Symmetric and non-symmetric elongation of vesicles in extensional flows
Andrew Spann (Stanford), Vivek Narsimhan (Stanford University), Eric Shaqfeh (Stanford University)
Computational Mechanics of Biomembranes
Mon 2:40 - 4:00
Barus-Holley 160
Previous experimental works have demonstrated elongation and tethering behaviors where vesicles form a dumbbell shape connected by a thin long neck. We present boundary integral simulations of dumbbell stretching transitions for vesicles in a uniaxial extensional flow that can be either symmetric or non-symmetric with respect to the size of the two dumbbells depending on the flow conditions. For high reduced volumes (greater 0.74 for matched inner/outer viscosity vesicles), a stable steady-state shape exists for the vesicle at extensional flows of any capillary number. For lower reduced volume vesicles where the vesicle's equilibrium shape becomes nonconvex, there exists a critical capillary number above which odd perturbations to the vesicle shape drive an asymmetric elongation transition. For vesicles with reduced volume below ~0.6, there exists a symmetric elongation transition where the neck thins continuously and the vesicle has no steady shape above a critical capillary number. We present several additional results that give a better physical understanding of these processes. To understand the onset of the asymmetric instability as reduced volume decreases, we show theoretical results that predict an ellipsoidal base state and a parabolic tension distribution in the limit of infinite capillary number for vesicles above the reduced volume stability threshold and confirm these results with simulation. We provide calculations of center-line pressure for the asymmetric instability that demonstrate a mechanism for the asymmetric instability as a competition between the internal pressure differentials from the membrane bending force and ambient flow. We compare our uniaxial extensional flow results to simulations in planar extensional flow.