Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-18T20:40:39.134Z Has data issue: false hasContentIssue false
  • English
  • Français

Effects of membrane hardness and scaling analysis for capsules in planar extensional flows

Published online by Cambridge University Press:  24 March 2014

P. Dimitrakopoulos
P. Dimitrakopoulos*
Affiliation:
Department of Chemical and Biomolecular Engineering, University of Maryland, College Park, MD 20742, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, we investigate computationally the effects of membrane hardness on the dynamics of strain-hardening capsules in planar extensional Stokes flows. As the flow rate increases, all capsules reach elongated steady-state configurations but the cross-section of the more strain-hardening capsules preserves its elliptical shape while the less strain-hardening capsules become lamellar. The capsule deformation in strong extensional flows is accompanied with very pointed edges, i.e. large edge curvatures and thus small local edge length scales, which makes the current investigation a multi-length interfacial dynamics problem. Our computational results for elongated strain-hardening capsules are accompanied with a scaling analysis which provides physical insight on the extensional capsule dynamics. The two distinct capsule conformations we found, i.e. the slender spindle and lamellar capsules, are shown to represent two different types of steady-state extensional dynamics. The former are stabilized mainly via the membrane’s shearing resistance and the latter via its area-dilatation resistance, associated with the elongation tension normal forces and thus both types differ from bubbles which are stabilized mainly via the lateral surface-tension normal forces. Our steady-state deformation results can be used to identify the elastic properties of a real capsule, i.e. the membrane’s shear and area-dilatation moduli, utilizing a single experimental technique.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Low-Reynolds-number flows: Boundary integral methods Biological Fluid Dynamics: Membranes
Type
Papers
Information
Journal of Fluid Mechanics , Volume 745 , 25 April 2014 , pp. 487 - 508
Copyright
© 2014 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

Acrivos, A. 1983 The breakup of small drops and bubbles in shear flows. Ann. N.Y. Acad. Sci. 404, 1–11.Google Scholar
Alexeev, A. & Balazs, A. C. 2007 Designing smart systems to selectively entrap and burst microcapsules. Soft Matt. 3, 1500–1505.Google Scholar
Barthès-Biesel, D. 1991 Role of interfacial properties on the motion and deformation of capsules in shear flow. Physica A 172, 103–124.Google Scholar
Barthès-Biesel, D., Diaz, A. & Dhenin, E. 2002 Effect of constitutive laws for two-dimensional membranes on flow-induced capsule deformation. J. Fluid Mech. 460, 211–222.CrossRefGoogle Scholar
Barthès-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.CrossRefGoogle Scholar
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.Google Scholar
Carin, M., Barthès-Biesel, D., Edwards-Lévy, F., Postel, C. & Andrei, D. C. 2003 Compression of biocompatible liquid-filled HSA-alginate capsules: determination of the membrane mechanical properties. Biotechnol. Bioengng 82, 207–212.Google Scholar
Chabert, M. & Viovy, J.-L. 2008 Microfluidic high-throughput encapsulation and hydrodynamic self-sorting of single cells. Proc. Natl Acad. Sci. USA 105, 3191–3196.Google Scholar
Chang, K. S. & Olbricht, W. L. 1993a Experimental studies of the deformation of a synthetic capsule in extensional flow. J. Fluid Mech. 250, 587–608.Google Scholar
Chang, K. S. & Olbricht, W. L. 1993b Experimental studies of the deformation and breakup of a synthetic capsule in steady and unsteady simple shear flow. J. Fluid Mech. 250, 609–633.Google Scholar
Cranston, H. A., Boylan, C. W., Carroll, G. L., Sutera, S. P., Williamson, J. R., Gluzman, I. Y. & Krogstad, D. J. 1984 Plasmodium falciparum maturation abolishes physiologic red cell deformability. Science 223, 400–403.CrossRefGoogle ScholarPubMed
Dimitrakopoulos, P. 2012 Analysis of the variation in the determination of the shear modulus of the erythrocyte membrane: Effects of the constitutive law and membrane modeling. Phys. Rev. E 85, 041917.Google Scholar
Dodson, W. R. III & Dimitrakopoulos, P. 2008 Spindles, cusps and bifurcation for capsules in Stokes flow. Phys. Rev. Lett. 101, 208102.Google Scholar
Dodson, W. R. III & Dimitrakopoulos, P. 2009 Dynamics of strain-hardening and strain-softening capsules in strong planar extensional flows via an interfacial spectral boundary element algorithm for elastic membranes. J. Fluid Mech. 641, 263–296.Google Scholar
Dodson, W. R. III & Dimitrakopoulos, P. 2010 Tank-treading of erythrocytes in strong shear flows via a non-stiff cytoskeleton-based continuum computational modeling. Biophys. J. 99, 2906–2916.CrossRefGoogle Scholar
Fiddes, L. K., Young, E. W. K., Kumacheva, E. & Wheeler, A. R. 2007 Flow of microgel capsules through topographically patterned microchannels. Lab on a Chip 7, 863–867.CrossRefGoogle ScholarPubMed
Fischer, T. M., Stöhr-Liesen, M. & Schmid-Schönbein, H. 1978 The red cell as a fluid droplet: tank tread-like motion of the human erythrocyte membrane in shear flow. Science 202, 894–896.Google Scholar
Ha, J. W. & Leal, L. G. 2001 An experimental study of drop deformation and breakup in extensional flow at high capillary number. Phys. Fluids 13, 1568–1576.CrossRefGoogle Scholar
Higley, M., Siegel, M. & Booty, M. R. 2012 Semi-analytical solutions for two-dimensional elastic capsules in Stokes flow. Proc. R. Soc. Lond. A 468, 2915–2938.Google Scholar
Hinch, E. J. & Acrivos, A. 1979 Steady long slender droplets in two-dimensional straining motion. J. Fluid Mech. 91, 401–414.Google Scholar
Hudson, S. D., Phelan, F. R., Handler, M. D. jr, Cabral, J. T., Migler, K. B. & Amis, E. J. 2004 Microfluidic analog of the four-roll mill. Appl. Phys. Lett. 85 (2), 335–337.CrossRefGoogle Scholar
Koleva, I. & Rehage, H. 2012 A comparison of different experimental methods for investigating the mechanical properties of plane polysiloxane membranes and capsule walls. Soft Matt. 8, 7672–7682.Google Scholar
Kessler, S., Finken, R. & Seifert, U. 2008 Swinging and tumbling of elastic capsules in shear flow. J. Fluid Mech. 605, 207–226.Google Scholar
Kumar, A. & Graham, M. D. 2012 Margination and segregation in confined flows of blood and other multicomponent suspensions. Soft Matt. 8, 10536–10548.Google Scholar
Kuriakose, S. & Dimitrakopoulos, P. 2011 Motion of an elastic capsule in a square microfluidic channel. Phys. Rev. E 84, 011906.Google Scholar
Kuriakose, S. & Dimitrakopoulos, P. 2013 Deformation of an elastic capsule in a rectangular microfluidic channel. Soft Matt. 9, 4284–4296.Google Scholar
Lac, E., Barthès-Biesel, D., Pelekasis, N. A. & Tsamopoulos, J. 2004 Spherical capsules in three-dimensional unbounded Stokes flows: effect of the membrane constitutive law and onset of buckling. J. Fluid Mech. 516, 303–334.Google Scholar
Leclerc, E., Kinoshita, H., Fujii, T. & Barthès-Biesel, D. 2012 Transient flow of microcapsules through convergent-divergent microchannels. Microfluid Nanofluid 12, 761–770.Google Scholar
Lensen, D., Breukelen, K. V., Vriezema, D. M. & Hest, J. C. M. V. 2010 Preparation of biodegradable liquid core PLLA microcapsules and hollow PLLA microcapsules using microfluidics. Macromol. Biosci. 10, 475–480.Google Scholar
Mohandas, N. & Chasis, J. A. 1993 Red blood cell deformability, membrane material properties and shape: regulation by transmembrane, skeletal and cytosolic proteins and lipids. Sem. Hem. 30, 171–192.Google Scholar
Park, S.-Y. & Dimitrakopoulos, P. 2013 Transient dynamics of an elastic capsule in a microfluidic constriction. Soft Matt. 9, 8844–8855.Google Scholar
Pieper, G., Rehage, H. & Barthès-Biesel, D. 1998 Deformation of a capsule in a spinning drop apparatus. J. Colloid Interface Sci. 202, 293–300.Google Scholar
Popel, A. S. & Johnson, P. C. 2005 Microcirculation and Hemorheology. Annu. Rev. Fluid Mech. 37, 43–69.Google Scholar
Pozrikidis, C. 2001 Interfacial dynamics for Stokes flow. J. Comput. Phys. 169, 250–301.Google Scholar
Pozrikidis, C.(Ed.) 2003 Modeling and Simulation of Capsules and Biological Cells. Chapman and Hall.Google Scholar
Prevot, M., Cordeiro, A. L., Sukhorukov, G. B., Lvov, Y., Besser, R. S. & Möhwald, H. 2003 Design of a microfluidic system to investigate the mechanical properties of layer-by-layer fabricated capsules. Macromol. Mater. Eng. 288, 915–919.Google Scholar
Rachik, M., Barthès-Biesel, D., Carin, M. & Edwards-Levy, F. 2006 Identification of the elastic properties of an artificial capsule membrane with the compression test: effect of thickness. J. Colloid Interface Sci. 301, 217–226.Google Scholar
Seiffert, S., Thiele, J., Abate, A. R. & Weitz, D. A. 2010 Smart microgel capsules from macromolecular precursors. J. Am. Chem. Soc. 132, 6606–6609.CrossRefGoogle ScholarPubMed
Skalak, R., Tozeren, A., Zarda, R. P. & Chien, S. 1973 Strain energy function of red blood cell membranes. Biophys. J. 13, 245–264.Google Scholar
Skalak, R., Özkaya, N. & Skalak, T. C. 1989 Biofluid mechanics. Annu. Rev. Fluid Mech. 21, 167–204.CrossRefGoogle Scholar
Skotheim, J. M. & Secomb, T. W. 2007 Red blood cells and other nonspherical capsules in shear flow: oscillatory dynamics and the tank-treading-to-tumbling transition. Phys. Rev. Lett. 98, 078301.CrossRefGoogle ScholarPubMed
Taylor, G. I. 1934 The formation of emulsions in definable fields of flow. Proc. R. Soc. Lond. A 146, 501–523.Google Scholar
Walter, J., Salsac, A. V., Barthès-Biesel, D. & Le Tallec, P. 2010 Coupling of finite element and boundary integral methods for a capsule in a Stokes flow. Intl J. Numer. Meth. Engng 83, 829–850.Google Scholar