On Elasticity of Spring Network Models Used in Blood Flow Simulations in Espresso∗

For the proper simulation of processes inside microfluidic devices, proper model for blood flow must be used. We use the lattice-Boltzmann method for the blood plasma flow and the immersed boundary method for the description of red blood cells and other components of blood. One of the four key mechanisms governing the elastic behaviour of a red blood cell is the in-plane shear modulus of elasticity. The membrane of red blood cell is modeled with a triangular network of springs with stretching coefficient k. Physical properties of the membrane is given by the in-plane shear modulus of elasticity μ. We study the dependence of the stretching coefficients of the springs on the in-plane shear modulus. First we derive analytical results for regular two dimensional networks. For networks, or meshes, covering the surface of three dimensional objects we first define the mesh density. Then we state the hypothesis deriving the relation between μ and k and finally we verify the hypothesis by numerous simulations.