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The red blood cell particle is important in the research studies of blood flow and drug delivery. The biconcave shape makes the motions of the red blood cell particle in fluids more complex than sphere or ellipsoid. Sedimentation behaviors of a red blood cell particle in long circular tubes are investigated by using the lattice Boltzmann method with the Galilean-invariant momentum exchange method. Different blockage ratios and the particle to fluid density ratios are considered. One periodic and two steady sedimentation modes are discovered. When the blockage ratio rises, the motion mode of particles changed from horizontal mode to inclined mode. With the increase of the particle to fluid density ratio, the sedimentation mode changed from the inclined mode to the horizontal mode, and the time of the particles reaching the stable state is obviously distinct in different sedimentation modes. Surprisingly, the oscillatory mode is observed in the larger blockage ratio and lower density ratio of particle to fluid. These works may be able to make active promotions to the research studies of blood circulation of humans.

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The pseudo-potential lattice Boltzmann model is versatile in modelling multiphase flows, since the mesoscopic interaction potential enables it to directly describe the nonideal effect evading the tracking or integrating of phase interface. In this paper, we develop an effective pseudo-potential lattice Boltzmann model to simultaneously realize the thermodynamic consistency, the extremely large density ratio and the adjustable surface tension. Decoupling the mesh space from the momentum space by a scale factor, denser lattice nodes depict the transition region more accurately. The high-precision explicit finite difference method further enhances the calculation accuracy of interaction force. The present model is validated to satisfy thermodynamic even at very low temperature, where the liquid-gas density ratio exceeds 1010. The spurious current can be suppressed to a very low level (<0.0007), despite the density ratio reaching tens of thousands. A modified pressure tension is introduced to tune the surface tension free from the influence of the density ratio. The numerical stability of multiphase simulations is significantly improved, and the droplet splashing is successfully reproduced at Reynolds number 25,000, while the density ratio is more than 10,000.