Curling dynamics of naturally curved surfaces : axisymmetric bio-membranes and elastic ribbons

摘要: Curling deformation of thin elastic surfaces appears in numerous natural and man-made structures where a spontaneous curvature is present. In this thesis, we couple theoretical approaches macroscopic experiments on ribbons to understand the dynamics curling opened bio-membranes, motivated by need better recent microscopic observations during egress Malaria infected red blood cells (MIRBC) bursting artificial polymersomes.In first part, study theoretically pore stability propagation an initially spherical bio-membrane. We model geometrically as revolution decentered Archimedean spiral, leading prescribed toroidal wrapping membrane. configuration, show how depends strongly both line-tension shear elasticity discuss these results relation MIRBCs membranes. Moreover, taking into account viscous dissipations, consequent calculate agrees quantitatively well with experimental data obtained opening MIRBCs. Our approach shows particular membrane dissipation resulting from surface redistribution dominates over outer dissipation.However, complexity geometry lack detailed images hamper development more accurate models coupling between flow fully understood. Subsequently, second part naturally curved different media conditions. At high Reynolds numbers, due tendency localize bending deformations when front travels down material, that reaches rapidly constant propagating velocity. regime, ribbon wraps itself compact roll whose size predicted through solitary wave solution associated Elastica. low however, closer hydrodynamic conditions membranes, strong lubrication forces induce non-compact curling. The overall spiraling increases time temporal decrease released power therefore such discovery sheds new light modeling polymersomes.