A lattice Boltzmann study on the large deformation of red blood cells in shear flow

The transient deformation of a liquid-filled elastic capsule, simulating a red blood cell, was studied in simple shear flow. The simulation is based on a hybrid method which introduces the immersed boundary concept in the framework of the multi-block lattice Boltzmann model. The method was validated by the study on deformation of an initially circular capsule with Hooke's membrane. Also studied were capsules with Skalak membrane of initially elliptical and biconcave shapes, which are more representative of a red blood cell. Membrane tank treading motion is observed. As the ratio between membrane dilation modulus and shear modulus increases, the capsule shows asymptotic behavior. For an initially elliptical capsule, it is found that the steady shape is independent of initial inclination angle. For an initially biconcave capsule, the tank treading frequency from two-dimensional modeling is comparable to that of real cells. Another interesting finding is that the tank treading velocity has not attained steady state when the capsule shape becomes steady; and at this state there is the internal vortex pair. The treading velocity continues to decrease and reaches a steady value when the internal vortex pair has developed into a single vortex.