Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-19T06:07:39.419Z Has data issue: false hasContentIssue false
  • English
  • Français

Motion of a tank-treading ellipsoidal particle in a shear flow

Published online by Cambridge University Press:  20 April 2006

Stuart R. Keller  and
Richard Skalak
Stuart R. Keller
Affiliation:
Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, NY 10027, U.S.A. Present address: Exxon Production Research Company, P.O. Box 2189, Houston, Texas 77001, U.S.A.
Richard Skalak
Affiliation:
Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, NY 10027, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

A theoretical model is developed for the motion of a human red blood cell in a shear field. The model consists of a tank-treading ellipsoidal membrane encapsulating an incompressible Newtonian liquid immersed in a plane shear flow of another incom- pressible Newtonian liquid. Equilibrium and energy considerations lead to a solution for the motion of the particle that depends on the ellipsoidal-axis ratios and the ratio of the inner- to outer-liquid viscosities. The effect of variation in these parameters is explored and it is shown that, depending on their values, one of two types of overall motion is exhibited: a steady stationary-orientation motion or an unsteady flipping motion. A qualitative agreement of the predicted behaviour of the model with experi- mental observations on red blood cells is found.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 120 , July 1982 , pp. 27 - 47
Copyright
© 1982 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Barthès-Biesel, D. 1980 Motion of a spherical microcapsule freely suspended in a linear shear flow. J. Fluid Mech. 100, 831–853.Google Scholar
Bessis, M. & Mohandas, N. 1975 Deformability of normal, shape-altered and pathological red cells. Blood Cells 1, 315–321.Google Scholar
Brennen, C. 1975 A concentrated suspension model for the Couette rheology of blood. Can. J. Chem. Engng 53, 126–133.Google Scholar
Brenner, H. & Bungay, P. M. 1971 Rigid particle and liquid-droplet models of red cell motion in capillary tubes. Fedn Proc. Fedn Socs Exp. Biol. 30, 1565–1576.Google Scholar
Chien, S. 1975 Biophysical behaviour of red cells in suspension. In The Red Blood Cell (ed. D. MacN. Surgeon), vol. 2, pp. 1031–1135. Academic.
Chien, S., Usami, S. & Bertles, J. F. 1970 Abnormal rheology of oxygenated blood in sickle cell anemia. J. Clin. Invest. 49, 623–634.Google Scholar
Chien, S., Sung, K. P., Skalak, R., Usami, S. & Tözeren, A. 1978 Theoretical and experimental studies on viscoelastic properties of erythrocyte membrane. Biophys. J. 24, 463–487.Google Scholar
Cokelet, G. R. & Meiselman, H. J. 1968 Rheological comparison of hemoglobin solutions and erythrocyte suspensions. Science 162, 275–277.Google Scholar
Cox, R. G. 1969 The deformation of a drop in a general time-dependent fluid flow. J. Fluid Mech. 37, 601–623.Google Scholar
Evans, E. A. & Fung, Y. C. 1972 Improved measurements of the erythrocyte geometry. Microvas. Res. 4, 335–347.Google Scholar
Evans, E. A. & Hochmuth, R. M. 1976 Membrane viscoelasticity. Biophys. J. 16, 1–11.Google Scholar
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. & Schmid-Schönbein, H. 1977 Tank tread motion of red cell membranes in viscometric flow: Behavior of intracellular and extracellular markers (with film). Blood Cells 3, 351–365.Google Scholar
Fischer, T. M., Stöhr-Liesen, M. & Schmid-Schönbein, H. 1978a The red cells as a fluid droplet: Tank tread-like motion of the human erythrocyte membrane in shear flow. Science 202, 894–896.Google Scholar
Fischer, T. M., Stöhr, M. & Schmid-Schönbein, H. 1978b Red blood cell (RBC) microrheology: Comparison of the behavior of single RBC and liquid droplets in shear flow. A.I.Ch.E. Symp. Series no. 182, 74, 38–45.Google Scholar
Gauthier, F. J., Goldsmith, H. L. & Mason, S. G. 1972 Flow of suspensions through tubes — X Liquid drops as models of erythrocytes. Biorheology 9, 205–224.Google Scholar
Goldsmith, H. L. 1967 Microscopic flow properties of red cells. Fedn Proc. Fedn Am. Socs Exp. Biol. 26, 1813–1820.Google Scholar
Goldsmith, H. L. & Marlow, J. 1972 Flow behavior of erythrocytes. I. Rotation and deformation in dilute suspensions. Proc. R. Soc. Lond. B 182, 351–384.Google Scholar
Goldsmith, H. L. & Mason, S. G. 1967 The microrheology of dispersions. In Rheology, Theory and Applications (ed. F. R. Eirich), vol. 4, pp. 85–250. Academic.
Guerlet, B., Barthès-Biesel, D. & Stoltz, J. F. 1977 Deformation of a sphered red blood cell freely suspended in a simple shear flow. Cardiovascular and Pulmonary Dynamics. INSERM (Journal of the Institute National de la Santéde la Recherche Médicale) 71, 257–264.Google Scholar
Jeffery, G. B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A 102, 161–179.Google Scholar
Keller, S. R. 1979a A model for everythrocyte tank-treading motion in a shear flow. In 1979 Advances in Bioengineering (ed. M. K. Wells), pp. 125–127. A.S.M.E.
Keller, S. R. 1979b On the surface area of the ellipsoid. Math. Comp. 33, 310–314.Google Scholar
Keller, S. R. & Skalak, R. 1980 Flipping motion of a tank-treading ellipsoid in a shear flow. In 1980 Advances in Bioengineering (ed. V. C. Mow), pp. 309–312. A.S.M.E.
Kholeif, I. A. & Weymann, H. D. 1974 Motion of a single red blood cell in plane shear flow. Biorheology 11, 337–348.Google Scholar
Kline, K. A. 1972 On a liquid drop model of blood rheology. Biorheology 9, 287–299.Google Scholar
Morris, D. R. & Williams, A. R. 1979 The effects of suspending medium viscosity on erythrocyte deformation and haemolysis in vitro. Biochim. Biophys. Acta 550, 288–296.Google Scholar
Richardson, E. 1974 Deformation and haemolysis of red cells in shear flow. Proc. R. Soc. Lond. A 338, 129–153.Google Scholar
Roscoe, R. 1967 On the rheology of a suspension of viscoelastic spheres in a viscous liquid. J. Fluid Mech. 28, 273–293.Google Scholar
Schmid-Schönbein, H. 1975 Erythrocyte rheology and the optimization of mass transport in the microcirculation. Blood Cells 1, 285–306.Google Scholar
Schmid-Schönbein, H. & Wells, R. 1969 Fluid drop-like transition of erythrocytes under shear. Science 165, 288–291.Google Scholar
Secomb, T. W. & Skalak, R. 1982 Surface flow of a viscoelastic membrane surrounded by viscous fluids. Quart. J. Mech. Appl. Math. (in the press).
Skalak, R. 1970 Extensions of extremum principles for slow viscous flow. J. Fluid Mech. 42, 527–548.Google Scholar
Skalak, R., Tözeren, A., Zarda, P. R. & Chien, S. 1973 Strain energy function of red blood cell membranes. Biophys. J. 13, 245–264.Google Scholar
Sutera, S., Mehrjardi, M. & Mohandas, N. 1975 Deformation of erythrocytes under shear. Blood Cells 1, 369–374.Google Scholar
Taylor, G. I. 1932 The viscosity of a fluid containing small drops of another fluid. Proc. R. Soc. Lond. A 138, 41–48.Google Scholar
Taylor, G. I. 1934 The formation of emulsions in definable fields of flow. Proc. R. Soc. Lond. A 146, 501–523.Google Scholar