Asymmetric Vesicle Instability in Extensional Flow

Previous researchers have chronicled the breakup of drops in an extensional flow as they stretch into a dumbbell shape with a long thin neck. Motivated by recent experimental observations, we study an apparently similar problem with vesicles, which are deformable but incompressible membranes that conserve area and volume. First, we simulate vesicles in an unbounded uniaxial extensional flow which are given general radial perturbations from an initially stable symmetric equilibrium state. For sufficiently low reduced volume ($<$ 0.74 at matched inner/outer viscosity) there exists a capillary number at which an asymmetric perturbation mode will grow, resulting in the formation of an asymmetric dumbbell shape with a thin connecting cylindrical bridge analogous to the shapes associated with drop breakup. Our simulations help elucidate a mechanism for this instability based on a competition between internal pressure differentials in the vesicle resulting from the membrane bending force and ambient flow. We compare and contrast this transition to the ``standard'' drop breakup transition.