Effect of elastic constitutive laws on the deformation of two-dimensional red blood cell

Deformation of two-dimensional red blood cell in linear shear flow is simulated using the immersed boundary method, in which the cell is modeled as a force source instead of a real body. The effect of three constitutive laws, i.e. Hookean, Neo-Hookean and Skalak elasticity, on the deformation is studied by simulating the cell movement in two linear shear flows. The results show that the effect of the constitutive laws gets more obvious as the shear rate increases. Both the aspect ratio and the inclination of the steady shapes get bigger, and the differences between the periods of the cell tank-treading motion become larger. For the same shear flow, the period with Hookean elasticity is less than the period with Neo-Hookean elasticity and bigger than the period with Skalak elasticity.     

Research on the spherical capsule motion in 3D simple shear flows

Deformation of the spherical capsule in 3D simple shear flow is simulated using the immersed boundary method. The capsule membrane is regarded as an elastic medium satisfying the Neo-Hookean or Skalak elasticity. The motions of the capsule under various capillary numbers are studied. The results show that the deformation of the capsule becomes larger as the capillary number increases; in the same shear flow, the deformation under Skalak law is smaller than that under Neo-Hookean; for small capillary number the Taylor parameter agrees well with the analytical solution, whereas for large capillary number it is less than the analytical solution. Those results are validated by previous works obtained by the boundary integral method and the immersed boundary method.