of cultured human endothelial cells causes rapid increases of intracellular calcium. Am. J. Physiol. Heart Circ. Physiol. 264 (6), H1745–H1752.Google Scholar
Somasundaran, P. 2006 Encyclopedia of Surface and Colloid Science. CRC Press.Google Scholar
Stone, H. A. 1990 A simple derivation of the time-dependent convective-diffusive equation for surfactant transport along a deforming interface. Phys. Fluids A 2, 111–112.Google Scholar
Sussman, M., Almgren, A. S., Bell, J. B., Colella, P., Howell, L. & Welcome, M. 1999 An adaptive level set approach for incompressible two-phase flows. J. Comput. Phys. 148, 81.Google Scholar
Sussman, M. & Puckett, E. G. 2000 A coupled level set and volume-of-fluid method for computing 3D and axisymmetric incompressible two-phase flows. J. Comput. Phys. 162 (2), 301–337.Google Scholar
Suzuki, A., Armstead, S. C. & Eckmann, D. M. 2004 Surfactant reduction in embolism bubble adhesion and endothelial damage. Anesthesiology 101, 97–103.Google Scholar
Swaminathan, T. N., Ayyaswamy, P. S. & Eckmann, D. M. 2009 Favourable conditions for exogenous surfactant-based intervention of gas embolism (in preparation).Google Scholar
Torres, D. J. & Brackbill, J. U. 2000 The point-set method: front tracking without connectivity. J. Comput. Phys. 165, 620.Google Scholar
Tryggvason, G., Bunner, B., Esmaeeli, A., Juric, D., Al-Rawahi, N., Tauber, W., Han, J., Nas, S. & Jan, Y. J. 2001 A front-tracking method for the computations of multiphase flow. J. Comput. Phys. 169, 708–759.CrossRefGoogle Scholar
Tsai, T. M. & Miksis, M. J. 1994 Dynamics of a drop in a constricted capillary tube. J. Fluid Mech. 274, 197–217.Google Scholar
Udaykumar, H. S., Tran, L., Belk, D. M. & Vanden, K. J. 2003 An Eulerian method for computation of multimaterial impact with ENO shock-capturing and sharp interfaces. J. Comput. Phys. 186, 136–177.Google Scholar
Unverdi, S. O. & Tryggvason, G. 1992 A front-tracking method for viscous incompressible, multi-fluid flows. J. Comput. Phys. 100 (1), 25–37.Google Scholar
Van Sint Annaland, M., Dijkhuizen, W., Deen, N. G. & Kuipers, J. A. M. 2006 Numerical simulation of gas bubbles behaviour using a 3D front tracking method. AIChE J. 52, 99–110.Google Scholar
Vlahakis, N. E. & Hubmayr, R. D. 2000 Invited review: plasma membrane stress failure in alveolar epithelial cells. J. Appl. Physiol. 89, 2490–2496.CrossRefGoogle ScholarPubMed
Wesseling, P. 1992 An Introduction to Multigrid Methods. John Wiley & Sons.Google Scholar
Yon, S. & Pozrikidis, C. 1998 A finite volume/boundary-element method for flow past interfaces in the presence of surfactants, with application to shear flow past a viscous drop. Comput. Fluids 27, 879–902.Google Scholar
Young, N. O., Goldstein, J. S. & Block, M. J. 1959 The motion of bubbles in a vertical temperature gradient. J. Fluid Mech. 6, 350.Google Scholar
Zhang, J., Eckmann, D. M. & Ayyaswamy, P. S. 2006 A front tracking method for a deformable intravascular bubble in a tube with soluble surfactant transport. J. Comput. Phys. 214, 366–396.Google Scholar