Commun. Comput. Phys., 9 (2011), pp. 1397-1413.


Three-Dimensional Lattice Boltzmann Simulation of Two-Phase Flow Containing a Deformable Body with a Viscoelastic Membrane

Toshiro Murayama 1, Masato Yoshino 2*, Tetsuo Hirata 3

1 Department of Mathematics and System Development Engineering, Interdisciplinary Graduate School of Science and Technology, Shinshu University, 4-17-1 Wakasato, Nagano-shi, Nagano 380-8553, Japan; and Satellite Venture Business Laboratory (SVBL), Shinshu University, 3-15-1 Tokida, Ueda-shi, Nagano 386-8567, Japan.
2 Department of Mechanical Systems Engineering, Faculty of Engineering, Shinshu University, 4-17-1 Wakasato, Nagano-shi, Nagano 380-8553, Japan; CREST, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi-shi, Saitama 332-0012, Japan.
3 Department of Mechanical Systems Engineering, Faculty of Engineering, Shinshu University, 4-17-1 Wakasato, Nagano-shi, Nagano 380-8553, Japan.

Received 11 November 2009; Accepted (in revised version) 24 December 2010
Available online 18 February 2011
doi:10.4208/cicp.111109.241210s

Abstract

The lattice Boltzmann method (LBM) with an elastic model is applied to the simulation of two-phase flows containing a deformable body with a viscoelastic membrane. The numerical method is based on the LBM for incompressible two-phase fluid flows with the same density. The body has an internal fluid covered by a viscoelastic membrane of a finite thickness. An elastic model is introduced to the LBM in order to determine the elastic forces acting on the viscoelastic membrane of the body. In the present method, we take account of changes in surface area of the membrane and in total volume of the body as well as shear deformation of the membrane. By using this method, we calculate two problems, the behavior of an initially spherical body under shear flow and the motion of a body with initially spherical or biconcave discoidal shape in square pipe flow. Calculated deformations of the body (the Taylor shape parameter) for various shear rates are in good agreement with other numerical results. Moreover, tank-treading motion, which is a characteristic motion of viscoelastic bodies in shear flows, is simulated by the present method.

AMS subject classifications: 76D99, 76T99, 74F10, 76M28, 74L15

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Key words: Lattice Boltzmann method (LBM), two-phase flow, viscoelastic membrane, shear flow, tank-treading motion.

*Corresponding author.
Email: s08t206@shinshu-u.ac.jp (T. Murayama), masato@shinshu-u.ac.jp (M. Yoshino), hirata@shinshu-u.ac.jp (T. Hirata)
 

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