Hostname: page-component-7c8c6479df-5xszh Total loading time: 0 Render date: 2024-03-28T09:29:36.628Z Has data issue: false hasContentIssue false

Flow of a spherical capsule in a pore with circular or square cross-section

Published online by Cambridge University Press:  01 December 2011

X.-Q. Hu
Affiliation:
Laboratoire Biomécanique et Bioingénierie (UMR CNRS 6600), Université de Technologie de Compiègne, BP 20529, 60205 Compiègne, France
A.-V. Salsac
Affiliation:
Laboratoire Biomécanique et Bioingénierie (UMR CNRS 6600), Université de Technologie de Compiègne, BP 20529, 60205 Compiègne, France
D. Barthès-Biesel*
Affiliation:
Laboratoire Biomécanique et Bioingénierie (UMR CNRS 6600), Université de Technologie de Compiègne, BP 20529, 60205 Compiègne, France
*
Email address for correspondence: dbb@utc.frc

Abstract

The motion and deformation of a spherical elastic capsule freely flowing in a pore of comparable dimension is studied. The thin capsule membrane has a neo-Hookean shear softening constitutive law. The three-dimensional fluid–structure interactions are modelled by coupling a boundary integral method (for the internal and external fluid motion) with a finite element method (for the membrane deformation). In a cylindrical tube with a circular cross-section, the confinement effect of the channel walls leads to compression of the capsule in the hoop direction. The membrane then tends to buckle and to fold as observed experimentally. The capsule deformation is three-dimensional but can be fairly well approximated by an axisymmetric model that ignores the folds. In a microfluidic pore with a square cross-section, the capsule deformation is fully three-dimensional. For the same size ratio and flow rate, a capsule is more deformed in a circular than in a square cross-section pore. We provide new graphs of the deformation parameters and capsule velocity as a function of flow strength and size ratio in a square section pore. We show how these graphs can be used to analyse experimental data on the deformation of artificial capsules in such channels.

Type
Papers
Copyright
Copyright © Cambridge University Press 2011

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

1. Barthès-Biesel, D. 2011 Modelling the motion of capsules in flow. Curr. Opin. Colloid Interface Sci. 16, 312.CrossRefGoogle Scholar
2. 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, 211222.CrossRefGoogle Scholar
3. Carin, M., Barthès-Biesel, D., Edwards-Lévy, F., Postel, C. & Andrei, D. 2003 Compression of biocompatible liquid-filled HSA-alginate capsules: determination of the membrane mechanical properties. Biotechnol. Bioengng 82, 207212.CrossRefGoogle ScholarPubMed
4. Cerda, E. & Mahadevan, L. 2003 Geometry and physics of wrinkling. Phys. Rev. Lett. 90 (7), 074302.CrossRefGoogle ScholarPubMed
5. Chu, T. X., Salsac, A.-V., Leclerc, E., Barthès-Biesel, D., Wurtz, H. & Edwards-Lévy, F. 2010 Comparison between measurements of elasticity and free amino group content of ovalbumin microcapsule membranes: discrimination of the cross-linking degree. J. Colloid Interface Sci. 355, 8188.CrossRefGoogle ScholarPubMed
6. Cole, E. T., Cad, D. & Benameur, H. 2008 Challenges and opportunities in the encapsulation of liquid and semi-solid formulations into capsules for oral administration. Adv. Drug Deliv. Rev. 60, 747756.CrossRefGoogle ScholarPubMed
7. Diaz, A. & Barthès-Biesel, D. 2002 Entrance of a bioartificial capsule in a pore. Comput. Model. Engng Sci. 3 (3), 321337.Google Scholar
8. Doddi, S. K. & Bagchi, P. 2008 Lateral migration of a capsule in a plane Poiseuille flow in a channel. Intl J. Multiphase Flow 34 (10), 966986.CrossRefGoogle Scholar
9. Fery, A. & Weinkamer, R. 2007 Mechanical properties of micro- and nanocapsules: single capsule measurements. Polymer 48, 72217235.CrossRefGoogle Scholar
10. Finken, R. & Seifert, U. 2006 Wrinkling of microcapsules in shear flow. J. Phys.: Condens. Matter 18 (15), L185L191.Google Scholar
11. Gibbs, B. F., Kermasha, S., Alli, I. & Mulligan, C. N. 1999 Encapsulation in the food industry: a review. Intl J. Food Sci. Nutr. 50, 213224.Google ScholarPubMed
12. Helmy, A. & Barthès-Biesel, D. 1982 Migration of a spherical capsule freely suspended in an unbounded parabolic flow. J. Méc. Théor. Appl. 1 (5), 859880.Google Scholar
13. Huang, K. S., Liu, M. K., Wu, C. H., Yen, Y. T. & Lin, Y. C. 2007 Calcium alginate microcapsule generation on a microfluidic system fabricated using the optical disk process. J. Micromech. Microengng 17, 14281434.CrossRefGoogle Scholar
14. Kuriakose, S. & Dimitrakopoulos, P. 2011 Motion of an elastic capsule in a square microfluidic channel. Phys. Rev. E 84, 011906.CrossRefGoogle Scholar
15. Lefebvre, Y. & Barthès-Biesel, D. 2007 Motion of a capsule in a cylindrical tube: effect of membrane pre-stress. J. Fluid Mech. 589, 157181.Google Scholar
16. Lefebvre, Y., Leclerc, E., Barthès-Biesel, D., Walter, J. & Edwards-Levy, F. 2008 Flow of artificial microcapsules in microfluidic channels: a method for determining the elastic properties of the membrane. Phys. Fluids 20 (12), 123102.Google Scholar
17. Luo, H. & Pozrikidis, C. 2007 Buckling of a pre-compressed or pre-stretched membrane. Intl J. Solids Struct. 44, 80748085.CrossRefGoogle Scholar
18. Miyazawa, K., Yajima, I., Kaneda, I. & Yanaki, T. 2000 Preparation of a new soft capsule for cosmetics. J. Cosmet. Sci. 51, 239252.Google Scholar
19. Pedley, T. J. 2010 Instability of uniform micro-organism suspensions revisited. J. Fluid Mech. 647, 335359.CrossRefGoogle Scholar
20. Pedley, T. J. & Kessler, J. O. 1992 Hydrodynamic phenomena in suspensions of swimming microorganisms. Annu. Rev. Fluid Mech. 24, 313358.CrossRefGoogle Scholar
21. Pozrikidis, C. 1992 Boundary Integral and Singularity Methods for Linearized Viscous Flow. Cambridge University Press.CrossRefGoogle Scholar
22. Pozrikidis, C. 1997 Introduction to Theoretical and Computational Fluid Dynamics. Oxford University Press.CrossRefGoogle Scholar
23. Pozrikidis, C. 2005 Numerical simulation of cell motion in tube flow. Ann. Biomed. Engng 33, 165178.CrossRefGoogle ScholarPubMed
24. Quéguiner, C. & Barthès-Biesel, D. 1997 Axisymmetric motion of capsules through cylindrical channels. J. Fluid Mech. 348, 349376.CrossRefGoogle Scholar
25. Rabanel, J. M., Banquy, X., Zouaoui, H., Mokhtar, M. & Hildgen, P. 2009 Progress technology in microencapsulation methods for cell therapy. Biotechnol. Prog. 25, 946963.CrossRefGoogle ScholarPubMed
26. Ramanujan, S. & Pozrikidis, C. 1998 Deformation of liquid capsules enclosed by elastic membranes in simple shear flow: large deformations and the effect of capsule viscosity. J. Fluid Mech. 361, 117143.Google Scholar
27. Risso, F. & Carin, M. 2004 Compression of a capsule: mechanical laws of membranes with negligible bending stiffness. Phys. Rev. E 69, 061601061608.CrossRefGoogle ScholarPubMed
28. Risso, F., Collé-Paillot, F. & Zagzoule, M. 2006 Experimental investigation of a bioartificial capsule flowing in a narrow tube. J. Fluid Mech. 547, 149173.CrossRefGoogle Scholar
29. 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, 829850.CrossRefGoogle Scholar
30. Yeh, C. H., Zhao, Q., Lee, S. J. & Lin, Y. C. 2009 Using a t-junction microfluidic chip for monodisperse calcium alginate microparticles and encapsulation of nanoparticles. Sensors Actuators 151, 231236.CrossRefGoogle Scholar
31. Zhang, H., Tumarkin, E., Peerani, R., Nie, Z., Sullan, R. M. A., Walker, G. C. & Kumacheva, E. 2006 Microfluidic production of biopolymer microcapsules with controlled morphology. J. Am. Chem. Soc. 128, 1220512210.CrossRefGoogle ScholarPubMed