We report on an experimental investigation of the propagation of gravity-capillary waves in a narrow channel with a pinned contact line. By using Fourier Transform Profilometry (FTP) we measure the static curved meniscus as well as the surface perturbation. By varying the channel width, between 7 and 15 times the capillary length, we show how edge constraints modify the surface curvature and therefore the dispersion relation. From the space-time resolved field, we obtain a decomposition of the linear mode onto transverse modes satisfying the condition of pinned contact line. This approach, in which we complement the theoretical model with experimental analysis, allows computations of wavenumbers and natural frequencies with a robust statistics. We verify experimentally the convergence of the model and the pertinence of the linear approximation. In addition, we analyze the relative contribution of the experimentally measured static meniscus. An excellent agreement between the computed natural frequencies and the forcing frequency confirms the contribution of the actual space-time resolved measured surface. These experimental results are an accurate estimation of the influence of the additional restoring force exerted by the pinned contact line on the deformed surface which increases the wave celerity. The local character of this effect is evidenced by the decrease of the shift of the dispersion relation as a function of the channel width.
Droplet evaporation has been intensively investigated in past decades owing to its emerging applications in diverse fields of science and technology. Yet the role transport mechanisms has been the subject of a heated debate, especially the presence of Marangoni flow in water droplets. This work aims to draw a clear picture of the switching transport mechanisms inside a drying pinned sessile water droplet in both the presence and absence of thermocapillarity by developing a comprehensive model that accounts for all pertinent physics in both phases as well as interfacial phenomena at the interfa…
For super-heated water on a substrate with hydrophobic patches immersed in a hydrophilic matrix, one can choose the temperature so that micro-bubbles will form, grow and merge on the hydrophobic patches and not on the hydrophilic matrix. Until covering a patch, making a pinned macro-bubble, a bubble has a contact angle $π-θ_2$, where $θ_2$ is the receding contact angle of water on the patch material. This pinned macro-bubble serves as the initial condition of a quasi-static growth process, à la Landau, leading to detachment through the formation of a neck, so long as depinning and dewetting of…
Evaporation of water droplets on a superhydrophobic substrate, on which the contact line is pinned, is investigated. While previous studies mainly focused on droplets with contact angles smaller than 90^\circ, here we analyze almost the full range of possible contact angles (10^\circ -150^\circ). The greater contact angles and pinned contact lines can be achieved by the use of superhydrophobic Carbon Nanofiber substrates. The time-evolutions of the contact angle and the droplet mass are examined. The experimental data is in good quantitative agreement with the model presented by Popov (Physica…
We report on new instabilities of the quasi-static equilibrium of water drops pinned by a hydrophobic inclined substrate. The contact line of a statically pinned drop exhibits three transitions of partial depinning: depinning of the advancing and receding parts of the contact line and depinning of the entire contact line leading to the drop's translational motion. We find a region of parameters where the classical Macdougall-Ockrent-Frenkel approach fails to estimate the critical volume of the statically pinned inclined drop.
Computational models based on the depth-averaged shallow water equations (SWE) offer an efficient choice to analyse velocity fields around hydraulic structures. Second-order finite volume (FV2) solvers have often been used for this purpose subject to adding an eddy viscosity term at sub-meter resolution, but have been shown to fall short of capturing small-scale field transients emerging from wave-structure interactions. The second-order discontinuous Galerkin (DG2) alternative is significantly more resistant to the growth of numerical diffusion and leads to faster convergence rates. These pro…
Unexpectedly distinct patterns in evaporation were observed over heated water. Although the patterns had chaotic aspects, they often showed geometric patterns. These patterns bore strong resemblance to the infrared emission patterns observable with a mid-infrared camera focused on the water surface. This similarity puts constraints on the mechanism of evaporation, and leads to a general hypothesis as to the nature of the evaporative process.
This study concerns the effects of pressure, spatial location, and application of oil emulsions on the resulting droplet size, eccentricity, as well as velocity distributions, all of which are crucial information in determining the dispersion dynamics of the droplets during the spray applications. Experiments were conducted with the abovementioned droplets information measured using digital inline holography (DIH). Results show that the volumetric droplet size distributions (VDSD) span widely from sub-200 um to over 2 mm in size. The application of an oil-in-water emulsion results largely in t…
It is shown that surface waves propagating against the external current, slowly varying in the horizontal direction in deep water, are governed by the equation which is tantamount to the Gross - Pitaevskii equation modelling the mean-field dynamics of Bose - Einstein condensate. The repulsive or attractive sign of the cubic term in the Gross -Pitaevskii equation is controlled by the choice of the carrier wavelength of the surface waves, while the spatial variation of the current plays the role of the external potential in that equation. The current profile can be easily controlled in the exper…
The behavior of an oil droplet pinned at the entrance of a micropore and subject to clossflow-induced shear is investigated numerically by solving the Navier-Stokes equation. We found that in the absence of crossflow, the critical transmembrane pressure required to force the droplet into the pore is in excellent agreement with a theoretical prediction based on the Young-Laplace equation. With increasing shear rate, the critical pressure of permeation increases, and at sufficiently high shear rates the oil droplet breaks up into two segments. The results of numerical simulations indicate that d…
The evaporation of a binary sessile ethanol-water droplet on an inclined substrate is studied experimentally just below the critical sliding angles for different substrate temperatures. A customized goniometer equipped with a CMOS camera and an infrared (IR) camera is used. The droplet is observed to remain pinned in the advancing side during the evaporation process, while the receding side contracts. The asymmetry in the advancing and receding contact angles of the droplet on inclined substrate results in complex thermo-solutal Marangoni convection that is captured through IR images. The drop…
We describe a technique of image analysis providing the time resolved shape of a water surface simultaneously with the three-component velocity field on this surface. The method relies on a combination of stereoscopic surface mapping and stereoscopic three-component Particle Imaging Velocimetry (PIV), using a seeding of the free surface by small polystyrene particles. The method is applied to an experiment of `weak turbulence' in which random gravity waves interact in a weakly non-linear regime. Time resolved fields of the water elevation are compared to the velocity fields on the water surfac…
We report experiments on the full space and time resolved statistics of capillary wave turbulence at the air-water interface. The three-dimensional shape of the free interface is measured as a function of time by using the optical method of Diffusing Light Photography associated with a fast camera. Linear and nonlinear dispersion relations are extracted from the spatio-temporal power spectrum of wave amplitude. When wave turbulence regime is reached, we observe power-law spectra both in frequency and in wave number, whose exponents are found in agreement with the predictions of capillary wave …
We present heterodyne detected transient grating measurements on water filled Vycor 7930 in the range of temperature 20 - 90 degrees C. This experimental investigation enables to measure the acoustic propagation, the average density variation due the liquid flow and the thermal diffusion in this water filled nano-porous material. The data have been analyzed with the model of Pecker and Deresiewicz which is an extension of Biot model to account for the thermal effects. In the whole temperature range the data are qualitatively described by this hydrodynamic model that enables a meaningful insigh…
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, …
We report an experimental investigation of the effect of finite depth on the statistical properties of wave turbulence at the surface of water in the gravity-capillary range. We tune the wave dispersion and the level of nonlinearity by modifying the depth of water and the forcing respectively. We use space-time resolved profilometry to reconstruct the deformed surface of water. When decreasing the water depth, we observe a drastic transition between weak turbulence at the weakest forcing and a solitonic regime at stronger forcing. We characterize the transition between both states by studying …
This paper investigates numerically the hydraulic conveying of solids through a 90$^{\circ}$ elbow that changes the flow direction from horizontal to vertical, in the very-narrow case where the ratio of pipe to particle diameters is less than 5. We performed resolved CFD-DEM (computational fluid dynamics - discrete element method) computations, in which we made use of the IB (immersed boundary) method of the open-source code CFDEM. We investigate the effects of the water flow and particle injection rate on the transport rate and sedimentation by tracking the granular structures appearing in th…
We report measurements of resonant thermal capillary oscillations of a hemispherical liquid gas interface obtained using a half bubble deposited on a solid substrate. The thermal motion of the hemispherical interface is investigated using an atomic force microscope cantilever that probes the amplitude of vibrations of this interface versus frequency. The spectrum of such nanoscale thermal oscillations of the bubble surface presents several resonance peaks and reveals that the contact line of the hemispherical bubble is pinned on the substrate. The analysis of these peaks allows to measure the …
