Dissolution-driven propulsion of floating solids.

We show that unconstrained asymmetric dissolving solids floating in a fluid can move rectilinearly as a result of attached density currents which occur along their inclined surfaces. Solids in the form of boats composed of centimeter-scale sugar and salt slabs attached to a buoy are observed to move rapidly in water with speeds up to 5 mm/s determined by the inclination angle and orientation of the dissolving surfaces. While symmetric boats drift slowly, asymmetric boats are observed to accelerate rapidly along a line before reaching a terminal velocity when their drag matches the thrust generated by dissolution. By visualizing the flow around the body, we show that the boat velocity is always directed opposite to the horizontal component of the density current. We derive the thrust acting on the body from its measured kinematics and show that the propulsion mechanism is consistent with the unbalanced momentum generated by the attached density current. We obtain an analytical formula for the body speed depending on geometry and material properties and show that it captures the observed trends reasonably. Our analysis shows that the gravity current sets the scale of the body speed consistent with our observations, and we estimate that speeds can grow slowly as the cube root of the length of the inclined dissolving surface. The dynamics of dissolving solids demonstrated here applies equally well to solids undergoing phase change and may enhance the drift of melting icebergs, besides unraveling a primal strategy by which to achieve locomotion in active matter.

Emergence of tip singularities in dissolution patterns.

Chemical erosion, one of the two major erosion processes along with mechanical erosion, occurs when a soluble rock-like salt, gypsum, or limestone is dissolved in contact with a water flow. The coupling between the geometry of the rocks, the mass transfer, and the flow leads to the formation of remarkable patterns, like scallop patterns in caves. We emphasize the common presence of very sharp shapes and spikes, despite the diversity of hydrodynamic conditions and the nature of the soluble materials. We explain the generic emergence of such spikes in dissolution processes by a geometrical approach. Singularities at the interface emerge as a consequence of the erosion directed in the normal direction, when the surface displays curvature variations, like those associated with a dissolution pattern. First, we demonstrate the presence of singular structures in natural interfaces shaped by dissolution. Then, we propose simple surface evolution models of increasing complexity demonstrating the emergence of spikes and allowing us to explain at long term by coarsening the formation of cellular structures. Finally, we perform a dissolution pattern experiment driven by solutal convection, and we report the emergence of a cellular pattern following well the model predictions. Although the precise prediction of dissolution shapes necessitates performing a complete hydrodynamic study, we show that the characteristic spikes which are reported ultimately for dissolution shapes are explained generically by geometrical arguments due to the surface evolution. These findings can be applied to other ablation patterns, reported for example in melting ice.

Streamwise Dissolution Patterns Created by a Flowing Water Film.

The dissolution of rocks by rainfall commonly generates streamwise parallel channels, yet the occurrence of these natural patterns remains to be understood. Here, we report the emergence in the laboratory of a streamwise dissolution pattern at the surface of an initially flat soluble material, inclined and subjected to a thin runoff water flow. Nearly parallel grooves about 1 mm wide and directed along the main slope spontaneously form. Their width and depth increase continuously with time until their crests emerge and channelize the flow. Our observations may constitute the early stage of the patterns observed in the field.

Direct numerical simulations of capillary wave turbulence.

This work presents direct numerical simulations of capillary wave turbulence solving the full three-dimensional Navier-Stokes equations of a two-phase flow. When the interface is locally forced at large scales, a statistical stationary state appears after few forcing periods. Smaller wave scales are generated by nonlinear interactions, and the wave height spectrum is found to obey a power law in both wave number and frequency, in good agreement with weak turbulence theory. By estimation of the mean energy flux from the dissipated power, the Kolmogorov-Zakharov constant is evaluated and found to be compatible with the exact theoretical value. The time scale separation between linear, nonlinear interaction, and dissipative times is also observed. These numerical results confirm the validity of the weak turbulence approach to quantify out-of equilibrium wave statistics.

Heterogeneous structure of granular aggregates with capillary interactions.

We investigate the spatial structure of cohesive granular matter with spheres floating at an air-liquid interface that form disordered close packings with pores in between. The interface is slowly lowered in a conical container to uniformly compress and study the system as a function of area fraction ϕ. We find that the free area distributions associated with Voronoi cells show significant exponential tails indicating greater heterogeneity compared with random distributions at low ϕ with a crossover towards a Γ distribution as ϕ is increased. Further, we find significant short range order as measured by the radial correlation function and the orientational order parameter even at low and intermediate ϕ, which is absent when particles interact only sterically.

Tuning the distance to equipartition by controlling the collision rate in a driven granular gas experiment.

In a granular gas experiment of magnetized particles confined in a thin layer, the rate of dissipative collisions is tuned by adjusting the amplitude of an external magnetic field. The velocity statistics are analyzed using the dynamic and static structure factors of transverse velocity modes. Using the fluctuating hydrodynamics theory, we measure the deviation from kinetic energy equipartition in this out-of-equilibrium system as a function of the dissipative collision rate. When the collision rate is decreased, the distance to equipartition becomes smaller, meaning that the dynamical properties of this granular gas approach by analogy those of a molecular gas in thermal equilibrium.

Patterns in magnetic granular media at the crossover from two to three dimensions.

We perform three-dimensional particle-based simulations of confined, vibrated, and magnetizable beads to study the effect of cell geometry on pattern selection. For quasi-two-dimensional systems, we reproduce previously observed macroscopic patterns such as hexagonal crystals and labyrinthine structures. For systems at the crossover from two to three dimensions, labyrinthine branches shorten and are replaced by triplets of beads forming upright triangles which self-organize into a herringbone pattern. This transition is associated with increases in both translational and orientational orders.

Uplift of an elastic membrane by a viscous flow.

The uplift of an initially flat elastic membrane by an upward viscous flow is investigated experimentally. The deformed shape of the membrane results from a balance between the flow pressure, the elastic response of the membrane, and the fluid weight. This last effect becomes non-negligible for a large enough deformed area. The usual theoretical approach supposes the presence of a prewetting film regularizing the viscous stresses according to Lister et al. [Phys. Rev. Lett. 111, 154501 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.154501]. Nevertheless, in our experiments without prewetting films, the measurements are correctly described with this theory in the elastic regime. Microscale roughness of membranes could introduce an equivalent characteristic scale in the problem. An alternative explanation could be provided by the appearance of a fluid lag filled with gas, for which a new theoretical framework has been recently proposed by Ball and Neufeld [Phys. Rev. Fluids 3, 074101 (2018)2469-990X10.1103/PhysRevFluids.3.074101]. We compare the two approaches and find that both describe reasonably our experiments. However, consistency tests of both models show that the prewetting film model is more appropriate to describe our experimental data.

Reduction of velocity fluctuations in a turbulent flow of gallium by an external magnetic field.

The magnetic field of planets or stars is generated by the motion of a conducting fluid through a dynamo instability. The saturation of the magnetic field occurs through the reaction of the Lorentz force on the flow. In relation to this phenomenon, we study the effect of a magnetic field on a turbulent flow of liquid gallium. The measurement of electric potential differences provides a signal related to the local velocity fluctuations. We observe a reduction of velocity fluctuations at all frequencies in the spectrum when the magnetic field is increased.

Experimental study of three-wave interactions among capillary-gravity surface waves.

In propagating wave systems, three- or four-wave resonant interactions constitute a classical nonlinear mechanism exchanging energy between the different scales. Here we investigate three-wave interactions for gravity-capillary surface waves in a closed laboratory tank. We generate two crossing wave trains and we study their interaction. Using two optical methods, a local one (laser doppler vibrometry) and a spatiotemporal one (diffusive light photography), a third wave of smaller amplitude is detected, verifying the three-wave resonance conditions in frequency and in wave number. Furthermore, by focusing on the stationary regime and by taking into account viscous dissipation, we directly estimate the growth rate of the resonant mode. The latter is then compared to the predictions of the weakly nonlinear triadic resonance interaction theory. The obtained results confirm qualitatively and extend previous experimental results obtained only for collinear wave trains. Finally, we discuss the relevance of three-wave interaction mechanisms in recent experiments studying gravity-capillary turbulence.

Transition to a labyrinthine phase in a driven granular medium.

Labyrinthine patterns arise in two-dimensional physical systems submitted to competing interactions, in fields ranging from solid-state physics to hydrodynamics. For systems of interacting particles, labyrinthine and stripe phases were studied in the context of colloidal particles confined into a monolayer, both numerically by means of Monte Carlo simulations and experimentally using superparamagnetic particles. Here we report an experimental observation of a labyrinthine phase in an out-of-equilibrium system constituted of macroscopic particles. Once sufficiently magnetized, they organize into short chains of particles in contact and randomly orientated. We characterize the transition from a granular gas state towards a solid labyrinthine phase, as a function of the ratio of the interaction strength to the kinetic agitation. The spatial local structure is analyzed by means of accurate particle tracking. Moreover, we explain the formation of these chains using a simple model.

Corneal nerve tortuosity in diabetic patients with neuropathy.

PURPOSE: Corneal confocal microscopy is a reiterative, rapid, noninvasive in vivo clinical examination technique capable of imaging corneal nerve fibers. Nerve fiber tortuosity may indicate a degenerative and attempted regenerative response of nerve fibers to diabetes. The purpose of this study was to define alterations in the tortuosity of corneal nerve fibers in relation to age, duration of diabetes, glycemic control, and neuropathic severity. METHODS: The cornea and collected images of the subbasal nerve plexus of 18 diabetic patients (stratified into mild, moderate, and severe neuropathic groups using conventional clinical measures of neuropathy) and 18 age-matched nondiabetic control subjects were scanned, and a novel mathematical paradigm was applied to quantify the extent of nerve tortuosity, which was termed the tortuosity coefficient (TC). RESULTS: TC was significantly different between the four clinical groups (F(3) = 12.2, P < 0.001). It was significantly greater in the severe neuropathic group than in control subjects (P < 0.003) and in the mild (P < 0.004) and moderate (P < 0.01) neuropathic groups. TC did not correlate significantly with the age (r = -0.003, P > 0.05), duration of diabetes (r = -0.219, P > 0.05), or hemoglobin A1c (HbA1c; r = 0.155, P > 0.05) of diabetic patients. CONCLUSIONS: Corneal confocal microscopy allows rapid, noninvasive in vivo evaluation of corneal nerve tortuosity. This morphologic abnormality relates to the severity of somatic neuropathy and may reflect an alteration in the degree of degeneration and regeneration in diabetes.

Energy flux measurement from the dissipated energy in capillary wave turbulence.

We study experimentally the influence of dissipation on stationary capillary wave turbulence on the surface of a liquid by changing its viscosity. We observe that the frequency power-law scaling of the capillary spectrum departs significantly from its theoretical value when the dissipation is increased. The energy dissipated by capillary waves is also measured and found to increase nonlinearly with the mean power injected within the liquid. Here we propose an experimental estimation of the energy flux at every scale of the capillary cascade. The latter is found to be nonconstant through the scales. For fluids of low enough viscosity, we found that both capillary spectrum scalings with the frequency and the newly defined mean energy flux are in good agreement with wave turbulence theory. The Kolmogorov-Zakharov constant is then experimentally estimated and compared to its theoretical value.

Speed of a swimming sheet in Newtonian and viscoelastic fluids.

We measure the swimming speed of a cylindrical version of Taylor's swimming sheet in viscoelastic fluids, and find that depending on the rheology, the speed can either increase or decrease relative to the speed in a Newtonian viscous fluid. The swimming stroke of the sheet is a prescribed propagating wave that travels along the sheet in the azimuthal direction. The measurements are performed with the sheet immersed in a fluid inside a cylindrical tank under torque-free conditions. Swimming speeds in the Newtonian case are found to be consistent with calculations using the Stokes equation. A faster swimming speed is found in a viscoelastic fluid that has a viscosity independent of shear rate. By contrast, a slower swimming speed is found with more complex shear-thinning viscoelastic fluids which have multiple relaxation time scales as well. These results are compared with calculations with Oldroyd-B fluids which find a decreasing swimming speed with Deborah number given by the product of the fluid elastic relaxation time scale and the driving frequency.

Decay of capillary wave turbulence.

We report on the observation of freely decaying capillary wave turbulence on the surface of a fluid. The capillary wave turbulence spectrum decay is found to be self-similar in time with the same power law exponent as the one found in the stationary regime, in agreement with weak turbulence predictions. The amplitude of all Fourier modes are found to decrease exponentially with time at the same damping rate. The longest wavelengths involved in the system are shown to be damped by a viscous surface boundary layer. These long waves play the role of an energy source during the decay that sustains nonlinear interactions to keep capillary waves in a wave turbulent state.

Shape and dynamics of seepage erosion in a horizontal granular bed.

We investigate erosion patterns observed in a horizontal granular bed resulting from seepage of water motivated by observation of beach rills and channel growth in larger scale land forms. Our experimental apparatus consists of a wide rectangular box filled with glass beads with a narrow opening in one of the side walls from which eroded grains can exit. Quantitative data on the shape of the pattern and erosion dynamics are obtained with a laser-aided topography technique. We show that the spatial distribution of the source of groundwater can significantly impact the shape of observed patterns. An elongated channel is observed to grow upstream when groundwater is injected at a boundary adjacent to a reservoir held at constant height. An amphitheater (semicircular) shape is observed when uniform rainfall infiltrates the granular bed to maintain a water table. Bifurcations are observed as the channels grow in response to the groundwater. We further find that the channels grow by discrete avalanches as the height of the granular bed is increased above the capillary rise, causing the deeper channels to have rougher fronts. The spatiotemporal distribution of avalanches increase with bed height when partial saturation of the bed leads to cohesion between grains. However, the overall shape of the channels is observed to remain unaffected indicating that seepage erosion is robust to perturbation of the erosion front.

Aggregation of frictional particles due to capillary attraction.

Capillary attraction between identical millimeter-sized spheres floating at a liquid-air interface and the resulting aggregation are investigated at low Reynolds number. We show that the measured capillary forces between two spheres as a function of distance can be described by expressions obtained using the Nicolson approximation at low Bond numbers for far greater particle sizes than previously assumed. We find that viscous hydrodynamic interactions between the spheres needs to be included to describe the dynamics close to contact. We then consider the aggregates formed when a third sphere is added after the initial two spheres are already in contact. In this case, we find that linear superposition of capillary forces describes the observed approach qualitatively but not quantitatively. Further, we observe an angular dependence of the structure due to a rapid decrease of capillary force with distance of separation, which has a tendency to align the particles before contact. When the three particles come into contact, they may preserve their shape or rearrange to form an equilateral triangle cluster-the lowest-energy state-depending on the competition between attraction between particles and friction. Using these observations, we demonstrate that a linear particle chain can be built from frictional particles with capillary attraction.