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Deformation of liquid capsules with incompressible interfaces in simple shear flow

Published online by Cambridge University Press:  26 April 2006

Hua Zhou  and
C. Pozrikidis
Hua Zhou
Affiliation:
Department of Applied Mechanics and Engineering Sciences, University of California at San Diego, La Jolla, CA 92093-0411, USA
C. Pozrikidis
Affiliation:
Department of Applied Mechanics and Engineering Sciences, University of California at San Diego, La Jolla, CA 92093-0411, USA
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Abstract

The transient deformation of liquid capsules enclosed by incompressible membranes whose mechanical properties are dominated by isotropic tension is studied as a model of red blood cell deformation in simple shear flow. The problem is formulated in terms of an integral equation for the distribution of the tension over the cell membrane which is solved using a point-wise collocation and a spectral-projection method. The computations illustrate the dependence of the deformed steady cell shape, membrane tank-treading frequency, membrane tension, and rheological properties of a dilute suspension, on the undeformed cell shape. The general features of the evolution of two-dimensional cells are found to be similar to those of three-dimensional cells, and the corresponding membrane tank-treading frequency and maximum tension are seen to attain comparable values. The numerical results are compared with previous asymptotic analyses for small deformations and available experimental observations, with satisfactory agreement. An estimate of the maximum shear stress for membrane breakup and red blood cell hemolysis is deduced on the basis of the computed maximum membrane tension at steady state.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 283 , 25 January 1995 , pp. 175 - 200
Copyright
© 1995 Cambridge University Press

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References

Barthégs-Biesel, D. 1980 Motion of a spherical microcapsule freely suspended in a linear shear flow. J. Fluid Mech. 100, 831–853.Google Scholar
Barthégs-Biesel, D. & Rallison, J. M. 1981 The time-dependent deformation of a capsule freely suspended in a linear shear flow. J. Fluid Mech. 113, 251–267.Google Scholar
Barthégs-Biesel, D. & Sgaier, H. 1985 Role of membrane viscosity in the orientation and deformation of a spherical capsule suspended in shear flow. J. Fluid Mech. 160, 119–135.Google Scholar
Beissinger, R. L. & Laugel, J.-F. 1987 Low-stress hemolysis in laminar blood flow: Bulk and surface effects in capillaries. AIChE J. 33, 99–108.Google Scholar
Brennen, C. 1975 A concentrated suspension model for the Couette rheology of blood. Can. J. Chem. Engng 53, 126–133.Google Scholar
Dintenfass, L. 1962 Considerations of the internal viscosity of red cells and its effect on the viscosity of whole blood. Angiology 13, 333–344.Google Scholar
Evans, E. A. & Fung, Y. C. 1972 Improved measurements of the crythrocyte geometry. Microvasc. Res. 4, 335–347.Google Scholar
Evans, E. A. & Hochmuth, R. M. 1976 Membrane viscoelasticity. Biophys. J. 16, 1–11.Google Scholar
Evans, E. A. & Skalak, R. 1980 Mechanics and Thermodynamics of Biomembranes. CRC Press.
Fischer, T. M. 1980 On the energy dissipation in a tank-treading human red blood cell. Biophys. J. 32, 863–868.Google Scholar
Fischer, T. M. 1992 Is the surface area of the red cell membrane skeleton locally conserved? Biophys. J. 61, 298–305.Google Scholar
Fischer, T. M., Stöhr-Liesen, M. & Schmid-Schöunbein, H. 1978 The red cell as a fluid droplet: Tank tread-like motion of the human crythrocyte membrane in shear flow. Science 202, 894–896.Google Scholar
Goldsmith, H. L. 1971 Deformation of human red cells in tube flow. Biorheology 7, 235–242.Google Scholar
Goldsmith, H. L. & Marlow, J. 1972 Flow behavior of crythrocytes. I. Rotation and deformation in dilute suspensions. Proc. R. Soc. Lond. B 182, 351–384.Google Scholar
Keller, S. R. & Skalak, R. 1982 Motion of a tank-treading ellipsoidal particle in a shear flow. J. Fluid Mech. 120, 27–47.Google Scholar
Kennedy, M. R., Pozrikidis, C. & Skalak, R. 1994 Motion and deformation of liquid drops and the rheology of dilute emulsions in simple shear flow. Computers and Fluids 23, 251–278.Google Scholar
Kholeif, I. A. & Weymann, H. D. 1974 Motion of a single red blood cell in plane shear flow. Biorheology 11, 337–348.Google Scholar
Krasny, R. 1986 A study of singularity formation in a vortex sheet by the point-vortex approximation. J. Fluid Mech. 167, 65–93.Google Scholar
Li, X. Z., Barthégs-Biesel, D. & Helmy, A. 1988 Large deformations and burst of a capsule freely suspended in an elongational flow. J. Fluid Mech. 187, 179–196.Google Scholar
Longuet-Higgins, M. S. & Cokelet, E. D. 1976 The deformation of steep surface waves on water I. A numerical method of computation. Proc. R. Soc. Lond. A 350, 1–26.Google Scholar
Niimi, H. & Sugihara, M. 1985 Cyclic loading on the red cell membrane in a shear flow: a possible cause of hemolysis. J. Biomech. Engng 107, 91–95.Google Scholar
Pozrikidis, C. 1990 The axisymmetric deformation of a red blood cell in uniaxial straining Stokes flow. J. Fluid Mech. 216, 231–254.Google Scholar
Pozrikidis, C. 1992 Boundary Integral and Singularity Methods for Linearized Viscous Flow. Cambridge University Press.
Pozrikidis, C. 1993 On the transient motion of ordered suspensions of liquid drops. J. Fluid Mech. 246, 301–320.Google Scholar
Pozrikidis, C. 1994 Effects of surface viscosity on the finite deformation of liquid drops and the rheology of dilute emulsions in simple shearing flow. J. Non-Newtonian Fluid Mech. 51, 161–178.Google Scholar
Pozrikidis, C. 1995 Finite deformation of liquid capsules enclosed by elastic membranes in simple shear flow. Submitted.
Richardson, E. 1974 Deformation and haemolysis of red cells in shear flow. Proc. R. Soc. Lond. A 338, 129–153.Google Scholar
Richardson, E. 1975 Applications of a theoretical model for haemolysis in shear flow. Biorheology 12, 27–37.Google Scholar
Schmid-Schöunbein, H. & wells, R. E. 1969 Fluid drop like transition of erythrocytes under shear stress. Science 165, 288–291.Google Scholar
Schowalter, W. R. 1978 Mechanics of Non-Newtonia Fluids. Pergamon Press.
Skalak, R., Özkaya, N. & Skalak, T. C. 1989 Biofluid mechanics. Ann. Rev. Fluid Mech. 21, 167–204.Google Scholar
Stone, H. 1994 Dynamics of drop deformation and breakup of viscous fluids. Ann. Rev. Fluid Mech. 26, 65–102.Google Scholar
Sugihara, M. & Niimi, H. 1984 Numerical approach to the motion of a red blood cell in Couette flow. Biorheology 21, 734–749.Google Scholar
Sutera, S. P. & Krogstad, D. J. 1991 Reduction of the surface-volume ratio: a physical mechanism contributing to the loss of red cell deformability in malaria. Biorheology 28, 221–229.Google Scholar
Sutera, S. P. & Mehrardi, M. H. 1975 Deformation and fragmentation of human red blood cells in turbulent shear flow. Biophys. J. 15, 1–10.Google Scholar
Sutera, S. P., Mueller, E. R. & Zahalak, G. I. 1990 Extensional recovery of an intact erythrocyte from a tank-treading motion. J. Biomech. Engng. 112, 250–256.Google Scholar
Sutera, S. P., Pierre, P. R. & Zahalak, G. I. 1989 Deduction of intrinsic mechanical properties of the erythrocyte membrane from observations of tank-treading in the rheoscope. Biorheology 26, 177–197.Google Scholar
Töuzeren, A., Skalak, R., Fedorciw, B., Sung, K. L. P. & Chien, S. 1984 Constitutive equations of erythrocyte membrane incorporating evolving preferred configuration. Biophys. J. 45, 541–549.Google Scholar
Tran-Son-Tay, R., Sutera, S. P. & Rao, P. R. 1984 Determination of red blood cell membrane viscosity from rheoscopic observations of tank-treading motion. Biophys. J. 46, 65–72.Google Scholar
Zahalak, G. I., Rao, P. R. & Sutera, S. P. 1987 Large deformations of a cylindrical liquid-filled membrane by a viscous shear flow. J. Fluid Mech. 179, 283–305.Google Scholar
Zhou, H., & Pozrikidis, C. 1993a The flow of suspensions in channels: single files of drops. Phys. Fluids A 5, 311–324.Google Scholar
Zhou, H. & Pozrikidis, C. 1936 The flow of ordered and random suspensions of two-dimensional drops in a channel. J. Fluid Mech. 255, 103–127.Google Scholar