Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-18T18:02:26.519Z Has data issue: false hasContentIssue false
  • English
  • Français

Finite deformation of liquid capsules enclosed by elastic membranes in simple shear flow

Published online by Cambridge University Press:  26 April 2006

C. Pozrikidis
C. Pozrikidis
Affiliation:
Department of Applied Mechanics and Engineering Sciences, University of California at San Diego, La Jolla, CA 92093-0411, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The transient deformation of liquid capsules enclosed by elastic membranes subject to simple shear flow is studied numerically using a new implementation of the boundary element method. The numerical results for capsules with spherical unstressed shapes and varying degrees of surface elasticity are compared with the predictions of an asymptotic theory for small deformations due to Barthès-Biesel and coworkers, and the significance of nonlinear effects due to finite deformation is assessed. It is found that the capsules exhibit continuous elongation when the dimensionless shear rate becomes larger than a critical threshold, in agreement with recent experimental observations of capsules with polymerized interfaces. Membrane failure at large deformations is discussed with respect to membrane thinning and development of excessive elastic tensions, and it is argued that the location where the membrane is likely to rupture due to continued deformation is insensitive to the precise mechanism of rupture. The numerical results suggest that a dilute suspension of capsules behaves like shear-thinning medium with some elastic properties. Results of oblate spheroidal capsules suggest that the points of maximum membrane thinning and tension coincide but their location depends upon the unstressed capsule shape.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 297 , 25 August 1995 , pp. 123 - 152
Copyright
© 1995 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

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. 1991 Role of interfacial properties on the motion and deformation of capsules in shear flow. Physica A 172, 103–124.Google Scholar
Barthégs-Biesel, D. & Chhim, V. 1981 The constitutive equation of a dilute suspension of spherical microcapsules. Intl J. Multiphase Flow 7, 493–505.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
Batchelor, G. K. 1970 The stress system in a suspension of force-free particles. J. Fluid Mech. 41, 545–570.Google Scholar
Brunn, P. O. 1980a On the rheology of viscous drops surrounded by an elastic shell. Biorheology 17, 419–430.Google Scholar
Brunn, P. O. 1980b The deformation of a viscous particle surrounded by an elastic shell in a general time-dependent linear flow field. J. Fluid Mech. 126, 533–544.Google Scholar
Chang, K. S. & Olbright, W. L. 1993 Experimental studies of the deformation of a synthetic capsule in extensional flow. J. Fluid Mech. 250, 587–608.Google Scholar
Evans, E. A. & Skalak, R. 1980 Mechanics and Thermodynamics of Biomembranes. CRC Press.
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 Fluids 23, 251–278.Google Scholar
Lacell, P. L., Evans, E. A. & Hochmuth, R. M. 1977 Erythrocyte membrane elasticity, fragmentation and lysis. Blood Cells 3, 335–350.Google Scholar
Lee, J. S. & Fung, Y. C. 1969 Modeling experiments of a single red blood cell moving in a capillary blood vessel. Microvascular Res. 1, 221–243.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
Novozhilov, V. V. 1962 Theory of Elasticity. Pergamon Press.
Peskin, C. S. & Mcqueen, D. M. 1980 Modeling prosthetic heart valves for numerical analysis of blood flow in the heart. J. Comput. Phys. 37, 113–132.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 deformation of liquid drops and the rheology of dilute emulsions in simple shearing flow. J. Non-Newtonian Fluid Mech. 51, 161–178.Google Scholar
Richardson, E. 1974 Deformation of haemolysis of red blood cells in shear flow. Proc. R. Soc. Lond. A 338, 129–153.Google Scholar
Schmid-Schöunbein, H. 1975 Erythrocyte rheology and the optimization of mass transport in the microcirculation. Blood Cells 1, 285–306.Google Scholar
Secomb, T. W. & Skalak, R. 1982 Surface flow of viscoelastic membranes in viscous fluids. Q. J. Mech. Appl. Maths 35, 233–247.Google Scholar
Skalak, R., Töuzeren, A., Zarda, R. P. & Chien, S. 1973 Strain energy function of red blood cell membranes. Biophys. J. 13, 245–264.Google Scholar
Stone, H. 1994 Dynamics of drop deformation and breakup in viscous fluids. Ann. Rev. Fluid Mech. 26, 65–102.Google Scholar
Sutera, S. P., Seshadri, V. P., Groce, A. & Hochmuth, R. M. 1970 Capillary blood flow. II. Deformable model cells in tube flow. Microvascular Res. 2, 420–433.Google Scholar
Zhou, H. & Pozrikidis, C. 1995 Deformation of capsules with incompressible interfaces in simple shear flow. J. Fluid Mech. 283, 175–200.Google Scholar