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

Abstract

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.

Lattice Boltzmann simulation of motion of red blood cell in constricted circular pipe flow

“…Grid convergence is checked for both Eulerian and Lagrangian grids. For Eulerian grid, the lattice resolutions and the number of particles in the membrane are determined by reference to the grid convergence test carried out in the previous paper (Murayama, et al, 2011b). As an example, when we carried out one case of the simulations for the constricted circular pipe flow with 1.25 times finer grid, we found that the calculated results of the deformation index and the velocity were almost the same as the results with the standard grid.…”

“…The other parameters are the same as those in Murayama et al (2011b). Note that the hydraulic equivalent diameters are used for L y and L d .…”

“…Since these fluids have their own character, it is required to distinguish them in some way to give different values of physical properties. In the present model, as in Murayama et al (2011b), these fluids are distinguished by an order parameter in the LBM for two-phase flows described later. However, the membrane is not autonomously determined but the region of the cubic lattices containing particles is assumed to be a membrane, so that the elastic force is applied to all vertices of the cubic lattices.…”

“…The number of Lagrangian points at the boundary of the pipe is N = 100. The other parameters are the same as those in Murayama et al (2011b). We perform the simulations for 0.04 ≤ Re ≤ 0.13, where Re is the Reynolds number defined as Re = ρ FB U t D 0 /μ FB , with U t being the terminal axial velocity of the body.…”

“…They discretized the three-dimensional capsule membrane into flat triangular elements, and the elastic forces acting at the triangle vertices are inserted into grid points in the LBM. The authors' group (Yoshino and Murayama, 2009;Murayama, et al, 2011a;Murayama, et al, 2011b) has also proposed a numerical method based on the LBM to simulate behavior of a deformable body with a viscoelastic membrane in fluid flows. They confirmed the validity of the method in fundamental flow problems, and demonstrated the potential for microscale two-phase flows.…”