ABSTRACT
Capsules and red blood cells suspended in flow exhibit a rich dynamics due to the deformability of the enclosing membranes. To accurately capture statics and dynamics, mechanical models of the membrane must be available incorporating shear elasticity, bending rigidity, and membrane viscosity. In the approach described in this chapter, the membrane of a red blood cell is modeled as a network of interconnected nonlinear springs emulating the cytoskeleton spectrin network. Dissipative forces in the network mimic the effect of the lipid bilayer. The macroscopic elastic properties of the network are analytically related to the spring parameters, circumventing ad-hoc adjustment. Chosen parameter values yield model membranes that reproduce optical tweezer stretching experiments. When probed with an attached oscillating microbead, predicted viscoelastic properties are in good agreement with experiments using magnetic optical twisting cytometry. In shear flow, red blood cells respond by tumbling at low shear rates and tank-treading at high shear rates. In transitioning between these regimes, the membrane exhibits substantial deformation controlled largely by flexural stiffness. Raising the membrane or internal fluid viscosity shifts the transition threshold to higher shear rates and reduces the tank-treading frequency. Simulations reveal that a purely elastic membrane devoid of viscous properties cannot adequately capture the cell dynamics. Results are presented to demonstrate the dependence of the transition thresholds from biconcave to parachute shapes in capillary flow on the cell properties and mean flow velocity.
