Hostname: page-component-76fb5796d-zzh7m Total loading time: 0 Render date: 2024-04-26T15:23:29.984Z Has data issue: false hasContentIssue false
  • English
  • Français

Deformation of spherical compound capsules in simple shear flow

Published online by Cambridge University Press:  16 June 2015

Zheng Yuan Luo ,
Long He  and
Bo Feng Bai
Zheng Yuan Luo
Affiliation:
State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, PR China
Long He
Affiliation:
State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, PR China
Bo Feng Bai*
Affiliation:
State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, PR China
*
†Email address for correspondence: bfbai@mail.xjtu.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

The deformation of a compound capsule (an elastic capsule with a smaller capsule inside) in simple shear flow is studied by using three-dimensional numerical simulations based on a front tracking method. The inner and outer capsules are concentric and initially spherical. Skalak et al.’s constitutive law is employed for the mechanics of both the inner and outer membranes. Our results concerning the deformation of homogeneous capsules (i.e. capsules without the inner capsules) are quantitatively in agreement with the predictions of previous numerical simulations and perturbation theories. Compared to homogeneous capsules, compound capsules exhibit smaller deformation. The deformations of both the inner and outer capsules are significantly affected by the capillary numbers of the inner and outer membranes and the volume ratio of the inner to the outer capsule. When the inner capsule is small, it presents smaller deformation than the outer capsule. However, when the inner capsule is sufficiently large, it can present larger deformation than the outer capsule, even if the inner membrane has much lower capillary number than the outer membrane. The underlying mechanisms are discussed: (i) the inner capsule is deformed by rotational flow with lower rate of strain rather than by simple shear flow that deforms the outer capsule, and thus the inner capsule exhibits smaller deformation; and (ii) when the inner and outer membranes are sufficiently close (i.e. the inner capsule is sufficiently large), the hydrodynamic interaction between the two membranes becomes significant, which is found to inhibit the deformation of the outer capsule but to promote the deformation of the inner capsule.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Biological Fluid Dynamics: Capsule/cell dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 775 , 25 July 2015 , pp. 77 - 104
Check for updates
Copyright
© 2015 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

Abreu, D., Levant, M., Steinberg, V. & Seifert, U. 2014 Fluid vesicles in flow. Adv. Colloid Interface Sci. 208, 129–141.CrossRefGoogle ScholarPubMed
Agresar, G., Linderman, J. J., Tryggvason, G. & Powell, K. G. 1998 An adaptive, Cartesian, front-tracking method for the motion, deformation and adhesion of circulating cells. J. Comput. Phys. 143, 346–380.CrossRefGoogle Scholar
Bagchi, P. & Kalluri, R. M. 2009 Dynamics of nonspherical capsules in shear flow. Phys. Rev. E 80, 016307.CrossRefGoogle ScholarPubMed
Bai, B., Luo, Z., Lu, T. & Xu, F. 2013a Numerical simulation of cell adhesion and detachment in microfluidics. J. Mech. Med. Biol. 13, 1350002.Google Scholar
Bai, B. F., Luo, Z. Y., Wang, S. Q., He, L., Lu, T. J. & Xu, F. 2013b Inertia effect on deformation of viscoelastic capsules in microscale flows. Microfluid. Nanofluid. 14, 817–829.CrossRefGoogle Scholar
Barthes-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
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.CrossRefGoogle Scholar
Chen, Y., Liu, X. & Shi, M. 2013 Hydrodynamics of double emulsion droplet in shear flow. Appl. Phys. Lett. 102, 051609.Google Scholar
Chu, L.-Y., Utada, A. S., Shah, R. K., Kim, J.-W. & Weitz, D. A. 2007 Controllable monodisperse multiple emulsions. Angew. Chem. Intl Ed. Engl. 46, 8970–8974.CrossRefGoogle ScholarPubMed
Doddi, S. K. & Bagchi, P. 2008 Lateral migration of a capsule in a plane Poiseuille flow in a channel. Intl J. Multiphase Flow 34, 966–986.CrossRefGoogle Scholar
Foessel, E., Walter, J., Salsac, A. V. & Barthes-Biesel, D. 2011 Influence of internal viscosity on the large deformation and buckling of a spherical capsule in a simple shear flow. J. Fluid Mech. 672, 477–486.CrossRefGoogle Scholar
Hosseini, S. M. & Feng, J. J. 2012 How malaria parasites reduce the deformability of infected red blood cells. Biophys. J. 103, 1–10.CrossRefGoogle ScholarPubMed
Kan, H. C., Udaykumar, H. S., Shyy, W. & Tran-Son-Tay, R. 1998 Hydrodynamics of a compound drop with application to leukocyte modeling. Phys. Fluids 10, 760–774.CrossRefGoogle Scholar
Kaoui, B., Harting, J. & Misbah, C. 2011 Two-dimensional vesicle dynamics under shear flow: effect of confinement. Phys. Rev. E 83, 066319.CrossRefGoogle ScholarPubMed
Kaoui, B., Kruger, T. & Harting, J. 2012 How does confinement affect the dynamics of viscous vesicles and red blood cells? Soft Matt. 8, 9246–9252.CrossRefGoogle Scholar
Kaoui, B., Kruger, T. & Harting, J. 2013 Complex dynamics of a bilamellar vesicle as a simple model for leukocytes. Soft Matt. 9, 8057–8061.CrossRefGoogle Scholar
Keller, S. R. & Skalak, R. 1982 Motion of a tank-treading ellipsoidal particle in a shear flow. J. Fluid Mech. 120, 27–47.CrossRefGoogle Scholar
Lac, E. & Barthes-Biesel, D. 2005 Deformation of a capsule in simple shear flow: effect of membrane prestress. Phys. Fluids 17, 072105.CrossRefGoogle Scholar
Lac, E., Barthes-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.CrossRefGoogle Scholar
Le, D. V. 2010 Effect of bending stiffness on the deformation of liquid capsules enclosed by thin shells in shear flow. Phys. Rev. E 82, 016318.CrossRefGoogle ScholarPubMed
Le, D. V. & Tan, Z. 2010 Large deformation of liquid capsules enclosed by thin shells immersed in the fluid. J. Comput. Phys. 229, 4097–4116.CrossRefGoogle Scholar
Levant, M. & Steinberg, V. 2014 Complex dynamics of compound vesicles in linear flow. Phys. Rev. Lett. 112, 138106.CrossRefGoogle ScholarPubMed
Li, X. Y. & Sarkar, K. 2008 Front tracking simulation of deformation and buckling instability of a liquid capsule enclosed by an elastic membrane. J. Comput. Phys. 227, 4998–5018.CrossRefGoogle Scholar
Luo, Z. Y., He, L., Wang, S. Q., Tasoglu, S., Xu, F., Demirci, U. & Bai, B. F. 2014 Two-dimensional numerical study of flow dynamics of a nucleated cell tethered under shear flow. Chem. Engng Sci. 119, 236–244.CrossRefGoogle Scholar
Luo, Z. Y., He, L., Xu, F. & Bai, B. F. 2015 Three-dimensional numerical simulation of vesicle dynamics in microscale shear flows. J. Nanosci. Nanotech. 15, 3081–3086.CrossRefGoogle ScholarPubMed
Luo, Z. Y., Wang, S. Q., He, L., Lu, T. J., Xu, F. & Bai, B. F. 2013a Front tracking simulation of cell detachment dynamic mechanism in microfluidics. Chem. Engng Sci. 97, 394–405.CrossRefGoogle Scholar
Luo, Z. Y., Wang, S. Q., He, L., Xu, F. & Bai, B. F. 2013b Inertia-dependent dynamics of three-dimensional vesicles and red blood cells in shear flow. Soft Matt. 9, 9651–9660.CrossRefGoogle ScholarPubMed
Olbricht, W. L., Rallison, J. M. & Leal, L. G. 1982 Strong flow criteria based on microstructure deformation. J. Non-Newtonian Fluid Mech. 10, 291–318.CrossRefGoogle Scholar
Omori, T., Ishikawa, T., Barthes-Biesel, D., Salsac, A. V., Imai, Y. & Yamaguchi, T. 2012 Tension of red blood cell membrane in simple shear flow. Phys. Rev. E 86, 056321.CrossRefGoogle ScholarPubMed
Omori, T., Ishikawa, T., Imai, Y. & Yamaguchi, T. 2013 Membrane tension of red blood cells pairwisely interacting in simple shear flow. J. Biomech. 46, 548–553.CrossRefGoogle ScholarPubMed
Pozrikidis, C. 2001 Effect of membrane bending stiffness on the deformation of capsules in simple shear flow. J. Fluid Mech. 440, 269–291.CrossRefGoogle Scholar
Qu, X. & Wang, Y. 2012 Dynamics of concentric and eccentric compound droplets suspended in extensional flows. Phys. Fluids 24, 123302.CrossRefGoogle Scholar
Rallison, J. M. 1984 The deformation of small viscous drops and bubbles in shear flows. Annu. Rev. Fluid Mech. 16, 45–66.CrossRefGoogle Scholar
Ramanujan, S. & Pozrikidis, C. 1998 Deformation of liquid capsules enclosed by elastic membranes in simple shear flow: large deformations and the effect of fluid viscosities. J. Fluid Mech. 361, 117–143.CrossRefGoogle Scholar
Salac, D. & Miksis, M. J. 2012 Reynolds number effects on lipid vesicles. J. Fluid Mech. 711, 122–146.CrossRefGoogle Scholar
Schmid-Schonbein, G. W., Shih, Y. Y. & Chien, S. 1980 Morphometry of human leukocytes. Blood 56, 866–875.CrossRefGoogle ScholarPubMed
Serebrennikova, Y. M., Patel, J., Milhous, W. K. & Garcia-Rubio, L. H. 2010 Quantitative analysis of morphological alterations in Plasmodium falciparum infected red blood cells through theoretical interpretation of spectral measurements. J. Theor. Biol. 265, 493–500.CrossRefGoogle ScholarPubMed
Shrivastava, S. & Tang, J. 1993 Large deformation finite element analysis of non-linear viscoelastic membranes with reference to thermoforming. J. Strain Anal. Eng. 28, 31–51.CrossRefGoogle Scholar
Skalak, R., Tozeren, A., Zarda, R. P. & Chien, S. 1973 Strain energy function of red blood cell membranes. Biophys. J. 13, 245–280.CrossRefGoogle ScholarPubMed
Smith, K. A., Ottino, J. M. & de la Cruz, M. O. 2004 Encapsulated drop breakup in shear flow. Phys. Rev. Lett. 93, 204501.CrossRefGoogle ScholarPubMed
Stone, H. A. & Leal, L. G. 1990 Breakup of concentric double emulsion droplets in linear flows. J. Fluid Mech. 211, 123–156.CrossRefGoogle Scholar
Sui, Y., Chew, Y. T., Roy, P. & Low, H. T. 2009 Inertia effect on the transient deformation of elastic capsules in simple shear flow. Comput. Fluids 38, 49–59.CrossRefGoogle Scholar
Tryggvason, G., Bunner, B., Esmaeeli, A., Juric, D., Al-Rawahi, N., Tauber, W., Han, J., Nas, S. & Jan, Y. J. 2001 A front-tracking method for the computations of multiphase flow. J. Comput. Phys. 169, 708–759.CrossRefGoogle Scholar
Unverdi, S. O. & Tryggvason, G. 1992 A front-tracking method for viscous, incompressible, multi-fluid flows. J. Comput. Phys. 100, 25–37.CrossRefGoogle Scholar
Veerapaneni, S. K., Young, Y. N., Vlahovska, P. M. & Blawzdziewicz, J. 2011 Dynamics of a compound vesicle in shear flow. Phys. Rev. Lett. 106, 158103.CrossRefGoogle ScholarPubMed
Walter, J., Salsac, A. V. & Barthes-Biesel, D. 2011 Ellipsoidal capsules in simple shear flow: prolate versus oblate initial shapes. J. Fluid Mech. 676, 318–347.CrossRefGoogle Scholar
Wang, J., Liu, J., Han, J. & Guan, J. 2013 Effects of complex internal structures on rheology of multiple emulsions particles in 2D from a boundary integral method. Phys. Rev. Lett. 110, 066001.Google ScholarPubMed
Yazdani, A. & Bagchi, P. 2012 Three-dimensional numerical simulation of vesicle dynamics using a front-tracking method. Phys. Rev. E 85, 056308.CrossRefGoogle ScholarPubMed
Yazdani, A. & Bagchi, P. 2013 Influence of membrane viscosity on capsule dynamics in shear flow. J. Fluid Mech. 718, 569–595.CrossRefGoogle Scholar
Zhao, M. Y. & Bagchi, P. 2011 Dynamics of microcapsules in oscillating shear flow. Phys. Fluids 23, 111901.CrossRefGoogle Scholar