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

In this paper, deformation of an elastic spherical capsule suspended in a shear flow is studied in detail using Lattice Boltzmann method for fluid flow simulation, immersed boundary method for fluid-membrane interaction and finite element method for membrane force analysis. While Lattice Boltzmann method is capable of implementing inertia effects, computations were carried out for small Reynolds number in which inertia effects are negligible. Effect of three membrane constitutive equations on capsule deformation, including Neo-Hookean, zero-thickness shell approximation and Skalak’s law with different 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 Skalak’s law implementing different area-dilation modulus. In general, behavior of all three constitutive laws are similar for nondimensional shear rates of less than 0.05 while some differences were observed for its values of 0.1 and 0.2. As an efficient computational framework, it is shown that combined Lattice Boltzmann, Immersed Boundary and Finite element method is a promising method for such flow configuration, implementing different membrane constitutive laws.