Advertisement

Suspensions of Capsules

  • D. Barthes-Biesel
Part of the International Centre for Mechanical Sciences book series (CISM, volume 370)

Abstract

The motion of capsules freely suspended into another liquid subjected to flow is studied. Experimental evidence regarding the deformation of artificial capsules or of red blood cells in shear flows is presented. Results of filtration experiments conducted on red cell suspensions are also discussed. The equations describing the mechanics of a single capsule are presented. Perturbation solutions obtained for initially spherical particles are discussed together with approximate solutions for ellipsoidal capsules. In the case of non spherical particles subjected to large deformations, numerical models must be devised, and some new results are presented.

Keywords

Shear Flow Capillary Number Viscosity Ratio Shear Elastic Modulus Simple Shear Flow 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Fung Y.C. (1981) Biomechanics, chapt. 4. New-York, Springer-Verlag.CrossRefGoogle Scholar
  2. 2.
    Skalak R., Özkaya N., Skalak T.C. (1989) Biofluid mechanics. Ann. Rev. Fluid Mech., 21, 167–204.ADSCrossRefGoogle Scholar
  3. 3.
    Hochmuth R.M., Berk D.A. (1984) Analytical solutions for shear deformation and flow of red cell membrane. J. Biomech. Eng., 106, 2–9.CrossRefGoogle Scholar
  4. 4.
    Hochmuth R.M., Waugh R.E. (1987) Erythrocyte membrane elasticity and viscosity. Ann. Rev. Physiol., 49, 209–219.CrossRefGoogle Scholar
  5. 5.
    Lardner T.J., Pujara P. (1980) Compression of spherical shells. Mech. Today, 5, 161–176.MathSciNetGoogle Scholar
  6. 6.
    Hiramoto Y. (1970) Rheological properties of sea-urchin eggs. Biorheology, 6, 201–234.Google Scholar
  7. 7.
    Chang K.S., Olbricht W.L. (1993) Experimental studies of the deformation of a synthetic capsule in extensional flow. J. Fluid Mech., 250, 587–608.ADSCrossRefGoogle Scholar
  8. 8.
    Chang K.S., Olbricht W.L. (1993) Experimental studies of the deformation and breakup of a synthetic capsule in steady and unsteady simple shear flow. J. Fluid Mech., 250, 609–633.ADSCrossRefGoogle Scholar
  9. 9.
    Burger A., Rehage H. (1992) From two-dimensional model networks to microcapsules, Ang. Makromol. Chem., 202–203, 31–44.CrossRefGoogle Scholar
  10. 10.
    Akchiche M. (1987) Thèse de Doctorat. Université de Compiègne.Google Scholar
  11. 11.
    Barthes-Biesel D. (1991) Role of interface properties on the motion and deformation of capsules in shear flow. Physica A., 172, 103–124.ADSCrossRefGoogle Scholar
  12. 12.
    Bentley B.J., Leal L.G. (1986) An experimental investigation of drop deformation and breakup in steady, two-dimensional linear flows. J. Fluid Mech., 167, 241–283.ADSCrossRefMATHGoogle Scholar
  13. 13.
    Schmid-Schonbein H., Wells R.E. (1969) Fluid to drop like transition of erythrocytes under shear. Science, 165, 288–291.ADSCrossRefGoogle Scholar
  14. 14.
    Pfafferott C., Wenby R., Meiselman H.J. (1982) Morphologic and internal viscosity aspects of red blood cell rheologic behaviour. Blood Cells, 8, 68–78.Google Scholar
  15. 15.
    Nash G.B. (1990) Filterability of blood cells: methods and clinical applications. Biorheology, 27, 873–882.Google Scholar
  16. 16.
    Fischer T.C., Wenby R.B., Meiselman H.J. (1992) Pulse shape analysis of RBC micropore flow via new software for the cell transit analyser (CTA). Biorheology, 29, 185–201.Google Scholar
  17. 17.
    Kieswetter H., Dauer U., Teitel P., Schmid-Schonbein H., Trapp R. (1982) The single erythrocyte rigidometer (SER) as a reference for RBC deformability. Biorheology, 19, 737–753.Google Scholar
  18. 18.
    Schmid-Schonbein H., Gaehtgens P. (1981) What is red cell deformability ? Scand. J. Clin. Lab. Invest., 41, Supp1. 156, 13–26.CrossRefGoogle Scholar
  19. 19.
    Drochon A., Barthes-Biesel D., Bucherer C., Lacombe C., Lelievre J.C. (1993) Viscous filtration of red blood cell suspensions.Biorheology, 30, 1–7.Google Scholar
  20. 20.
    Barthes-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.ADSCrossRefMATHGoogle Scholar
  21. 21.
    Skalak R., Tozeren A., Zarda R.P., Chien S. (1973) Strain energy function of red blood cell membranes. Biophys. J., 13, 245–264.CrossRefGoogle Scholar
  22. 22.
    Evans E.A. (1973) A new material concept for the red cell membrane. Biophys. J., 13, 926–940.CrossRefGoogle Scholar
  23. 23.
    Brunn P.O. (1983) The deformation of a viscous particle surroundéd by an elastic shell in a general time-dependent linear flow field. J. Fluid Mech. 126, 533–544.ADSCrossRefMATHGoogle Scholar
  24. 24.
    Rallison J.M. and Acrivos A. A numerical study of the deformation and burst of a viscous drop in an extensional flow. J. Fluid Mech., 1978, 89, 191–200.ADSCrossRefMATHGoogle Scholar
  25. 25.
    Pozrikidis C. Boundary integral and singularity methods for linearized viscous flow. Cambridge University Press, 1992.Google Scholar
  26. 26.
    Barthes-Biesel D. (1980) Motion of a microcapsule in shear flow J. Fluid Mech., 100, 831–853.MathSciNetADSCrossRefMATHGoogle Scholar
  27. 27.
    Barthes-Biesel D., Sgaier H. (1985) Role of membrane viscosity in the orientation and deformation of a capsule suspended in shear flow. J. Fluid Mech., 160, 119–135.MathSciNetADSCrossRefMATHGoogle Scholar
  28. 28.
    Keller S.R., Skalak R. (1982) Motion of a tank-treading ellipsoidal particle in a shear flow. J. Fluid Mech., 120, 27–47.ADSCrossRefMATHGoogle Scholar
  29. 29.
    Tran-Son-Tay R., Sutera S.P., Rao P.R. (1984) Determination of RBC membrane viscosity from rheoscopic observations of tank-treading motion. Biophys. J., 46, 65–72.CrossRefGoogle Scholar
  30. 30.
    Tran-Son-Tay R., Sutera S.P., Zahalak G.I., Rao P.R. (1987) Membrane stress and internal pressure in a RBC freely suspended in a shear flow. Biophys. J. 51, 915–924.CrossRefGoogle Scholar
  31. 31.
    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
  32. 32.
    Li X.Z., Barthes-Biesel D. & Helmy A. (1988), Large deformations and burst of a capsule freely suspended in an elongational flow. J. Fluid Mech. 187, 179–196.ADSCrossRefMATHGoogle Scholar
  33. 33.
    Pozrikidis C. (1990) The axisymmetric deformation of a red blood cell in uniaxial straining Stokes flow. J. Fluid Mech., 216, 231–254.ADSCrossRefMATHGoogle Scholar
  34. 34.
    Pozrikidis C. 1995 Finite deformation of liquid capsules enclosed by elastic membranes in simple shear flow. J. Fluid Mech., 297, 123–152.ADSCrossRefMATHGoogle Scholar
  35. 35.
    Zhou H. & Pozrikidis C. (1995) Deformation of liquid capsules with incompressible interfaces in simple shear flow. J. Fluid Mech. 283, 175–200.ADSCrossRefMATHGoogle Scholar
  36. 36.
    Helmy A. and Barthès-Biesel D. (1982) Migration of a spherical capsule freely suspended in an unbounded parabolic flow. J. de Mécanique Théorique et Appliquée. 1, 859–880.MATHGoogle Scholar
  37. 37.
    Halpern D. and Secomb T.W. (1989) The squeezing of red blood cells through capillaries with near minimal diameters. J. Fluid Mech., 203, 381–400.MathSciNetADSCrossRefMATHGoogle Scholar
  38. 38.
    Secomb T.W., Skalak R., Ozkaya N. & Gross J.F. (1986) Flow of axisymmetric red blood cells in narrow capillaries. J. Fluid Mech., 163, 405–423.ADSCrossRefGoogle Scholar
  39. 39.
    Leyrat-Maurin, A. (1993) Thèse de Doctorat. Université de Compiègne.Google Scholar
  40. 40.
    Leyrat-Maurin, A., Barthes-Biesel, D. Motion of a spherical capsule through a hyperbolic constriction. J. Fluid Mech., 1994, 279, 135–163.ADSCrossRefMATHGoogle Scholar
  41. 41.
    Quéguiner C. (1995) Thèse de Doctorat. Université de Compiègne.Google Scholar
  42. 42.
    Quéguiner C., Barthes-Biesel D. (1996) Flow of capsules through cylindrical channels. Submitted to J. Fluid Mech.Google Scholar
  43. 43.
    Chien S., Schmid-Schönbein G.W., Sung K.L.P., Schmalzer E.A. and Skalak R. (1984) Viscoelastic properties of leukocytes in White Cell Mechanics: basic science and clinical aspects, Alan R. Liss Inc 1984, 19–51.Google Scholar

Copyright information

© Springer-Verlag Wien 1996

Authors and Affiliations

  • D. Barthes-Biesel
    • 1
  1. 1.Compiègne University of TechnologyCompiègneFrance

Personalised recommendations