Numerical simulation of capsule deformation in simple shear flow

The transient deformation of two-dimensional non-circular and three-dimensional non-spherical capsules in simple shear flow is studied numerically, using the hybrid immersed boundary and multi-block lattice Boltzmann method recently proposed by the present authors. The capsules are modeled as Newtonian liquid drops enclosed by elastic membranes; the liquids inside and outside the capsule have the same physical properties. The present results show important different behaviors between two-dimensional and three-dimensional capsules in shear flow. For two-dimensional non-circular capsules without considering the membrane bending rigidity, or considering the bending with the minimum bending-energy configurations (shapes at which the bending-energy has a global minimum) being uniform-curvature shapes, the capsules will always achieve the steady tank treading motion (a capsule deforms to a steady shape with a steady inclination and the membrane rotates around the liquid inside). However, for three-dimensional non-spherical capsules without membrane bending rigidity, such a steady mode does not exist; with the shear rate decreasing, the three-dimensional capsules’ motion changes from swinging mode (a capsule undergoes periodic shape deformation and inclination oscillation while its membrane is rotating around the liquid inside) to flipping mode. The deformation of two-dimensional capsules, with their initial non-circular shapes taken as the minimum bending-energy configurations, is also considered. It is quite interesting to find such two-dimensional capsules behave qualitatively similar to three-dimensional capsules: there is a swinging-to-flipping transition induced by lowering the shear rate.