Cilia and flagella are hair-like appendages that protrude from the surface of a variety of eukaryotic cells and deform in a wavelike fashion to transport fluids and propel cells. Motivated by the ubiquity of non-Newtonian fluids in biology, we address mathematically the role of shear-dependent viscosities on both the waving flagellar locomotion and ciliary transport by metachronal waves. Using a two-dimensional waving sheet as model for the kinematics of a flagellum or an array of cilia, and allowing for both normal and tangential deformation of the sheet, we calculate the flow field induced by a small-amplitude deformation of the sheet in a generalized Newtonian Carreau fluid up to order four in the dimensionless waving amplitude. The net flow induced at far from the sheet can be interpreted either as a net pumping flow or, in the frame moving with the sheet, as a swimming velocity. At leading order (square in the waving amplitude), the net flow induced by the waving sheet and the rate of viscous dissipation is the same as the Newtonian case, but is different at the next nontrivial order (four in the waving amplitude). If the sheet deforms both in the directions perpendicular and parallel to the wave progression, the shear-dependence of the viscosity leads to a nonzero flow induced in the far field while if the sheet is inextensible, the non-Newtonian influence is exactly zero. Shear-thinning and shear-thickening fluids are seen to always induce opposite effects. When the fluid is shear-thinning, the rate of working of the sheet against the fluid is always smaller than in the Newtonian fluid, and the largest gain is obtained for antiplectic metachronal waves. Considering a variety of deformation kinematics for the sheet, we further show that in all cases transport by the sheet is more efficiency in a shear-thinning fluid, and in most cases the transport speed in the fluid is also increased. Comparing the order of magnitude of the shear-thinning contributions with past work on elastic effects as well as the magnitude of the Newtonian contributions, our theoretical results, which beyond the Carreau model are valid for a wide class of generalized Newtonian fluids, suggest that the impact of shear-dependent viscosities on transport could play a major biological role.

International audienceWe consider the deformation of gas bubbles rising in different liquids over a wide range of Morton numbers, from O(10−11) to O(1), and bubble diameters. We have collected data from the literature and performed new experiments for relatively large Morton numbers. A simple expression is proposed to describe the evolution of the bubble deformation, which is consistent with the analytical solution of Moore ["The rise of a gas bubble in a viscous liquid," J. Fluid Mech. 6, 113 (1959)]. It appears that deformation can be predicted correctly by considering the Morton and Weber numbers. The variation of the bubble interfacial area is also analyzed; this quantity is very important for the case of bubbly flow modeling but has not been measured directly to date

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Abstract:The advent of nanotechnology has triggered novel developments and applications for polymer-based membranes with embedded or coated nanoparticles. As an example, interaction of laser radiation with metallic and carbon nanoparticles has shown to provide optically triggered responses in otherwise transparent media. Incorporation of these materials inside polymers has led to generation of plasmonic and photothermal effects through the enhanced optical absorption of these polymer composites. In this work, we focus on the photothermal effects produced in polydimethylsiloxane (PDMS) membranes with embedded carbon nanoparticles via light absorption. Relevant physical parameters of these composites, such as nanoparticle concentration, density, geometry and dimensions, are used to analyze the photothermal features of the membranes. In particular, we analyze the heat generation and conduction in the membranes, showing that different effects can be achieved and controlled depending on the physical and thermal properties of the composite material. Several novel applications of these light responsive membranes are also demonstrated, including low-power laser-assisted micro-patterning and optomechanical deformation. Furthermore, we show that these polymer-nanoparticle composites can also be used as coatings in photonic and microfluidic applications, thereby offering an attractive platform for developing light-activated photonic and optofluidic devices.