Liquid Wedge Research Articles

Coalescence-induced propulsion of droplets on a superhydrophilic wire

Droplet transport on a cylindrical wire has applications in numerous fields such as fog collection, mist elimination, filtration, and oil/water separation. This work reports a droplet transport phenomenon on a superhydrophilic wire that shows a transient velocity powered not by the gradient of substrate geometry or wettability but primarily by the surface-to-kinetic energy transition that occurs along the axial direction upon coalescence. The transition efficiency is mainly limited by the viscous friction at the local liquid wedge, a relationship that a modified Ohnesorge number can capture.

Controllable droplet self-transport on multi-bioinspired slippery liquid-infused microstructure surface

Inspired by Nepenthes pitcher plant, the surface infused by slippery liquid could significantly reduce the adhesive force and facilitate the movement of droplet. Combined with the gradient structure of cactus spine, the slippery liquid-infused microstructure surfaces (SLIMS) could achieve the droplet self-transport without external energy input. However, combined with experimental findings on the SLIMS with uniformly rough structure, the self-transport distance is still limited by the wedge angle and droplet volume. Although the transport distance can be improved by reducing the wedge angle and increasing the droplet volume, we have demonstrated the control of transport distance by processing different structures on the surface. Benefited from the directional wettability of the V-shaped prism microarray (VPM) surface, the self-transport distance could be controlled in the case of fixed liquid volume and wedge angle. A fraction of the lubricating oil would be squeeze away when the droplet with larger density was dropped on the surface, which can form local contact between droplet and VPM structure. This would result in the imbalance Laplace pressure along the movement direction, which can be further manipulated by the VPM structure. The multi-bioinspired surface provides a new insight for precise liquid manipulation, which could promote liquid directional transport developments in theoretical analysis and further practical applications.

A criterion for the pinning and depinning of an advancing contact line on a cold substrate

The influence of solidification on the spreading of liquids is addressed in the situation of an advancing liquid wedge on a cold substrate at $T_p < T_f$, of infinite thermal conductivity, where $T_f$ is the melting temperature. We propose a model derived from lubrication theory of contact-line dynamics, where an equilibrium between capillary pressure and viscous stress is at play, adapted here for the geometry of a quadruple line where the vapour, liquid, solidified liquid and basal substrate meet. The Stefan thermal problem is solved in an intermediate region between molecular and mesoscopic scales, allowing to predict the shape of the solidified liquid surface. The apparent contact angle versus advancing velocity $U$ exhibits a minimal value, which is set as the transition from continuous advancing to pinning. We postulate that this transition corresponds to the experimentally observed critical velocity, dependent on undercooling temperature $T_f-T_p$, below which the liquid is pinned and advances with stick-slip dynamics. The analytical solution of the model shows a qualitatively fair agreement with experimental data. We discuss on the way to get better quantitative agreement, which in particular can be obtained when the mesoscopic cut-off length is made temperature-dependent.

An accurate inner diameter measurement.

The inaccurate deflection behavior of the probing system degrades the performance of the diameter-measuring machines. In this experiment, the probing is improved, applying an autocollimator and an angular positioning datum. We have devised this datum using a liquid wedge. A ring gauge is chosen as a workpiece to evaluate the deflection behavior of the probing system. The improved uncertainty of the probing is found as low as 40 nm. Subsequently, the inner diameter of the ring gauge is measured on this experimental setup. By employing a simulation, we aligned the workpiece. The deflections of the stylus are optimized to achieve zero deflection error at the zenith points. Consequently, the swing of the probe at the zenith points is combined with the rectilinear displacement of the workpiece to estimate the inner diameter. The uncertainty of the measurement of the ring gauge is improved up to 140 nm.

A theoretical model of thermo-dynamic interpretation for the Pettit effect and associated heat transport processes

Based on several fundamental preassumptions, a one-dimensional convection-diffusion equation for heat transport inside liquid wedges causing the Pettit effect is proposed. With a hot or cold thermode placed at the middle of the liquid wedge, the average temperature of the liquid wedge determined from the convection-diffusion equation proposed shows a maximum, which corresponds to a particular liquid flow rate. The state achieved at this maximum temperature is believed to be the most stable for its minimum interfacial energy. The theory suggests a thermodynamic mechanism, which drives the liquid to flow in directions corresponding to those observed in experiments. It is believed that this work improves the thermodynamic interpretation proposed previously since the new-form convection-diffusion equation is more rigorously deduced and is thus more accurate. In addition, the work also presents a detailed theoretical analysis for heat transport. The results show that, in practical situations, the manifested heat-transport behaviors of a liquid wedge are governed by conductive heat transfer because convective heat flow is self-balancing due to the restriction by the law of mass conservation. Meanwhile, based on the asymmetric features of the conductive heat flows transiting within two different halves of the liquid wedge, a closed-loop formed by connecting a hot-thermode-driven liquid wedge and a cold-thermode-driven liquid wedge is proposed such that a hot thermode-cold thermode loop can lead to controllable heat transfer with which targeted heating or cooling may be realized. The effect may reveal the technical principles upon which novel small-size thermal engines, pumps, heaters, and coolers can be built.

Stabilisation of a laser beam with a liquid filled wedge with variable angle

The paper studies the properties of a liquid-filled prism with variable angle for laser beam stabilisation in space. The liquid wedge deflection method is intended for stabilizing the HeNe laser used in interferometers designed to measure displacement. This paper presents a test of the system, experimental verification, and estimation of accuracy. The assumption was made that the displacement range is 10−5 rad, and the resolution is 10-7 rad. Liquids with different properties were tested. The possible control frequencies were checked. Compensation under the natural conditions of laser operation has been shown.

Rotational diffusion of partially wetted colloids at fluid interfaces

HypothesisRotational Brownian diffusions of colloidal particles at a fluid interface play important roles in particle self-assembly and in surface microrheology. Recent experiments on translational Brownian motion of spherical particles at the air-water interface show a significant slowing down of the translational diffusion with respect to the hydrodynamic predictions (Boniello et al., 2015). For the rotational diffusions of partially wetted colloids, slowing down of the particle dynamics can be also expected. ExperimentsHere, the rotational dynamics of Janus colloids at the air-water interface have been experimentally investigated using optical microscopy. Bright field and fluorescent microscopies have been used to measure the in-plane and out-of-plane particle rotational diffusions exploiting the Janus geometry of the colloids we fabricated. FindingsOur results show a severe slowing down of the rotational diffusion Dr,⊥ connected to the contact line motion and wetting-dewetting dynamics occurring on particle regions located at opposite liquid wedges. A slowing down of the particle rotational diffusion about an axis parallel to the interfacial normal Dr,|| was also observed. Contact line fluctuations due to partial wetting dynamics lead to a rotational line friction that we have modelled in order to describe our results.

Thin wedge evaporation/condensation controlled by the vapor dynamics in the atmosphere.

Evaporation or condensation in the vicinity of the immobile (pinned) contact line in an atmosphere of some inert (noncondensable) gas is considered here in a partial wetting configuration. Such a problem is relevant to many situations, in particular to a drop or a liquid film drying in open air. The thermal effects are not important and the mass exchange rate is controlled by the vapor dynamics in the gas. By following previous works, we account for the weak coupling between the diffusion in the gas and flow in the liquid through the Kelvin effect. Such a problem is nonlocal because of the diffusion in the gas. For generality, we consider a geometry of a liquid wedge posed on a flat and homogeneous substrate surrounded by a gas phase with a diffusion boundary layer of uniform thickness [Formula: see text]. Similarly to the moving contact line problem, the phase change leads to the hydrodynamic contact line singularity. The asymptotic analysis of this problem is carried out for the liquid wedge of the length [Formula: see text]. Three asymptotic regions are identified: the microscopic one (in which the singularity is relaxed, in the present case with the Kelvin effect) and two intermediate regions. The Kelvin effect alone turns to be sufficient to relax the singularity. The scaling laws for the interface slope and mass evaporation/condensation flux in each region are discussed. It is found that the difference of the apparent contact angle (i.e., interface slope in the second intermediate region) and the equilibrium contact angle is inversely proportional to the square root of [Formula: see text] and square root of the microscopic length, whatever is the singularity relaxation mechanism.

Tunable angular shearing interferometer based on wedged liquid crystal cells.

The concept of a liquid crystal wedge as a tunable angular shearing interferometer is introduced and demonstrated to combine both high stability and high tunability. Different wedges are fabricated from planar aligned nematic liquid crystal cells with thickness gradients. These wedges are shown to produce stable interferograms from the polarization interference between the ordinary and extraordinary waves propagating in different directions at the output of the cell. The fringe periods, ranging from 70μm to 1.25mm, can be precisely controlled by a low voltage. Despite the wedge-shaped structure, no inhomogeneity has been detected when the wedge is driven adiabatically and the interferograms are uniform over regions as large as 5×5 mm. Moreover, dynamical measurements show that the wedges behave as a succession of multiple cells with different thickness, giving rise to a moving front of stabilizing fringes when driven dynamically. All the observations show that the device is suitable for large beam size and tunable shearing interferometry, with attractive features for applications such as phase sensing, photoalignment or photolithography.

Numerical and experimental investigation of oblique shock wave reflection off a water wedge

Shock wave interaction with solid wedges has been an area of much research in past decades, but so far very few results have been obtained for shock wave reflection off liquid wedges. In this study, numerical simulations are performed using the inviscid Euler equations and the stiffened gas equation of state to study the transition angles, reflection patterns and triple point trajectory angles of shock reflection off solid and water wedges. Experiments using an inclined shock tube are also performed and schlieren photography results are compared to simulations. Results show that the transition angles for the water wedge cases are within 5.3 % and 9.2 %, for simulations and experiments respectively, compared to results obtained with the theoretical detachment criterion for solid surfaces. Triple point trajectory angles are measured and compared with analytic solutions, agreement within $1.3^{\circ }$ is shown for the water wedge cases. The transmitted wave in the water observed in the simulation is quantitatively studied, and two different scenarios are found. For low incident shock Mach numbers, $M_{s}=1.2$ and 2, no shock wave is formed in the water but a precursor wave is induced ahead of the incident shock wave and passes the information from the water back into the air. For high incident shock Mach numbers, $M_{s}=3$ and 4, precursor waves no longer appear but instead a shock wave is formed in the water and attached to the Mach stem at every instant. The temperature field in the water is measured in the simulation. For strong incident shock waves, e.g. $M_{s}=4$, the temperature increment in the water is up to 7.3 K.

Numerical simulation of liquid jet impact on a rigid wall

Basic points of a numerical technique for computing high-speed liquid jet impact on a rigid wall are presented. In the technique the flows of the liquid and the surrounding gas are governed by the equations of gas dynamics in the density, velocity, and pressure, which are integrated by the CIP-CUP method on dynamically adaptive grids without explicitly tracking the gas-liquid interface. The efficiency of the technique is demonstrated by the results of computing the problems of impact of the liquid cone and the liquid wedge on a wall in the mode with the shockwave touching the wall by its edge. Numerical solutions of these problems are compared with the analytical solution of the problem of impact of the plane liquid flow on a wall. Applicability of the technique to the problems of the high-speed liquid jet impact on a wall is illustrated by the results of computing a problem of impact of a cylindrical liquid jet with the hemispherical end on a wall covered by a layer of the same liquid.

Prediction of static contact angles on the basis of molecular forces and adsorption data.

At a three-phase contact line, a liquid bulk phase is in contact with and coexists with a very thin layer of adsorbed molecules. This adsorbed film in the immediate vicinity of a liquid wedge modifies the balance of forces between the liquid and solid phases such that, when included in the balance of forces, a quantitative relationship emerges between the adsorbed film thickness and the static contact angle. This relationship permits the prediction of static contact angles from molecular forces and equilibrium adsorption data by means of quantities that are physically meaningful and measurable. For n-alkanes on polytetrafluoroethylene, for which there are experimental data available on adsorption and contact angles, our computations show remarkable agreement with the data. The results obtained are an improvement on previously published calculations-particularly for alkanes with a low number of carbon atoms, for which adsorption is significant.

Experimental Phenomena and Exploratory Theoretical Driving Mechanisms for Directional Flows Occurring in λ-Type Heated/Cooled thin Liquid Wedges Confined Between Fluidic Interfaces

The work reports some new experimental and theoretical results regarding the abnormal behaviors of liquid flows taking place in a thin liquid wedge situated under an as symmetric temperature gradient. These experimental results, obtained using particle image velocimetry (PIV) technique, are additional to those having been reported previously by the same research group. More specifically, a tangential directional flow can be induced when a sufficiently thin liquid wedge confined in two fluidic interfaces is heated or cooled at a point. The flows caused by point heating are in direction toward the thinner region of the liquid wedge whereas those caused by point cooling flow in the opposite direction, toward the thicker region. In theory, these flows are here interpreted as driven by thermodynamic mechanisms rather than by usual thermo-capillary effects. Theoretical results show that the presence of the flow is necessary for such a point-heated/cooled liquid wedge to evolve toward the minimum of interfacial energy. Under the free-force boundary conditions, the flow velocity predicted in theory is in good agreement with the experimental data in direction, scale of order, and variation behaviors with changing experimental conditions.

Cratering of a solid body due to liquid impact

An impact between a high-speed liquid and a solid body leading to cratering during the impact is considered. The problem formulation is presented within the framework of a self-similar velocity potential flow for a liquid wedge impacting the solid wall. A linear constitutive relation is adopted, which links the speed of cratering with the pressure and shear stresses. The solution procedure is based on the integral hodograph method. It converts the boundary-value problem for the complex potential in the fluid domain into a system of integral equations which are solved using the method of successive approximations. The obtained solution is used to investigate the cratering mechanics during the impact. The results are presented in terms of the interface shape, the free surface shape, streamline patterns and pressure distribution along the interface.

Liquid impact on a permeable solid body

The free surface flow and the hydrodynamic loads generated by impact between a liquid wedge and a permeable solid body are investigated. The study is carried out within the framework of self-similar solution, which is realistic for this kind of configuration and over the short period of impact. We study the effect of liquid penetration through the porous/perforated solid surface on the pressure distribution and flow pattern. An integral hodograph method is employed to convert the differential equation in the fluid domain into integral equations along the axes of a parameter plane, from which the problem corresponding to the impermeable solid surface is a special case. The system of integral equations are solved numerically using the method of successive approximations. Results are presented for streamline patterns and pressure distribution along the solid surface of permeable wedges.

Displacement flows under elastic membranes. Part 2. Analysis of interfacial effects

We investigate the injection of inviscid gas into the narrow liquid-filled gap between a rigid base plate and an overlying elastic sheet. After an early-time transient in which the gas deflects the sheet into a large blister, the viscous liquid displaced by the expanding bubble starts to accumulate in a wedge which advances as the elastic sheet peels away from the base. We analyse theoretically the subsequent interaction between viscous forces, elastic (bending or tension) forces and capillary forces. Asymptotic expressions are derived for the speed of spreading of the bubble, which reveal that the effect of the capillary pressure drop at the bubble tip is to suck down the sheet over the liquid wedge and thereby reduce the speed. We show that the system passes through three different asymptotic regimes in sequence. At early times, capillary effects are weak and hence the spreading of the bubble is controlled dominantly by the viscous-peeling process at the wedge tip. The capillary forces grow in importance with time, and at late times they dominate viscous effects and balance with elastic forces, leading to quasi-static spreading. Finally, at very late times, the capillary suction generates a narrow bottleneck at the wedge tip, which pushes a large ridge of liquid ahead of it. These results hold in the framework of standard lubrication theory as well as with an improved lubrication model, which takes into account films of wetting liquid deposited behind the advancing bubble tip. The predictions of the model are shown to be in excellent agreement with the Navier–Stokes simulations and experimental results from Part 1 of this work.

Can hydrodynamic contact line paradox be solved by evaporation–condensation?

We investigate a possibility to regularize the hydrodynamic contact line singularity in the configuration of partial wetting (liquid wedge on a solid substrate) via evaporation–condensation, when an inert gas is present in the atmosphere above the liquid. The no-slip condition is imposed at the solid–liquid interface and the system is assumed to be isothermal. The mass exchange dynamics is controlled by vapor diffusion in the inert gas and interfacial kinetic resistance. The coupling between the liquid meniscus curvature and mass exchange is provided by the Kelvin effect. The atmosphere is saturated and the substrate moves at a steady velocity with respect to the liquid wedge. A multi-scale analysis is performed. The liquid dynamics description in the phase-change-controlled microregion and visco-capillary intermediate region is based on the lubrication equations. The vapor diffusion is considered in the gas phase. It is shown that from the mathematical point of view, the phase exchange relieves the contact line singularity. The liquid mass is conserved: evaporation existing on a part of the meniscus and condensation occurring over another part compensate exactly each other. However, numerical estimations carried out for three common fluids (ethanol, water and glycerol) at the ambient conditions show that the characteristic length scales are tiny.

Effects of nanoparticle behaviors and interfacial characteristics on subcooled nucleate pool boiling over microwire

The flow and heat transfer characteristics of nanofluid were attracting many researchers during the last two decades. Convection heat transfer in it is especially important for its potential applications. Therefore, it is crucial to study the nanoparticle behaviors near the near wall region and the interfacial property, which are dominant in nanofluid convection heat transfer. In this investigation, stable nanofluid was prepared with alumina nanoparticles (30nm in diameter) and deionized water. The nanoparticle behaviors near the liquid wedge of bubbles were observed by high-speed CCD camera. The effects of nanoparticle behaviors in this region and the interfacial characteristics at the liquid–vapor interface on convection of nanofluid were experimentally investigated. Flocculent nanoparticle clustering was observed swirling near the liquid wedge, when the heat flux is relatively small. The microscopic morphology of the nanoparticle deposition layer at the heated surface was characterized by SEM images. It seems that the deposition layers could modify the morphology, but it also delays the detachment of small bubbles from the heated surface. While n-butanol was included as surfactant which will change the liquid/vapor interfacial property, it intensifies the nanoparticle deposition for low heat flux conditions. The analysis shows that the critical heat flux of nanofluid can be obviously improved when n-butanol was included in the nanofluid. It also shows that the inhibited bubble growth and enhanced nanoparticle clustering in the liquid wedge region are the main reason for the heat transfer deterioration when increasing the amount of surfactant in nanofluid. A comparative experiment indicates that the effect of surfactant on convection heat transfer is greater than the unstable deposition formed by nanoparticles.

Moffatt vortices induced by the motion of a contact line

AbstractA recent hydrodynamic theory of liquid slippage on a solid substrate (Kirkinis &amp; Davis, Phys. Rev. Lett., vol. 110, 2013, 234503) gives rise to a sequence of eddies (Moffatt vortices) that co-move with a moving contact line (CL) in a liquid wedge. The presence of these vortices is established through secular equations that depend on the dynamic contact angle $\alpha $ and capillary number Ca. The limiting case $\alpha \rightarrow 0$ is associated with the appearance of such vortices in a channel. The vortices are generated by the relative motion of the interfaces, which in turn is due to the motion of the CL. This effect has yet to be observed in experiment.

Step index fibre using laser interferometer

A model is suggested to describe the fringe shift which occurs due to the phase variations of cladded glass fibre introduced between the two plates of the liquid wedge interferometer illuminated with a He–Ne laser. The fringe shift of the phase object which appears in the denominator of the Airy distribution formula of the multiple beam interference is represented in the harmonic term. An experiment is conducted using liquid wedge interferometer where the step index glass fibre of a nearly quadratic thickness variation is introduced between the two plates of the interferometer. The obtained fringe shift shows a good agreement with the proposed quadratic model. The Matlab code is written to plot the interferometer fringes comprising the shift of the step index fibre. Secondly, recognition of elliptical fibres is outlined using tomographic imaging. Finally, results and concluding remarks are given.