A lattice Boltzmann method for a two-phase flow containing solid bodies with viscoelastic membranes

Abstract

Abstract.A lattice Boltzmann method (LBM) for two-phase flows containing solid bodies with viscoelastic membranes is proposed. The method is based on the two-phase LBM, in which one phase is regarded as the solid phase. In the present model, the membrane is assumed to be composed of identical particles that are connected to their neighboring particles by elastic springs to take account of stretching and compression effects. The method is applied to two representative problems, namely the behavior of a viscoelastic body under shear flow and the motion of a viscoelastic body in a Poiseuille flow. Tank-tread motion and axial migration, which are both characteristic of the motion of viscoelastic bodies, are simulated by using the method. These results indicate that the method is capable of simulating the complex behavior of viscoelastic bodies in capillaries, such as the motion of red blood cells in blood flows.

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

“…They discretized the 3D capsule membrane into flat triangular elements, and the elastic forces acting at the triangle vertices are inserted in LBM nodes. The authors [20] have recently investigated behavior of a deformable body with viscoelastic membranes in two-dimensional flows. In the present study, we extend the numerical method to three-dimensions, and moreover, 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.…”

Lateral migration and equilibrium shape and position of a single red blood cell in bounded Poiseuille flows

“…Studying the dynamical behaviors (such as deformability and the motion) of the RBCs suspending in fluid flow becomes an essential problem in biomedical and biochemical industries and these studies may serve as a useful and practical method in designing the cells separating microfluid devices based on their mechanical properties such as size, deformability and etc [2]. Many researchers in mathematics, physics and mechanics, biology, and medicine have studied this problem by using various entities, such as particles, drops, capsules, vesicles and RBCs theoretically [3,4], experimentally [5,6,7,8,9,10,11], and numerically [7,12,13,14,15,16,17,18,20,21,22,23]. But most studies have been limited to the Stokes flow or the cells are restricted to the sphere or ellipse.…”

“…B. Kaoui et al studied the cross-streamline noninertial migration of a suspended vesicle in an unbounded (bounded by Coupier et al [7]) Poiseuille flow at low Reynolds numbers by using the boundary integral method and found that the vesicle deforms and migrates toward the center of the flow [16]. M. Yoshino and T. Murayama applied the lattice Boltzmann method (LBM) to study the motion of a viscoelastic body in a Poiseuille flow and observed that the equilibrium position is very close to the centerline for a low elasticity and it is at a certain position between the centerline and the wall for a larger elasticity [14]. Danker et al investigated the effect of viscosity ratio on migration of vesicles in a Poiseuille flow by theoretical analysis and predicted coexistence of two types of shapes: bulletlike shape and parachutelike shape [22].…”

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

“…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.…”