An immersed boundary lattice Boltzmann approach to simulate deformable liquid capsules and its application to microscopic blood flows

In this paper, we develop an immersed boundary lattice Boltzmann approach to simulate deformable capsules in flows. The lattice Boltzmann method is utilized to solve the incompressible flow field over a regular Eulerian grid, while the immersed boundary method is employed to incorporate the fluid-membrane interaction with a Lagrangian representation of the capsule membrane. This algorithm was validated for the Laplace relationship, the dispersion relationship for interfacial waves and the drag coefficient for cylinders; excellent agreement with theoretical results was observed. Furthermore, simulations of single and multiple red blood cells in shear and channel flows were performed. Several characteristic hemodynamic and hemorheological features were successfully reproduced, including the tank-treading motions, cell migration from the vessel wall, slipper-shaped cell deformation, cell-free layers, blunt velocity profiles and the Fahraeus effect. These simulations therefore demonstrate the potential usefulness of this computational model for microscopic biofluidic systems. However, extension of this algorithm to three-dimensional situations is necessary for more realistic simulations.