Pair-collision between heterogeneous capsules in simple shear: Effect of membrane stiffness and membrane constitutive laws

Deformability of red blood cells affects hydrodynamic properties of blood and thereby physiological functions in many cardiovascular diseases, e.g. in sickle cell anemia and malaria, the cell membrane becomes stiff affecting their circulation through microvessels. Here, we numerically simulate the hydrodynamic interaction between a pair of cell-like capsules in a free shear flow, using a front-tracking method. The membrane is modeled using various constitutive equations. By varying the stiffness of one capsule (C$_{2})$ and keeping all other parameters constant, we find a significant effect on the deformation and trajectory of the other (C$_{1})$. Increasing the stiffness of C$_{2}$ surprisingly increases the peak deformation of C$_{1}$ while decreasing the cross-stream shift in its trajectory However, the relative trajectory between capsules remains the same. Effects of constitutive laws and difference in behaviors between capsules and drops are investigated explaining underlying physics.