The motion of a gas-liquid interface along a solid wall is influenced by the capillary forces resulting from the interface's shape and its interaction with the solid, where it forms a dynamic contact angle. Capillary models play a significant role in the management of cryogenic propellants in space, where surface tension dominates the behaviour of gas-liquid interfaces. Yet, most empirical models have been derived in configurations dominated by viscous forces. In this study, we experimentally investigate the wetting of a low-viscosity, highly wetting fluid in a reduced gravity environment. Our setup consisted of a transparent and diverging U-tube in which capillary forces sustain the liquid motion. Combining Particle Image Velocimetry (PIV) and high-speed backlighting visualization, the experimental campaign allowed for measuring the interface evolution and the velocity field within the liquid under varying gravity levels. This work reports on the preliminary results from the image velocimetry and shows that the velocity profile within the tube is close to parabolic until a short distance from the interface. Nevertheless, classic 1D models for capillary rise face difficulties reproducing the interface dynamics, suggesting that the treatment of the surface tension in these problems must be reviewed.
Using the FLUIDICS (Fluid Dynamics in Space) experiment in the International Space Station, turbulence of capillary waves at the air-water interface is experimentally investigated in weightlessness. Capillary waves are excited in a spherical container partially filled with water and undergoing sinusoidal or random oscillations. The fluctuations of the interface, recorded with two capacitive probes are analyzed by means of the frequency power spectrum of wave elevation. For high enough forcing amplitudes, we report power-law spectra with exponents close to the prediction of weak wave turbulence…
The fluid dynamics video shows three-dimensional experimental and numerical investigations of open channel flows in microgravity. The dynamic reorientation of the free surface from 1g to 0g environment can be observed in a wedge-shaped channel for subcritical and for supercritical flow rate with a collapse of the interface. In addition three-dimensional computations determine important characteristics of the flow, such as the free surface shape, the velocity field, the dynamics of the reorientation and the flow rate depended collapse of the free surface. The good agreement validates the capabi…
The diffusion-driven growth of a foam ball is a phenomenon that appears in many manufacturing process as well as in a variety of geological phenomena. Usually these processes are greatly affected by gravity, as foam is much lighter than the surrounding liquid. However, the growth of the foam free of gravity effects is still very relevant, as it is connected to manufacturing in space and to the forma- tion of rocks in meteorites and other small celestial bodies. The aim of this research is to investigate experimentally the growth of a bubble cloud growing in a gas-supersaturated liquid in micro…
Ongoing development of fuel storage and delivery systems for space probes, interplanetary vehicles, satellites and orbital platforms continues to drive interest in propellant management systems that utilize surface tension to retain, channel and control flow in microgravity environments. Although it has been known for decades that capillary flows offer an ideal method of fuel management, there has been little research devoted to the general stability properties of such flows. In this work, we demonstrate theoretically why capillary flows which channel wetting liquids in slender open triangular…
The first large length-scale capillary rise experiments were conducted by R. Siegel using a drop tower at NASA LeRC shortly after the 1957 launch of Sputnik I. Siegel was curious if the wetting fluid would expel from the end of short capillary tubes in a low-gravity environment. He observed that although the fluid partially left the tubes, it was always pulled back by surface tension, which caused the fluid to remain pinned to the tubes' end. By exploiting tube geometry and fluid properties, we demonstrate that such capillary flows can in fact eject a variety of jets and drops. This fluid dyna…
The present study aims to investigate the motion of buoyant rings in vertical soap films. Thickness differences and related bi-dimensional densities are considered as the motor leading to bi-dimensional buoyancy. We show how this effect can be re-interpreted thanks to surface tension profiles in soap films. We propose a model involving surface tension profiles in order to describe the motion of buoyant particles in vertical soap films, and compare it to experimental data.
The bubble size distribution below a breaking wave is of paramount interest when quantifying mass exchanges between the atmosphere and oceans. Mass fluxes at the interface are driven by bubbles that are small compared to the Hinze scale $d_h$, the critical size below which bubbles are stable, even though individually these are negligible in volume. Combining experimental and numerical approaches, we report a power law scaling 3/2 of the diameter of small bubble size distribution, for sufficiently large separation of scales between the injection size and the Hinze scale. From an analysis of ind…
A multi-parametric transient numerical simulation of the start-up of a large diameter Pulsating Heat Pipe (PHP) specially designed for future experiments on the International Space Station (ISS) are compared to the results obtained during a parabolic flight campaign supported by the European Space Agency. Since the channel diameter is larger than the capillary limit in normal gravity, such a device behaves as a loop thermosyphon on ground and as a PHP in weightless conditions; therefore, the microgravity environment is mandatory for pulsating mode. Because of a short duration of microgravity d…
We investigate the interplay of thermophoretic force and interfacial tension on the capillary filling dynamics of a Newtonian nanofluid in a microchannel. In our model, we also consider an intricate thermofluidic coupling by taking the temperature dependence of viscosity aptly into account. This, in turn, determines the evolution of the viscous resistive force as the capillary front progresses, and presents an involved inter-connection between the driving thermophoretic force and the viscous resistive force. The two distinct regimes of particle transport in a fluid medium, delineated by partic…
The role of surface tension and wettability in the dynamics of air-liquid interfaces during immiscible fluid displacement flows in capillary tube driven by pressure has been investigated. The contact angle and capillary number drive the force wetting processes which is controlled by the balance between the capillary and the viscous lubrication forces. The dynamic wetting condition with the critical capillary number is studied analytically and validated experimentally, which demonstrates that the critical capillary number is associated with the contact angle, slip length and capillary radius.
High frequency thickness mode ultrasound is an energy-efficient way to atomize high-viscosity fluid at high flow rate into fine aerosol mists of micron-sized droplet distributions. However the complex physics of the atomization process is not well understood. It is found that with low power the droplet vibrates at low frequency (O[100 Hz]) when driven by high-frequency ultrasound (O[1 MHz] and above). To study the mechanism of the energy transfer that spans these vastly different timescales, we measure the droplet's interfacial response to 6.6~MHz ultrasound excitation using high-speed digital…
We calculate the average volumetric flux versus pressure drop of bubbles moving in a single capillary tube with varying diameter, finding a square-root relation from mapping the flow equations onto that of a driven overdamped pendulum. The calculation is based on a derivation of the equation of motion of a bubble train from considering the capillary forces and the entropy production associated with the viscous flow. We also calculate the configurational probability of the positions of the bubbles.
This is a computational study of gravity-driven fingering instabilities in unsaturated porous media. The governing equations and corresponding numerical scheme are based on the work of Nieber et al. [Ch. 23 in Soil Water Repellency, eds. C. J. Ritsema and L. W. Dekker, Elsevier, 2003] in which non-monotonic saturation profiles are obtained by supplementing the Richards equation with a non-equilibrium capillary pressure-saturation relationship, as well as including hysteretic effects. The first part of the study takes an extensive look at the sensitivity of the finger solutions to certain key p…
We propose a combined computational approach based on the multi-phase-field and the lattice Boltzmann method for the motion of solid particles under the action of capillary forces. The accuracy of the method is analyzed by comparison with the analytic solutions for the motion of two parallel plates of finite extension connected by a capillary bridge. The method is then used to investigate the dynamics of multiple spherical solid bodies connected via capillary bridges. The amount of liquid connecting the spheres is varied, and the influence of the resulting liquid-morphology on their dynamics i…
We present experiments to study the relaxation of a nano-scale cylindrical perturbation at one of the two interfaces of a thin viscous free-standing polymeric film. Driven by capillarity, the film flows and evolves towards equilibrium by first symmetrizing the perturbation between the two interfaces, and eventually broadening the perturbation. A full-Stokes hydrodynamic model is presented which accounts for both the vertical and lateral flows, and which highlights the symmetry in the system. The symmetrization time is found to depend on the membrane thickness, surface tension, and viscosity.
Capillary driven flow is a famous problem in fluid dynamics which dates back to Leonardo da Vinci. In this paper, we apply an analytic approximation method for highly nonlinear problem, namely the homotopy analysis method (HAM), to a model of the meniscus movement in a uniform vertical circular tube. Convergent explicit series solution is successfully obtained. Our results agree well with the numerical results given by the symbolic computing software Mathematica using six-order Runge-Kutta methods. More importantly, our analytic solution is valid in the whole region of physical parameters, and…
We observe capillary-driven binding between thin, equilateral triangular prisms at a flat air-water interface. The edge length of the equilateral triangle face is 120 $μm$, and the thickness of the prism is varied between 2 and 20 $μm$. For thickness to length (T/L) ratios of 1/10 or less, pairs of triangles preferentially bind in either a tip-to-tip or tip-to-midpoint edge configurations; for pairs of particles of thickness T/L = 1/5, the tip of one triangle binds to any position along the other triangle's edge. The distinct binding configurations for small T/L ratios result from physical bow…
Liquid-infused surfaces (LIS) are a promising technique for reducing friction, fouling and icing in both laminar and turbulent flows. Previous work has demonstrated that these surfaces are susceptible to shear-driven drainage. Here, we report a different failure mode using direct numerical simulations of a turbulent channel flow with liquid-infused longitudinal grooves. When the liquid-liquid surface tension is small and/or grooves are wide, we observe traveling-wave perturbations on the interface with amplitudes larger than the viscous sublayer of the turbulent flow. These capillary waves ind…
Using air to displace a viscous fluid contained in Hele-Shaw cell can create a fingering pattern at the interface between the fluids, if the capillary number exceeds a critical value. This Saffman-Taylor instability is revisited for the inverse case of a viscous fluid displacing air, when partially wettable hydrophilic particles are lying on the walls. Though the inverse case is otherwise stable, the presence of the particles results in a fingering instability at low capillary number. This capillary-driven instability is driven-by the integration of particles into the interface which results f…
We present an analytical and numerical study of the two-dimensional capillary-driven thin film equation. In particular, we focus on the intermediate asymptotics of its solutions. Linearising the equation enables us to derive the associated Green's function and therefore obtain a complete set of solutions. Moreover, we show that the rescaled solution for any summable initial profile uniformly converges in time towards a universal self-similar attractor that is precisely the rescaled Green's function. Finally, a numerical study on compact-support initial profiles enables us to conjecture the ext…
We investigate the behaviour of accelerating contact lines in an unsteady quasi-capillary channel flow. The configuration consists of a liquid column that moves along a vertical 2D channel, open to the atmosphere and driven by a controlled pressure head. Both advancing and receding contact lines were analyzed to test the validity of classic models for dynamic wetting and to study the flow field near the interface. The operating conditions are characterized by a large acceleration, thus dominated by inertia. The shape of the moving meniscus was retrieved using Laser-Induced Fluorescence (LIF)-b…
The theoretical and numerical models for gravity driven coating flow on upper cylinder and sphere are formulated. Using a perturbation method, the governing equations which depend on one Bond number $Bo$ are derived for a liquid film flow down the outside of a horizontal cylinder and a sphere. They can be simplified to one-dimensional form due to the symmetries. The general structure of the two-dimensional and axisymmetric capillary waves under high $Bo$ condition is focused on. An asymptotic theory is used to solve for the free-surface profiles in the outer and inner region, respectively. Eve…
The long-duration fluid physics experiments on a thermocapillary-driven flow have been carried out on the Japanese experiment module 'Kibo' aboard the International Space Station (ISS) since 2008. In these experiments, various aspects of thermocapillary convection in a half-zone (HZ) liquid bridge of high Prandtl number fluid have been examined under the advantages of the long-duration high-quality microgravity environment. This fluid dynamics video introduce a pinch off of liquid bridge of 30 mm in diameter as a part of the on-orbit experiments. The effect of thermocapillary-driven flow on th…
Thin viscous liquid films driven by capillarity are well described in the lubrication theory through the thin film equation. In this article, we present an analytical solution of this equation for a particular initial profile: a stepped perturbation. This initial condition allows a linearization of the problem making it amenable to Fourier analysis. The solution is obtained and characterized. As for a temperature step in the heat equation, self-similarity of the first kind of the full evolution is demonstrated and a long-term expression for the excess free energy is derived. In addition, hydro…
Remarkably, the interface of a fluid droplet will produce visible capillary waves when exposed to acoustic waves. For example, a small ($\sim\! 1 μ$L) sessile droplet will oscillate at a low $\sim\!10^2$~Hz frequency when weakly driven by acoustic waves at $\sim\!10^6$~Hz frequency and beyond. We measured such a droplet's interfacial response to 6.6~MHz ultrasound to gain insight into the energy transfer mechanism that spans these vastly different timescales, using high-speed microscopic digital transmission holography, a unique method to capture three-dimensional surface dynamics at nanometer…
The analysis of numerical simulations describing the collapse of capillary cavities reveals that the jets originated from the bursting of bubbles are driven by the condition that the dimensionless liquid flow rate per unit length directed towards the axis of symmetry, $q_\infty$, remains nearly constant in time. This observation, which is justified in physical terms because liquid inertia prevents appreciable changes in $q_\infty$ during the short time scale characterizing the jet ejection process, together with the fact that bubble bursting jets are produced from the bottom of a conical cavit…
The Washburn law has always played a critical role for ceramics. In the microscale, surface forces take over volume forces and the phenomenon of spontaneous infiltration in narrow interstices becomes of particular relevance. The Lattice Boltzmann method is applied in order to ascertain the role of surface reaction and subsequent deformation of a single capillary in 2D for the linear Washburn behavior. The proposed investigation is motivated by the problem of reactive infiltration of molten silicon into carbon preforms. This is a complex phenomenon arising from the interplay between fluid flow,…
The effects of elasticity on filament thinning and breakup are investigated in microchannel cross flow. When a viscous solution is stretched by an external immiscible fluid, a low 100 ppm polymer concentration strongly affects the breakup process, compared to the Newtonian case. Qualitatively, polymeric filaments show much slower evolution, and their morphology features multiple connected drops. Measurements of filament thickness show two main temporal regimes: flow- and capillary-driven. At early times both polymeric and Newtonian fluids are flow-driven, and filament thinning is exponential. …
One mechanism for airway closure in the lung is the surface-tension-driven instability of the mucus layer which lines the airway wall. We study the instability of an axisymmetric layer of viscoplastic Bingham liquid coating the interior of a rigid tube, which is a simple model for an airway that takes into account the yield stress of mucus. An evolution equation for the thickness of the liquid layer is derived using long-wave theory, from which we also derive a simpler thin-film evolution equation. In the thin-film case, we show that two branches of marginally-yielded static solutions of the e…
We study numerically the hydrodynamics of dip coating from a suspension and report a mechanism for colloidal assembly and pattern formation on smooth and uniform substrates. Below a critical withdrawal speed of the substrate, capillary forces required to deform the meniscus prevent colloidal particles from entering the coating film. Capillary forces are overcome by hydrodynamic drag only after a minimum number of particles organize in a close-packed formation within the meniscus. Once within the film, the formed assembly moves at nearly the withdrawal speed and rapidly separates from the next …
Rapid and sustained condensate droplet departure from a surface is key towards achieving high heat transfer rates in condensation, a physical process critical to a broad range of industrial and societal applications. Despite progress in enhancing condensation heat transfer through inducing its dropwise mode with hydrophobic materials, sophisticated surface engineering methods that can lead to further enhancement of heat transfer are still highly desirable. Here, by employing a three-dimensional, multiphase computational approach, we present an effective out-of-plane biphilic surface topography…
We demonstrate controlled material transport driven by temperature gradients in thin freely suspended smectic films. The films with submicrometer thicknesses and lateral extensions of several millimeters were studied in microgravity during suborbital rocket flights. In-plane temperature gradients cause two specific Marangoni effects, directed flow and convection patterns. At low gradients, practically thresholdless, flow transports material with a normal (negative) temperature coefficient of the surface tension, $dσ/dT<0$, from the hot to the cold film edge. That material accumulates at the co…
Capillary phenomena are involved in many industrial processes, especially those dealing with composite manufacturing. However, their modelling is still challenging. Therefore, a finite element setting is proposed to better investigate this complex issue. The variational formulation of a liquid-air Stokes system is established, while the solid substrate is described through boundary conditions. Expressing the weak form of Laplace's law over liquid-air, liquid-solid and air-solid interfaces, leads to a natural enforcement of the mechanical equilibrium over the wetting line, without imposing expl…
It is usually expected that surface tension driven flow dominates at small scales. Evaporation from the meniscus of ethanol/methanol confined in a capillary induces Marangoni convection at the meniscus which has been investigated by previous researchers. However, Marangoni convection is unexpectedly absent at an evaporating water meniscus confined inside a small micro-channel which is reported in this work. The velocity near the water meniscus is studied using confocal micro-PIV. The water meniscus is formed at the end of a micro-channel filled with water keeping the meniscus exposed to atmosp…
The migration of liquids in porous media, such as sand, has been commonly considered at high saturation levels with liquid pathways at pore dimensions. In this letter we reveal a low saturation regime observed in our experiments with droplets of extremely low volatility liquids deposited on sand. In this regime the liquid is mostly found within the grain surface roughness and in the capillary bridges formed at the contacts between the grains. The bridges act as variable-volume reservoirs and the flow is driven by the capillary pressure arising at the wetting front according to the roughness le…
We report on the capillary-driven levelling of a topographical perturbation at the surface of a free-standing liquid nanofilm. The width of a stepped surface profile is found to evolve as the square root of time. The hydrodynamic model is in excellent agreement with the experimental data. In addition to exhibiting an analogy with diffusive processes, this novel system serves as a precise nanoprobe for the rheology of liquids at interfaces in a configuration that avoids substrate effects.
