Skip to main content Accessibility help
×
Home

Rheology of a dense suspension of spherical capsules under simple shear flow

  • D. Matsunaga (a1), Y. Imai (a2), T. Yamaguchi (a3) and T. Ishikawa (a1) (a3)

Abstract

We present a numerical analysis of the rheology of a dense suspension of spherical capsules in simple shear flow in the Stokes flow regime. The behaviour of neo-Hookean capsules is simulated for a volume fraction up to ${\it\phi}=0.4$ by graphics processing unit computing based on the boundary element method with a multipole expansion. To describe the specific viscosity using a polynomial equation of the volume fraction, the coefficients of the equation are calculated by least-squares fitting. The results suggest that the effect of higher-order terms is much smaller for capsule suspensions than rigid sphere suspensions; for example, $O({\it\phi}^{3})$ terms account for only 8 % of the specific viscosity even at ${\it\phi}=0.4$ for capillary numbers $Ca\geqslant 0.1$ . We also investigate the relationship between the deformation and orientation of the capsules and the suspension rheology. When the volume fraction increases, the deformation of the capsules increases while the orientation angle of the capsules with respect to the flow direction decreases. Therefore, both the specific viscosity and the normal stress difference increase with volume fraction due to the increased deformation, whereas the decreased orientation angle suppresses the specific viscosity, but amplifies the normal stress difference.

Copyright

Corresponding author

Email address for correspondence: yimai@pfsl.mech.tohoku.ac.jp

References

Hide All
Bagchi, P. & Kalluri, R. M. 2010 Rheology of a dilute suspension of liquid-filled elastic capsules. Phys. Rev. E 81, 056320.
Barthès-Biesel, D. & Chhim, V. 1981 The constitutive equation of a dilute suspension of spherical microcapsules. Intl J. Multiphase Flow 7, 493505.
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, 251267.
Batchelor, G. K. 1970 The stress system in a suspension of force-free particles. J. Fluid Mech. 41, 545570.
Batchelor, G. K. & Green, J. T. 1972 The determination of the bulk stress in a suspension of spherical particles to order c2. J. Fluid Mech. 56, 401427.
Beenakker, C. W. J. 1986 Ewald sum of the Rotne–Prager tensor. J. Chem. Phys. 85 (3), 15811582.
Clausen, J. R. & Aidun, C. K. 2010 Capsule dynamics and rheology in shear flow: particle pressure and normal stress. Phys. Fluids 22 (12), 123302.
Clausen, J. R., Reasor, D. A. & Aidun, C. K. 2010 Parallel performance of a lattice-boltzmann/finite element cellular blood flow solver on the IBM blue gene/p architecture. Comput. Phys. Commun. 181 (6), 10131020.
Clausen, J. R., Reasor, D. A. & Aidun, C. K. 2011 The rheology and microstructure of concentrated non-colloidal suspensions of deformable capsules. J. Fluid Mech. 685, 202234.
Durlofsky, L. J. & Brady, J. F. 1989 Dynamic simulation of bounded suspensions of hydrodynamically interacting particles. J. Fluid Mech. 200, 3967.
Einstein, A. 1906 Eine neue bestimmung der moleküldimensionen. Ann. Phys. 19, 289306.
Freund, J. B. 2007 Leukocyte margination in a model microvessel. Phys. Fluids 19 (2), 023301.
Greengard, L. & Rokhlin, V. 1987 A fast algorithm for particle simulations. J. Comput. Phys. 73 (2), 325348.
Gross, M., Kruger, T. & Varnik, F. 2014 Rheology of dense suspensions of elastic capsules: normal stresses, yield stress, jamming and confinement effects. Soft Matt. 10, 43604372.
Guazzelli, E. & Morris, F. J. 2012 A Physical Introduction to Suspension Dynamics. Cambridge University Press.
Krieger, I. M. & Dougherty, T. J. 1959 A mechanism for non-newtonian flow in suspensions of rigid spheres. Trans. Soc. Rheol. 3 (1), 137152.
Kruger, T., Gross, M., Raabe, D. & Varnik, F. 2013 Crossover from tumbling to tank-treading-like motion in dense simulated suspensions of red blood cells. Soft Matt. 9, 90089015.
Li, X., Charles, R. & Pozrikidis, C. 1996 Simple shear flow of suspensions of liquid drops. J. Fluid Mech. 320, 395416.
Loewenberg, M. & Hinch, E. J. 1996 Numerical simulation of a concentrated emulsion in shear flow. J. Fluid Mech. 321, 395419.
Matsunaga, D., Imai, Y., Omori, T., Ishikawa, T. & Yamaguchi, T. 2014 A full GPU implementation of a numerical method for simulating capsule suspensions. J. Biomech. Sci. Engng 14, 00039.
Onoda, G. Y. & Liniger, E. G. 1990 Random loose packings of uniform spheres and the dilatancy onset. Phys. Rev. Lett. 64, 27272730.
Pozrikidis, C. 1992 Boundary Integral and Singularity Methods for Linearized Viscous Flow. Cambridge University Press.
Pozrikidis, C. 1995 Finite deformation of liquid capsules enclosed by elastic membranes in simple shear flow. J. Fluid Mech. 297, 123152.
Pozrikidis, C. 2003 Modeling and Simulation of Capsules and Biological Cells. Chapman and Hall/CRC.
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, 117143.
Tan, M. H.-Y., Le, D.-V. & Chiam, K.-H. 2012 Hydrodynamic diffusion of a suspension of elastic capsules in bounded simple shear flow. Soft Matt. 8, 22432251.
Veerapaneni, K. S., Rahimian, A., Biros, G. & Zorin, D. 2011 A fast algorithm for simulating vesicle flows in three dimensions. J. Comput. Phys. 230 (14), 56105634.
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 (7), 829850.
Ying, L., Biros, G. & Zorin, D. 2004 A kernel-independent adaptive fast multipole algorithm in two and three dimensions. J. Comput. Phys. 196 (2), 591626.
Zhao, H. & Shaqfeh, E. S. G. 2013 The dynamics of a non-dilute vesicle suspension in a simple shear flow. J. Fluid Mech. 725, 709731.
Zinchenko, A. Z. & Davis, R. H. 2000 An efficient algorithm for hydrodynamical interaction of many deformable drops. J. Comput. Phys. 157 (2), 539587.
Zinchenko, A. Z. & Davis, R. H. 2005 A multipole-accelerated algorithm for close interaction of slightly deformable drops. J. Comput. Phys. 207 (2), 695735.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed