La déformation de matériaux élastique dont l'une au moins des dimensions est petite apparaît dans un grand nombre de structures naturelles ou artificielles pour lesquelles une courbure spontanée est présente. Dans ces travaux de thèse, nous couplons plusieurs approches théoriques à des expériences macroscopiques sur des rubans élastiques afin de comprendre la dynamique d'enroulement de biomembranes ouvertes d'un trou. La motivation est issue d'observations récentes d'enroulements obtenues au cours de la sortie de parasites de la Malaria de globules rouges infectés, et de l'explosion de vésicules polymère. Dans une première partie, nous étudions théoriquement la stabilité d'un pore et la propagation de l'enroulement sur une biomembrane sphérique ouverte. Nous modélisons de façon géométrique l'enroulement toroïdal de la membrane par une spirale d'Archimède de révolution et décentrée. Avec cette hypothèse, nous montrons que la stabilité du pore vis-à-vis de l'enroulement dépend fortement de la tension de ligne et du cisaillement et nous discutons ces résultats dans le cadre de l'enroulement de membranes MIRBCs. De plus, en prenant en compte les différentes sources de dissipation, nous obtenons un très bon accord entre les données expérimentales obtenues pour les MIRBCs et la dynamique d'enroulement obtenue par le calcul. Notre approche montre en particulier que la dissipation dans la membrane due à la redistribution de la matière durant l'enroulement domine sur la dissipation visqueuse dans le milieu.Cependant, la complexité de la géométrie sphérique, ainsi que le nombre limité d'observations microscopiques à l'échelle de la membrane sont une entrave au développement de modèles plus détaillés qui permettraient de décrire complètement le couplage entre écoulement et déformation. Nous avons donc étudié dans une seconde partie la déformation d'enroulement dans le cas de rubans élastiques ayant une courbure spontanée dans différents milieux visqueux et pour différentes conditions élastiques. A grands nombres de Reynolds, en raison de la localisation de la courbure pour les rubans au cours de la propagation du front d'enroulement le long du matériau, nous montrons que l'enroulement atteint rapidement une vitesse de propagation constante. Dans ce régime, le ruban s'enroule sur lui-même de façon compacte, sur un cylindre dont la taille est prévue à partir de la solution de l'onde stationnaire pour l'Elastica. A faible nombre de Reynolds, cependant, se rapprochant des conditions d'enroulement d'une membrane microscopique, nous mettons en évidence l'influence des forces de lubrification sur la nature non-compacte de l'enroulement. La taille globale de la spirale de ruban augmente dans le temps conduisant à une diminution de la puissance élastique libérée et donc à une diminution de la vitesse. Nous discutons dans quelle mesure ces résultats peuvent faire avancer la modélisation de l'enroulement dans les MIRBCs et les vésicules polymère. / 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 and macroscopic experiments on elastic ribbons to understand the dynamics of curling of opened bio-membranes, motivated by the need to better understand recent microscopic observations during egress of Malaria infected red blood cells (MIRBC) and bursting of artificial polymersomes.In a first part, we study theoretically pore stability and curling propagation of an initially opened spherical bio-membrane. We model geometrically curling deformation as the revolution of a decentered Archimedean spiral, leading to a prescribed toroidal wrapping of the membrane. In this configuration, we show how the stability of a pore to curling depends strongly on both line-tension and shear elasticity and we discuss these results in relation to the curling of MIRBCs membranes. Moreover, taking into account viscous dissipations, the consequent dynamics we calculate agrees quantitatively well with experimental data obtained during opening of MIRBCs. Our approach shows in particular how the membrane dissipation resulting from the surface redistribution dominates curling dynamics over outer viscous dissipation.However, the complexity of the spherical geometry and the lack of detailed images in microscopic observations hamper the development of more accurate models where the coupling between flow and deformation is fully understood. Subsequently, we study in a second part the curling deformation of macroscopic naturally curved elastic ribbons in different viscous media and elastic conditions. At high Reynolds numbers, due to the tendency of ribbons to localize bending deformations when a curling front travels down the material, we show that curling reaches rapidly a constant propagating velocity. In this regime, the ribbon wraps itself into a compact roll whose size is predicted through the solitary wave solution of the associated Elastica. At low Reynolds numbers, however, closer to the hydrodynamic conditions of curling in microscopic membranes, we show that the strong lubrication forces induce a non-compact curling. The overall size of the spiraling ribbon increases in time leading to a temporal decrease of the released elastic power and therefore a consequent decrease in velocity. We discuss how such discovery sheds a new light on the modeling of curling in MIRBCs and polymersomes.

Nous nous sommes intéressés à l'auto-enroulement de films de polydimethylsiloxane (PDMS) oxydés dans des vapeurs de solvant. Brièvement, des films minces de PDMS sont obtenus par enduction sous centrifugation. Ces films sont ensuite exposés à un plasma d'oxygène, ce qui a pour conséquence d'oxyder et de rigidifier leurs surfaces. Lorsque ces systèmes sont exposés à certains solvants en phase gazeuse, le PDMS non-oxydé gonfle. Cela mène à l'auto-enroulement des films et donc à la formation de capillaires. Ce mécanisme est intéressant pour la fabrication de canaux microfluidiques car ce qui deviendra la surface interne desdits canaux peut-être caractérisé et fonctionalisé avant l'enroulement.Dans un premier chapitre, différents aspects de l'auto-enroulement sont passés en revue théoriquement et numériquement.Un second chapitre expérimental est dédié à l'étude de la couche oxydée par nano-indentation AFM. Les propriétés mécaniques du système composite (couche dur sur substrat mou) sont mesurées et interprétées au moyen d'un nouveau modèle pour extraire notamment l'épaisseur du film oxydé.Dans un troisième chapitre, l'auto-enroulement des tubes lui-même est étudié. Le diamètre interne des capillaires obtenus en fonction de paramètres expérimentaux est examiné et confronté à la théorie. Plusieurs démonstrations de principe de tube avec une surface interne fonctionnalisée sont fournies.Enfin, pour répondre à des problématiques d'intégration des systèmes dans une structure microfluidique plus complexe, une méthode innovante est proposée dans un quatrième et dernier chapitre. Basée sur l'impression jet d'encre de moules sacrificiels, la méthode est d'abord mise en place expérimentalement. De nombreuses démonstrations de principe du vaste potentiel de cette idée sont ensuites proposées. / The guideline of this work is the spontaneous rolling of oxidized polydimethylsiloxane (PDMS) thin films in organic solvant vapors. Briefly, thin films of PDMS are produced by spin coating. Those films are then exposed to oxygen plasma which oxidizes and hardens their surfaces. When those systems are immersed in appropriate solvent vapors, non oxidized PDMS selectively swells. This leads to the spontaneous rolling of the films and thus to the formation of capillaries. This mechanism is of great interest for the fabrication of microfluidic channels because what is to become the inner surface of those channels can be characterized and functionalized prior to rolling.In a first chapter, different aspects of spontaneous rolling are reviewed theoretically and numerically.A second chapter is dedicated to the investigation of the oxide layer by AFM nanoindentation. The mechanical properties of the composite system (hard layer on a soft substrate) are measured and interpreted with a new model in order to extract in particular the thickness of the oxide layer.A third chapter dwells on engineering of the rolled-up tubes. The inner diameter of the capillaries as a function of experimental parameters is measured and confronted to theory. We present tubes with various inner surface functionalizations as a proof of concept of the method.Finally, in order to solve the issue of the integration of the system in a wider structure, an innovative method is proposed in a final fourth chapter. Based on the fabrication of a sacrificial mold by inkjet printing, the method is first established and implemented. Several proof-of-concept systems are then displayed in order to demonstrate the great potential of that idea.

In this paper we study a methodology for the numerical simulation of stable structures of fluid membranes and vesicles in biological organisms. In particular, we discuss the effects of spontaneous curvature on vesicle cell membranes under the bending energy for given volume and surface area. The geometric modeling of the vesicle shapes are undertaken by means of surfaces generated as Partial Differential Equations (PDEs). We combine PDE based geometric modeling with numerical optimization in order to study the stable shapes adopted by the vesicle membranes. Thus, through the PDE method we generate a generic template of a vesicle membrane which is then efficiently parameterized. The parameterization is taken as a basis to set up a numerical optimization procedure which enables us to predict a series of vesicle shapes subject to given surface area and volume.

Lipid bilayers are key components of biomembranes; they are self-assembled two-dimensional structures, primarily serving as barriers to the leakage of cell's contents. Lipid bilayers are typically charged in aqueous solution and may electrostatically interact with each other and with their environment. In this work, we investigate electrostatics of charged lipid bilayers with the main focus on the binding and bending of the bilayers. We first present a theoretical approach to charge-correlation attractions between like-charged lipid bilayers with neutralizing counterions assumed to be localized to the bilayer surface. In particular, we study the effect of nonzero ionic sizes on the attraction by treating the bilayer charges (both backbone charges and localized counterions) as forming a two-dimensional ionic fluid of hard spheres of the same diameter <i>D</i>. Using a two-dimensional Debye-H??ckel approach to this system, we examine how ion sizes influence the attraction. We find that the attraction gets stronger as surface charge densities or counterion valency increase, consistent with long-standing observations. Our results also indicate non-trivial dependence of the attraction on separations <i>h</i>: The attraction is enhanced by ion sizes for <i>h</i> ranges of physical interest, while it crosses over to the known <i>D</i>-independent universal behavior as <i>h</i> &rarr; &infin;; it remains finite as <i>h</i> &rarr; 0, as expected for a system of finite-sized ions. We also study the preferred curvature of an asymmetrically charged bilayer, in which the inner leaflet is negatively charged, while the outer one is neutral. In particular, we calculate the relaxed area difference &Delta; <i>A</i>₀ and the spontaneous curvature <i>C</i>₀ of the bilayer. We find &Delta; <i>A</i>₀ and <i>C</i>₀ are determined by the balance of a few distinct contributions: net charge repulsions, charge correlations, and the entropy associated with counterion release from the bilayer. The entropic effect is dominant for weakly charged surfaces in the presence of monovalent counterions only and tends to expand the inner leaflet, leading to negative &Delta; <i>A</i>₀ and <i>C</i>₀. In the presence of even a small concentration of divalent counterions, however, charge correlations counterbalance the entropic effect and shrink the inner leaflet, leading to positive &Delta; <i>A</i>₀ and <i>C</i>₀. We outline biological implications of our results.

Lipid bilayers are key components of biomembranes; they are self-assembled two-dimensional structures, primarily serving as barriers to the leakage of cell's contents. Lipid bilayers are typically charged in aqueous solution and may electrostatically interact with each other and with their environment. In this work, we investigate electrostatics of charged lipid bilayers with the main focus on the binding and bending of the bilayers. We first present a theoretical approach to charge-correlation attractions between like-charged lipid bilayers with neutralizing counterions assumed to be localized to the bilayer surface. In particular, we study the effect of nonzero ionic sizes on the attraction by treating the bilayer charges (both backbone charges and localized counterions) as forming a two-dimensional ionic fluid of hard spheres of the same diameter <i>D</i>. Using a two-dimensional Debye-Hückel approach to this system, we examine how ion sizes influence the attraction. We find that the attraction gets stronger as surface charge densities or counterion valency increase, consistent with long-standing observations. Our results also indicate non-trivial dependence of the attraction on separations <i>h</i>: The attraction is enhanced by ion sizes for <i>h</i> ranges of physical interest, while it crosses over to the known <i>D</i>-independent universal behavior as <i>h</i> &rarr; &infin;; it remains finite as <i>h</i> &rarr; 0, as expected for a system of finite-sized ions. We also study the preferred curvature of an asymmetrically charged bilayer, in which the inner leaflet is negatively charged, while the outer one is neutral. In particular, we calculate the relaxed area difference &Delta; <i>A</i>₀ and the spontaneous curvature <i>C</i>₀ of the bilayer. We find &Delta; <i>A</i>₀ and <i>C</i>₀ are determined by the balance of a few distinct contributions: net charge repulsions, charge correlations, and the entropy associated with counterion release from the bilayer. The entropic effect is dominant for weakly charged surfaces in the presence of monovalent counterions only and tends to expand the inner leaflet, leading to negative &Delta; <i>A</i>₀ and <i>C</i>₀. In the presence of even a small concentration of divalent counterions, however, charge correlations counterbalance the entropic effect and shrink the inner leaflet, leading to positive &Delta; <i>A</i>₀ and <i>C</i>₀. We outline biological implications of our results.

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