We consider the unsteady regimes of an acoustically-driven jet that forces a recirculating flow through successive reflections on the walls of a square cavity. The specific question being addressed is to know whether the system can sustain states of low-dimensional chaos when the acoustic intensity driving the jet is increased, and, if so, to characterise the pathway and underlying physical mechanisms. We adopt two complementary approaches, both based on data extracted from numerical simulations: (i) We first characterise successive bifurcations through the analysis of leading frequencies. Two successive phases in the evolution of the system are singled out in this way, both leading to potentially chaotic states. The two phases are separated by a drastic simplification of the dynamics that immediately follows the emergence of intermittency. The second phase also features a second intermediate state where the dynamics is simplified due to frequency-locking. (ii) Nonlinear time series analysis enables us to reconstruct the attractor of the underlying dynamical system, and to calculate its correlation dimension and leading Lyapunov exponent. Both these quantities bring confirmation that the state preceding the dynamic simplification that initiates the second phase is chaotic. Poincar\'e maps further reveal that this chaotic state in fact results from a dynamic instability of the system between two non-chaotic states respectively observed at slightly lower and slightly higher acoustic forcing.
Abstract The transport of small amounts of liquids on solid surfaces is fundamental for microfluidics applications. Technologies allowing control of droplets of liquid on flat surfaces generally involve the generation of a wettability contrast. This approach is however limited by the resistance to motion caused by the direct contact between the droplet and the solid. We show here that this resistance can be drastically reduced by preventing direct contact with the help of dual-length scale micro-structures and the concept of “liquid-surfaces”. These new surfaces allow the gentle transport of droplets along defined paths and with fine control of their speed. Moreover, their high adhesion permits the capture of impacting droplets, opening new possibilities in applications such as fog harvesting and heat transfer.
The transport of small quantities of liquid on a solid surface is inhibited by the resistance to motion caused by the contact between the liquid and the solid. To overcome such resistance, motion can be externally driven through gradients in electric fields, but these all inconveniently involve the input of external energy. Alternatively, gradients in physical shape and wettability - the conical shape of cactus spines to create self-propelled motion. However, such self-propelled motion to date has limited success in overcoming the inherent resistance to motion of the liquid contact with the solid. Here we propose a simple solution in the form of shaped-liquid surface, where solid topographic structures at one length scale provides the base for a smaller length-scale liquid conformal layer. This dual-length scale render possible slippery surfaces with superhydrophobic properties. Combined to an heterogeneous topography, it provides a gradient in liquid-on-liquid wettability with minimal resistance to motion and long range directional self-propelled droplet transport. Moreover, the liquid-liquid contact enables impacting droplets to be captured and transported, even when the substrate is inverted. These design principles are highly beneficial for droplet transport in microfluidics, self-cleaning surfaces, fog harvesting and in heat transfer.
We demonstrate spontaneous bidirectional motion of droplets on liquid infused surfaces in the presence of a topographical gradient, in which the droplets can move either toward the denser or the sparser solid fraction area. Our analytical theory explains the origin of this bidirectional motion. Furthermore, using both lattice Boltzmann simulations and experiments, we show that the key factor determining the direction of motion is the wettability difference of the droplet on the solid surface and on the lubricant film. The bidirectional motion is shown for various combinations of droplets and lubricants, as well as for different forms of topographical gradients.
The self-sustained turbulent shear or mixing layer that develops at the interface between a channel and a lateral cavity is the leading mechanism that drives the transfer of momentum and mass in these open-channel flows. Therefore, quantifying the interactions between large-scale vortical structures and the enhanced velocity fluctuations at the interface is critical to understand the physical processes which control the exchanges between the cavity and the main channel. In this investigation, we carry out hydrodynamic experiments in a straight, rectangular channel with a lateral square cavity. We measure the velocity field in a horizontal plane using particle image velocimetry to study the dynamics and statistics of the mixing layer, including the effects of the adverse pressure gradient at the downstream corner. By combining proper-orthogonal decomposition with a vortex identification technique, we investigate the motion of coherent structures and calculate the histograms of their trajectories, capturing also additional phenomena such as the vortex splitting, and the interaction of the mixing layer with inner vortices formed inside the cavity. We finally quantify the mass transport capacity of the mixing layer, from the statistics of the transverse velocity at the interface.
An emerging long obstacle placed in a boundary layer developing under a free surface generates a complex horseshoe vortex (HSV) system, which is composed of a set of vortices exhibiting a rich variety of dynamics. The present experimental study examines such flow structure and characterizes precisely, using particle image velocimetry (PIV) measurements, the evolution of the HSV geometrical and dynamical properties over a wide range of dimensionless parameters (Reynolds number $Re_{h}\in [750,8300]$ , boundary layer development ratio $h/\unicode[STIX]{x1D6FF}\in [1.25,4.25]$ and obstacle aspect ratio $W/h\in [0.67,2.33]$ ). The dynamical study of the HSV is based on the categorization of the motions of HSV vortices that result in an enhanced specific bi-dimensional typology, separating a coherent (due to vortex–vortex interactions) and an irregular evolution (due to the appearance of small-scale instabilities). This precise categorization is made possible thanks to the use of vortex tracking methods applied to PIV measurements; a semi-empirical model for the motion of the HSV vortices is then proposed to highlight some important mechanisms of the HSV dynamics, such as (i) the influence of the surrounding vortices on vortex motion and (ii) the presence of a phase shift between the motion of all vortices. Finally, the study of the HSV’s geometrical properties (vortex position and characteristic lengths and frequencies) evolution with the flow parameters shows that strong dependencies exist between the streamwise extension of the HSV and the obstacle width, and between the HSV vortex number and its elongation. Comparison of these data with prior studies for immersed obstacles reveals that emerging obstacles lead to greater adverse pressure gradients and down-flows in front of the obstacle. This implies a precocious separation of the boundary layer, leading to a larger HSV streamwise extension, and a lower vertical extension of the HSV, leading to smaller HSV vortices.
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