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In the present study, the motion and deformation of a red blood cell in the incompressible viscous flow is simulated using the lattice Boltzmann method combined with the immersed boundary method. The lattice Boltzmann method is used to solve the flow field, whereas the immersed boundary method is used to simulate the dynamics of the red blood cell. The red blood cell is considered as an elastic boundary immersed in the fluid domain. The main advantage of the lattice Boltzmann method is that it solves only an algebraic equation. In the immersed boundary method the fluid domain is descretized using a regular Eulerian grid, while the immersed boundary is represented in the Lagrangian coordinates. The Eulerian grid points would not necessarily coincide with the Lagrangian points. The fluid- immersed boundary interaction is modeled using an appropriate form of delta function. The effects of the no-slip condition are taken into account via a forcing term added to the Navier-Stokes Equations (here the lattice Boltzmann equation). In the present study, the tank-treading motion of a red blood cell in the viscous shear flow is simulated. The results are found to be in good agreement with the available experimental and numerical ones.

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In the current study, the motion and deformation of an elastic membrane in a two-dimensional channel with and without a groove is simulated using a combined lattice Boltzmann-immersed boundary method. The lattice Boltzmann method is used to solve the fluid flow equations and the immersed boundary method is used to incorporate the fluid-membrane interaction. The elastic membrane is considered as a flexible boundary immersed in the flow domain. In the immersed boundary method, the membrane is represented in the Lagrangian coordinates while the fluid domain is discretized on a uniform fixed Eulerian grid. The interaction between the fluid and the membrane is modeled using Dirac delta function. The effects of no-slip boundary condition are enforced by addition of a forcing term to the lattice Boltzmann equation. Depending on the flow rate, the initial location and stiffness of the elastic membrane, the size of the groove, the membrane only rotates inside the groove or the flow moves it out of the groove. The results are presented in terms of flow velocity and pressure fields and membrane configuration at different times. Comparison between the present results and the available numerical and experimental ones shows good agreement between them.

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In this paper, motion of a flexible membrane and hydrodynamic interaction of multiple membranes in a microchannel are simulated by developing a computer code written in C. The membranes are considered as flexible boundaries immersed in the fluid. First a single biconcave shaped membrane with high rigidity is considered. Due to the rigidity of the membrane, it experiences tumbling motion and its vertical displacement becomes oscillatory. Then, the effects of initial position of a circular membrane on its deformation, vertical velocity and displacement are investigated. It was observed that as the initial location of the membrane approaches the channel’s central axis, its vertical displacement and velocity decreased, but its horizontal velocity component increased. Finally, the simultaneous motion of multiple membranes in a microchannel and their interaction with each other and with flow are evaluated. The membranes do not collide and hence the collision mechanism is not modeled. It was found that the upstream membrane experienced greatest deformation and the greatest force was exerted on it by the fluid on it. In addition, simultaneous presence of multiple membranes would result in a reduction in the flow velocity. The current numerical results have good agreement with the available valid numerical ones.