Two-dimensional vesicle dynamics under shear flow: Effect of confinement

Abstract

Dynamics of a single vesicle under shear flow between two parallel plates is studied in two-dimensions using lattice-Boltzmann simulations. We first present how we adapted the lattice-Boltzmann method to simulate vesicle dynamics, using an approach known from the immersed boundary method. The fluid flow is computed on an Eulerian regular fixed mesh while the location of the vesicle membrane is tracked by a Lagrangian moving mesh. As benchmarking tests, the known vesicle equilibrium shapes in a fluid at rest are found and the dynamical behavior of a vesicle under simple shear flow is being reproduced. Further, we focus on investigating the effect of the confinement on the dynamics, a question that has received little attention so far. In particular, we study how the vesicle steady inclination angle in the tank-treading regime depends on the degree of confinement. The influence of the confinement on the effective viscosity of the composite fluid is also analyzed. At a given reduced volume (the swelling degree) of a vesicle we find that both the inclination angle, and the membrane tank-treading velocity decrease with increasing confinement. At sufficiently large degree of confinement the tank-treading velocity exhibits a nonmonotonous dependence on the reduced volume and the effective viscosity shows a nonlinear behavior.

Complex dynamics of a bilamellar vesicle as a simple model for leukocytes

“…Both membranes interact purely hydrodynamically. The distance between the plates is chosen as such that the effect of wall confinement is negligible [10,11].…”

“…All fluids are considered to be incompressible, Newtonian and of the same viscosity η. Their flow is solved by the lattice-Boltzmann method and the fluid-vesicle two-way coupling is achieved employing the immersed boundary method (see [10] for details). Both vesicle membranes are locally inextensible and experience resistance to bending with the same rigidity κ.…”

Simulation of vesicle using level set method solved by high order finite element

“…Then decreasing α leads to attain a biconcave shape which is also a characteristic of red blood cells (see figure 3(d)). Figure 3 shows our results (blue dots) plotted vs the one obtained in [7] (red line) with a Lattice Boltzmann method. We see a good agreement between the two models.…”

“…For these reasons, several methods have been developed such as lattice Boltzmann methods [7], integral boundary method [8], phase field method [9], level set method [6,10,11] and a numerical method based on a contact algorithm to simulate RBC clusters in bifurcations [12]. These methods have their own advantages and drawbacks.…”

Numerical Simulation of the Motion of Inextensible Capsules in Shear Flow Under the Effect of the Natural State

“…On the other side, tank-treading velocity increases almost linearly with respect to increasing of swelling ratio in the narrower channel, while in the wider domain the increasing of tank-treading velocity has slowed down until it arrives almost maximum around s * ∼ 0.9. The same qualitative tendency is given in [27]- [32]. We also keep track of the area and the perimeter of the capsule during the simulations.…”