Commun. Comput. Phys., 16 (2014), pp. 1031-1055.

Hydrodynamic Interaction of Elastic Capsules in Bounded Shear Flow

D. V. Le 1, Zhijun Tan 2*

1 Institute of High Performance Computing, Agency for Science, Technology and Research, 1 Fusionopolis Way, #16-16 Connexis, Singapore 138632.
2 School of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou 510275, China; Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou 510275, China.

Received 9 August 2013; Accepted (in revised version) 16 April 2014
Available online 8 August 2014


This paper presents a modified Loop's subdivision algorithm for studying the deformation of a single capsule, the hydrodynamic interaction between two capsules and the hydrodynamic diffusion of a suspension of capsules in bounded shear flow. A subdivision thin-shell model is employed to compute the forces generated on the surface of the elastic capsule during deformation. The capsule surface is approximated using the modified Loop's subdivision scheme which guarantees bounded curvature and C^1 continuity everywhere on the limit surface. The present numerical technique has been validated by studying the deformation of a spherical capsule in shear flow. Computations are also performed for a biconcave capsule over a wide range of shear rates and viscosity ratios to investigate its dynamics. In addition, the hydrodynamic interaction between two elastic capsules in bounded shear flow is studied. Depending on the wall separation distance, the trajectory-bifurcation points that separate reversing and crossing motions for both spherical and biconcave capsules can be found. Compared to the spherical capsules, the biconcave capsules exhibit additional types of interaction such as rotation and head-on collision. The head-on collision results in a large trajectory shift which contribute to the hydrodynamic diffusion of a suspension. A suspension of a large number of biconcave capsules in shear flow is also simulated to show the ability of the modified scheme in running a large-scale simulation over a long period of time.

AMS subject classifications: 65M06, 76D05, 74F10, 92C10

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Key words: Thin shell, elastic capsules, red-blood cells, subdivision surfaces, immersed boundary method, Navier-Stokes equations.

*Corresponding author.
Email: (D. V. Le), (Z. Tan)

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