Lattice Boltzmann simulation of three-dimensional capsule deformation in a shear ow with different membrane constitutive laws

In this paper, the deformation of an elastic spherical capsule suspended in a shear ow is studied in detail using Lattice Boltzmann method for uid ow simulation, immersed boundary method for uid-membrane interaction and nite element method for membrane force analysis. While Lattice Boltzmann method is capable of implementing inertia eects, computations were carried out for small Reynolds number in which inertia eects are negligible. Eects of three membrane constitutive equations on capsule deformation, including Neo-Hookean, zero-thickness shell approximation and Skalakʹs law with dierent area-dilation modulus, are studied in detail. Results presented in the form of Taylor deformation parameter, inclination angle and period of tank-treading motion of capsule, show close agreement between those obtained from Neo-Hookean and zero-thickness shell approximation with previous published ones. Such agreement is partially observed for Skalakʹs law implementing dierent area-dilation modulus. In general, behaviors of all three constitutive laws are similar for nondimensional shear rates of less than 0.05 while some dierences were observed for its values of 0.1 and 0.2. As an ecient computational framework, it is shown that combined Lattice Boltzmann, Immersed Boundary and Finite element method is a promising method for such ow conguration, implementing dierent membrane constitutive laws.