Thermal and viscous forces compete for dominance at the microscopic length-scales which govern the behaviour of many soft or biological systems. We study three systems of increasing complexity with the central goal of understanding the statistical or hydrodynamic nature of their mechanics. First we study experiments that have been conducted on ferromagnetic colloidal rods. At equilibrium, the magnetically pinned rod is observed to randomly flip between two orientational states, which our theoretical analysis shows is due to a competition between entropic and Hamiltonian forces. We show analytically how entropic forces can arise by considering the coupling between observed and unobserved variables of a system. Experiments in which a rod is driven out of equilibrium by a rotating field display three phases of steady-state behaviour as a function of driving frequency. Using Brownian dynamics simulations we match the lower critical frequency to the experimentally obtained values, showing that thermal fluctuations play an important role in this regime and propose a simple argument to demonstrate that hydrodynamic interactions between the substrate and rod affect the upper critical frequency. We then turn to the biophysical topic of cell locomotion in viscoelastic media. In order to study how bacterial flagella interact with similarly-sized polymers in their environment, we construct a Stokesian dynamics model of a helical filament and bead--spring polymer. Simulating their interaction first for a pinned--rotating helix, then for a swimming helix, we demonstrate that large polymers become hydrodynamically entrained by the flagellum and coil around it, causing both pinned and swimming flagella to expend more work. For the swimming helix, this results in a reduction of swimming speed on average. Finally, we consider an active nematic fluid confined to a channel and show that the inclusion of a passive colloid induces a global state of coherent flow maintained by the intrinsic activity of the system. This flow is persistent, and transports the colloid with it along the channel. By this mechanism, a passive colloid is able to spontaneously induce its own transport through an otherwise quiescent fluid.

La capacité des leucocytes à se déplacer dans tout l’organisme est indispensable pour une réponse immunitaire rapide et efficace. Leur migration, dite amiboïde, est caractérisée par une vitesse importante (10-20 μm/min) et une grande adaptabilité face aux divers environnements qu’ils rencontrent, qu’ils soient bidimensionnels comme la paroi luminale endothéliale ou tridimensionnels (3D) comme les tissus. Telle qu'actuellement décrite, la migration amiboïde requiert de l’adhésion ou de la friction avec un support solide. Nous avons ici montré que les lymphocytes T effecteurs sont capables de nager sans interaction avec un support solide. Le mécanisme de propulsion est basé sur le flux rétrograde d’actine qui entraine une brosse protéique de molécules transmembranaires liées au cytosquelette entrant en interaction avec le medium. Par ailleurs, lors de leur migration sur la surface luminale des parois endothéliales, les leucocytes sont soumis à un flux important et s’orientent par rapport au flux via des mécanismes mal déterminés. Nous avons montré que l’orientation des lymphocytes et des neutrophiles respectivement dans le sens ou à contresens d’un flux peut s’expliquer sans détection moléculaire du stress hydrodynamique. Le lamellipode pour les neutrophiles et l’uropode pour les lymphocytes est non-adhérent et s’oriente dans le flux comme une girouette dans le vent. La polarisation avant-arrière réaligne l’ensemble de la cellule dans le même sens que l’extrémité orientée par le flux. Le mécanotactisme des leucocytes sous flux repose ainsi sur des mécanismes passifs, c’est-à-dire sans mécanotransduction. / A fast and efficient immunity response needs leukocytes’ability to migrate within the entire organism. Their migration, called amoeboid, is characterized by a high speed (10-20 μm.min-1) and a great adaptability to move through various environment, either two-dimensional as luminal endothelial surface or tri-dimensional (3D) environment as tissue. Since the observation of leukocytes migrating without adhesion through solid 3D medium, amoeboid migration is described as requiring either adhesion or friction with solid support to permit motility. We showed here that effector T lymphocytes are able to swim without any interaction with solid substrate. Propulsion is based on actin retrograde flow coupled with transmembrane proteins linked to cytoskeleton (like integrins) which drag a brush of polymeric molecules in interaction with the medium. Furthermore, cell guidance is required for many crucial functions as organism growth or immune system. However, when crawling on luminal endothelial surfaces, cells are exposed to blood flow and they robustly orient either with or against the flow with unknown mechanisms. We showed that lymphocytes and neutrophils flow orientation can be explain without any molecular flow sensor of shear stress. Lamellipodium for neutrophils and uropod for lymphocytes is non-adherent and orients in the direction of flow like a wind vane. Front-rear cell polarization aligns the axis of the whole cell with the non-adherent pole oriented by flow. Flow mechanotaxis of leukocytes relies on passive mechanisms without mechanotransduction.