RESEARCH PAPER Numerical Simulation of Tank-Treading and Tumbling Motion of Red Blood Cell in the Poiseuille Flow in a Microchannel With and Without Obstacle Ashkan Ghafouri 1 • Reza Esmaily 2 • As’ad Alizadeh 1 Received: 30 March 2017 / Accepted: 17 July 2018 / Published online: 28 August 2018 Ó Shiraz University 2018 Abstract In the present study, the dynamics of a red blood cell (RBC) in a simple microchannel and in a microchannel with obstacle is simulated using combined lattice Boltzmann-immersed boundary method. The fluid flow field is solved for using LBM and the interaction between the fluid and the RBC is simulated using the IBM. The RBC is considered as a deformable boundary immersed in the fluid flow. When the RBC is stiffer, the flow passage is further blocked due to the lack of flexibility of the RBC causing the flow velocity to decrease and greater drag force (resistance force against the motion of cell) from the fluid to be exerted on it. As a result, the pressure around the RBC increases and becomes even higher than the inlet pressure of microchannel. This increased pressure is thought to be the reason of many serious diseases including cardiovascular diseases. If the number of RBCs used in the simulation increases, the pressure increase would be more appreciable. In addition, the high-flexibility RBC experienced tank-treading motion due to its low elastic and bending coefficients whereas for the low-flexibility RBC the tumbling motion took place. The mechanical properties of RBCs are the determining factor in the distribution of hematocrit in microcirculation. The current results showed good agreement with the available results. Keywords Lattice Boltzmann method (LBM)  Immersed boundary method (IBM)  Red blood cell  Interaction 1 Introduction Red blood cells are a momentous part in blood because of their large number density. Being highly flexible particles, RBCs are primary cell species impressing the rheological properties of blood. RBC may exhibit reduced flexibility and stronger aggregation in many pathological situations, such as hypertension, heart disease, malaria, diabetes, and sickle cell anemia (Popel and Johnson 2005). Due to the advances in micro-machine technology, experiments have been done on RBCs in a microchannel with constriction (Faivre et al. 2006; Kang et al. 2008; Fujiwara et al. 2009). The lattice Boltzmann method (LBM) in combination with immersed boundary method (IBM) has been used for simulating the motion and deformation of elastic bodies immersed in fluid flow including RBCs. Feng and Michaelides (2004) proposed the first model of IBM–LBM. Their combined method involved most of the desirable properties of LBM and IBM. In general, it is so powerful in solving the problems involving structure deformation (Feng and Michaelides 2004). This method was improved by Wu and Shu (2010). They implicitly calculated and applied the forces caused by the fluid acting on the immersed boundary, which in fact had a significant impact on the cost and accuracy. Zhang et al. (2007, 2008, 2009), and Zhang (2011) studied the dynamic behavior of RBCs in both the shear flow and channel flow and investigated several & Reza Esmaily reza_esmaily82@yahoo.com Ashkan Ghafouri a.ghafouri@iauahvaz.ac.ir As’ad Alizadeh asad.alizadeh2010@gmail.com; asad.alizadeh@iauahvaz.ac.ir 1 Department of Mechanical Engineering, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran 2 Department of Mechanical Engineering, Mahabad Branch, Islamic Azad University, Mahabad, Iran 123 Iran J Sci Technol Trans Mech Eng (2019) 43:627–638 https://doi.org/10.1007/s40997-018-0233-2