A flexible sheet in uniform parallel flow is studied in order to quantify its fluid dynamic drag and fluid-elastic stability characteristics. An experimental campaign is undertaken that involves a cantilevered sheet in air flow characterised by Reynolds numbers of order R=10^4-10^6. The properties of the sheet include: constant mass per unit area; small but finite flexural rigidity; varying aspect ratios from within the range 0.43<l/L<1, where L and l denote the length and width respectively; and tension applied at the trailing edge. The unique aspect of the present work is an investigation into the influence of in-plane tension on both the fluid drag and fluid-elastic stability of the sheet. In the absence of tension, the configuration resembles a flag and the drag coefficient is observed to decrease with increasing aspect ratio and Reynolds number. In the presence of tension, the fluid drag is significantly reduced in the region below the critical flow velocity at which convected wave instabilities appear. This critical flow velocity can be increased through the moderate application of in-plane tension. Under lateral tension, the drag of the sheet is given to good approximation by the turbulent boundary layer drag law for a flat plate. Once stability is lost, however, the drag coefficient increases rapidly with Reynolds number due to convected waves travelling over the sheet's surface.
This paper explores the fluid-elastic response of a cantilevered flexible sheet in the presence of uniform airflow. The leading edge of the sheet is clamped, while at the trailing edge, in-plane tension is applied to provide additional rigidity to the sheet's small but finite bending stiffness. We outline a series of experiments performed in a wind tunnel with the purpose of examining fluid-elastic instabilities. In particular, we examine the role of in-plane tension induced rigidity and how it influences static divergence and convected wave instabilities. The flow is characterised by Reynolds…
The so-called Landau-Levich-Deryaguin problem treats the coating flow dynamics of a thin viscous liquid film entrained by a moving solid surface. In this context, we use a simple experimental set-up consisting of a partially-immersed rotating disc in a liquid tank to study the role of inertia, and also curvature, on liquid entrainment. Using water and UCON$^{\mbox{TM}}$ mixtures, we point out a rich phenomenology in the presence of strong inertia : ejection of multiple liquid sheets on the emerging side of the disc, sheet fragmentation, ligament formation and atomization of the liquid flux ent…
Reconfigurable kirigami mesostructure enables modulation of lift and drag
Laboratoire d’Hydrodynamique (LadHyX), CNRS, École polytechnique, Institut Polytechnique de Paris（拉伊达克斯水动力学实验室，法国国家科学研究中心，巴黎综合理工学院，巴黎理工学院）；Unsteady Flow Diagnostics Laboratory, Institute of Mechanical Engineering, École Polytechnique Fédérale de Lausanne (EPFL)（非定常流动诊断实验室，机械工程学院，洛桑联邦理工学院）；Department of Biological and Environmental Engineering, Cornell University（生物与环境工程系，康奈尔大学）
A classical problem in fluid mechanics is the motion of an axisymmetric vortex sheet evolving under the action of surface tension, surrounded by an inviscid fluid. Lagrangian descriptions of these dynamics are well-known, involving complex nonlocal expressions for the radial and longitudinal velocities in terms of elliptic integrals. Here we use these prior results to arrive at a remarkably compact and exact Eulerian evolution equation for the sheet radius $r(z,t)$ in an explicit flux form associated with the conservation of enclosed volume. The flux appears as an integral involving the pairwi…
The dispersed phase in turbulence can vary from almost inviscid fluid to highly viscous fluid. By changing the viscosity of the dispersed droplet phase, we experimentally investigate how the deformability of dispersed droplets affects the global transport quantity of the turbulent emulsion. Different kinds of silicone oil are employed to result in the viscosity ratio, $ζ$, ranging from $0.53$ to $8.02$. The droplet volume fraction, $ϕ$, is varied from 0\% to 10\% with a spacing of 2\%. The global transport quantity, quantified by the normalized friction coefficient $c_{f,ϕ}/c_{f,ϕ=0}$, shows a…
Recently, an unusual scaling law has been observed in circular hydraulic jumps and has been attributed to a supposed missing term in the local energy balance of the flow [\cite{bhagat_2018}]. In this paper, we show that - though the experimental observation is valuable and interesting - this interpretation is presumably not the good one. When transposed to the case of a axial sheet formed by two impinging liquid jets, the assumed principle leads in fact to a velocity distribution in contradiction with the present knowledge for this kind of flows. We show here how to correct this approach by ke…
We investigate freely expanding liquid sheets made of either simple Newtonian fluids or solutions of high molecular water-soluble polymer chains. A sheet is produced by the impact of a drop on a quartz plate covered with a thin layer of liquid nitrogen that suppresses shear viscous dissipation thanks to an inverse Leidenfrost effect. The sheet expands radially until reaching a maximum diameter and subsequently recedes. Experiments indicate the presence of two expansion regimes: the capillary regime, where the maximum expansion is controlled by surface tension forces and does not depend on the …
Polymer additives are commonly utilized to manipulate bubbly flows in various applications. Here, we investigate the effects of clean and contaminated bubbles driven upwards (upflow) in Newtonian and viscoelastic turbulent channel flows. Interface-resolved direct numerical simulations are performed to examine sole and combined effects of soluble surfactant and viscoelasticity using an efficient 3D finite-difference/front-tracking method. The incompressible flow equations are solved fully coupled with the FENE-P viscoelastic model and the equations governing interfacial and bulk surfactant conc…
The hydrodynamic drag at a lipid bilayer surface determines in part the flow properties of suspensions of cells and liposomes. Given the fluidity of lipid bilayers, it is not obvious a priori whether solid-like no-slip, liquid-like no-stress, or intermediate boundary conditions apply at the water-bilayer interface. Though no-slip conditions have been widely assumed for many decades, this fundamental aspect of membrane rheology has, to our knowledge, never been directly measured for free bilayers. We applied light sheet fluorescence microscopy to image freely diffusing phospholipid vesicles and…
We experimentally study linear and nonlinear waves on the surface of a fluid covered by an elastic sheet where both tension and flexural waves take place. An optical method is used to obtain the full space-time wave field, and the dispersion relation of waves. When the forcing is increased, a significant nonlinear shift of the dispersion relation is observed. We show that this shift is due to an additional tension of the sheet induced by the transverse motion of a fundamental mode of the sheet. When the system is subjected to a random noise forcing at large scale, a regime of hydro-elastic wav…
The sedimentation of a surfactant-laden deformable viscous drop acted upon by an electric field is considered theoretically. The convection of surfactants in conjunction with the the combined effect electrohydrodynamic flow and sedimentation leads to a locally varying surface tension, which subsequently alters the drop dynamics via the interplay of Marangoni, Maxwell and hydrodynamic stresses. Assuming small capillary number and small electric Reynolds number, we employ a regular perturbation technique to solve the coupled system of governing equations. It is shown that when a leaky dielectric…
We study steady-state oscillations of an elastic Hele-Shaw cell excited by traveling pressure waves over its upper surface. The fluid within the cell is bounded by two asymmetric elastic sheets which are connected to a rigid surface via distributed springs and modeled by the linearized plate theory. Modal analysis yields the frequency response of the configuration as a function of three parameters: the fluidic Womersley number and two ratios of elastic stress to viscous pressure for each of the sheets. These ratios, analogous to the Capillary number, combine the effects of fluid viscosity and …
A wetting liquid is driven through a thin gap due to surface tension and when the gap boundaries are elastic, the liquid deforms the gap as it rises. But when the fluid boundaries are also permeable (or poroelastic), the liquid can permeate the boundaries as the fluid rises and change their properties, for example by swelling and softening, thereby altering the dynamics of the rise. In this paper, we study the dynamics of capillary rise between two poroelastic sheets to understand the effects of boundary permeability and softening. We find that if the bending rigidity of sheets is reduced, due…
Motivated by the redrawing of hot glass into thin sheets, we investigate the shape and stability of a thin viscous sheet that is inhomogeneously stretched in an imposed non-uniform temperature field. We first determine the associated base flow by solving the long-timescale stretching flow of a flat sheet as a function of two dimensionless parameters: the normalized stretching velocity $α$, and a dimensionless width of the heating zone $β$. This allows us to determine the conditions for the onset of an out-of-plane wrinkling instability stated in terms of an eigenvalue problem for a linear part…
Flight on the two-dimensional air-water interface, with body weight supported by surface tension, is a unique locomotion strategy well adapted for the environmental niche on the surface of water. Although previously described in phylogenetically basal aquatic insects like stone flies, the biomechanics of interfacial flight has never been analyzed. Here, we report interfacial flight as an adapted behaviour in water-lily beetles (Galerucella nymphaeae, Linnaeus 1758) which are also dexterous airborne fliers. We present the first quantitative biomechanical model of interfacial flight in insects, …
Unsteady simulations of horizontal ribbon growth of silicon were performed that included both Marangoni and buoyancy effects. A chaotic flow was observed dominated by strong Marangoni-driven jets emerging near the local temperature minima on the free surface. This oscillatory flow caused the vertical position of the leading edge of the sheet to fluctuate, resulting in corrugations on the top surface of the ribbon. Additionally, larger amplitude and wavelength nonuniformities appeared on the bottom of the sheet resulting in a sheet with varying thickness. Lastly, the unsteady flow caused tempor…
