Numerical simulation of the phase separation in binary lipid membrane under the effect of stationary shear flow

A numerical simulation of the phase separation in binary lipid membrane under the effect of stationary shear flow is performed. We numerically solved the modified two-dimensional time-dependent Ginzburg-Landau (TDGL) equations with an external velocity term, employing the CDS (i.e., Cell Dynamical System) technique. In the present simulation, stationary shear flows with different shear rates are taken into account. The evolution process of the phase separation is illustrated macroscopically via the snapshot figures and simulated scattering patterns at several typical moments. For each case, the growth exponents of the characteristic domain sizes in both directions parallel and perpendicular to the flow are studied, and the domain area as well. Also, the behavior of the excess viscosity has been investigated, which is a peculiar rheological indicator of such a membrane system with domain structures.