The study of RBC deformation in capillaries with a lattice boltzmann method for surfactant covered-droplets

This study aims at analyzing the shape change of red blood cells in the process of streaming through a capillary smaller than the red blood cell diameter. The characteristics of its shape change and velocity can potentially lead to an indicator of a variety of diseases. We approach this problem with considering red blood cells as surfactant covered droplets. This assumption is justified by the fact that the cell membrane liquefies under high pressure in small capillaries, and this allows the marginalization of the mechanical properties of the membrane. The red blood cell membrane is in fact a macrocolloid containing lipid surfactant. When liquefied, it can be treated as a droplet of immiscible hemoglobin covered with lipid surfactant in plasma surrounding. The merit is to analyze the effect of the flow condition and domain geometry on the surfactant concentration change over the droplet interface, and the effect of this change on the surface tension of the droplet. The distribution of the surfactant is calculated by enforcing conservation of the surfactant mass concentration on the interface, leading to a convection diffusion equation. The equation takes account of the effects of the normal and Marangoni stresses as a boundary condition on the interface between the immiscible fluids. The gradient in the surface tension adversely determines the droplet shape by effecting a local change in the capillary number, and influences its velocity by retarding the local surface velocity. The choice of the Gunstensen model is motivated by its capability of handling incompressible fluids, and the locality of the application of the surface tension. We used the same concept to investigate the dynamic shape change of the RBC while flowing through the microvasculature, and explore the physics of the Fahraeus, and the Fahraeus-Lindqvist effects.