A multi-component lattice Boltzmann model with non-uniform interfacial tension module for the study of blood flow in the microvasculature

This study aims at analyzing the red blood cell (RBC) deformation and velocity while streaming through venules and through capillaries whose diameters are smaller than the RBC size. The characteristics of the RBC shape change and velocity can potentially help in diagnosing diseases. In this work, the RBC is considered as a surfactant-covered droplet. This is justified by the fact that the cell membrane liquefies under pressure in the capillaries, and this allows the marginalization of its mechanical properties. The RBC membrane is in fact a macro-colloid containing lipid surfactant. When liquefied, it can be considered as a droplet of immiscible hemoglobin covered with lipid surfactant in a plasma surrounding. The local gradient in the surface tension due to non-uniform local interface surfactant distribution is neglected here, and a non-uniform zonal-averaged value of surface tension representative of the surfactant bulk zonal concentration is rather implemented. The interplay between the surface tension geometry and the hydrodynamic conditions determines the droplet shape by affecting a change in its Weber number, and influences its velocity. The Gunstensen lattice Boltzmann model for immiscible fluids is used here since it provides independent adjustment of the local surface tension, and allows the use of fluids with viscosity contrast. The proposed concept was used to investigate the dynamic shape change of the RBC while flowing through the microvasculature, and to explore the Fahraeus and the Fahraeus-Lindqvist effects.