Liquid Surface Energy Research Articles

Preface to the HTC 2012 special issue

This special issue contains fully reviewed papers, emanating from presentations given at high temperature capillarity (HTC) 2012. HTC 2012 was the seventh conference in this series, following conferences held in Athens, Greece (2009); Alicante, Spain (2007); Sanremo, Italy (2004); Kurashiki, Japan (2000); Krakow, Poland (1997); and Smolenice, Slovakia (1994). High temperature capillarity 2012 followed the format of previous HTC conferences, based on a single-session conference focused on invited lectures, selected submitted oral presentations, and a poster session running the duration of the conference which allowed for extended discussions. Topics included the surface energy of liquids and solids, the thermodynamics of wetting versus the kinetics of spreading, adsorption and complexions, solid–liquid and solid–solid interface morphology and structure, dewetting, capillarity at solid interfaces, the role of interfaces in processing, and surface stresses. In general, HTC 2012 included a series of presentations aimed at bridging the gap between atomistic versus continuum approaches to interfaces, and their role in HTC phenomena. The sequence of manuscripts in this special issue opens with three review papers. The first covers the topic of wetting of ceramics by silicon alloys [1], the second discusses our current understanding of dissolutive wetting [2], and the third explores wetting and joining of high temperature materials based on diborides [3]. The section containing full manuscripts opens with a paper describing a new software tool for simulating interface morphology [4], followed by a series of papers on interface thermodynamics [5–12], and non-reactive and reactive wetting systems [13–26]. This is followed by a series of papers exploring the use of sessile drop experiments, reactive wetting, and applied joining and processing. The organizers (N. Frage, E. Rabkin and W. D. Kaplan) would like to thank the HTC Scientific Committee and the 2012 Advisory Committee for their input and assistance. Special thanks are extended to the Joining and Welding Research Institute of Osaka University for supporting student participation in HTC, and to MACAN (an EU funded FP7 project) for supporting invited speakers. BenGurion University of the Negev and the Technion–Israel Institute of Technology are kindly acknowledged for supporting the participation of local students.

Spinodal decomposition and droplets entrapment in monotectic solidification

In this article, we present two models to simulate solidification morphologies in monotectic alloys. With the first model, we investigate the morphological evolution under the influence of spinodal decomposition. The model requires that a gradient energy contribution for the concentration field should be incorporated, in order to stabilize phase separation when the liquid concentration is inside the region of miscibility gap. The free energy of the system in this model is derived from direct interpolation of the bulk energy densities. This, however, results in simulation regions in nanometer scale due to contributions from the chemical free energy of the system to the total surface excess. With the second model, our purpose is to develop a phase-field model to simulate scales that are larger than nanometer, where the departures from equilibrium are very small resulting in phase concentrations outside the spinodal region. In view of this, we exclude the concentration gradient contribution to the grand chemical potential functional, and develop a model based on [M. Plapp, Phys. Rev. E 84, 031601 (2011); A. Choudhury and B. Nestler, Phys. Rev. E 85, 021602 (2012)]. The advantage is that the free energy excess across the interface at equilibrium disappears, and hence it is easier to derive the required surface energies with higher interface widths. Due to this benefit, we employ the method to simulate the dynamic entrapment process in the monotectic reaction and study the influence of liquid(1) - liquid(2) surface energy and undercooling on the entrapment process.

A218 水噴流によるキャリーアンダーの発生機構に関する研究(OS8 高温ガス炉・高速炉・金属燃料)

Bubble carry-under into the water pool was examined. In experiments, a water jet from a nozzle of 5mm in diameter plunged into the water pool. The present experimental results showed that the water jet disintegrated into small drops on the way from the nozzle outlet to the pool surface when the flow rate of the water jet was small; the carry-under was observed. As flow rate of the water jet was increased, the surface of the water jet became smooth and no perturbation was observed; the carry-under was not observed in this situation. As the flow rate of the water jet was further increased, large waves came to appear on the water jet surface; the carry-under was observed again. From these observations, the criterion of the carry-under was obtained through energy balance: kinetic energy of liquid jet and surface energy of pool-surface.

Motion of liquid droplets on a superhydrophobic oleophobic surface

Developing a superhydrophobic oleophobic material is achieved by two criteria: low surface energy and properly designed surface morphology. The relationships among surface tensions, contact angles, contact angle hystereses, roll-off angles, and surface morphologies of such materials are studied. Numerical formulae related to the surface energy of liquids and solids are used to predict the wetting behavior of superhydrophobic and oleophobic materials. Using chemical and geometrical modifications, a superhydrophobic oleophobic surface was prepared. Good agreement between the predicted and measured contact angles and roll-off angles were obtained. The effect of the contact angle hysteresis on the roll-off angle is described to understand the motion of a droplet when the droplet begins to roll off.

A model of liquid film breakdown formed due to impingement of a two-phase jet on a horizontal surface

The present work aims to provide an explanation to the phenomenon of breakdown of the thin liquid film created by impinging two-phase, liquid–gas jet. Existing in the literature models describe merely the breakdown of single phase liquid films. The model presented here is based on examination of mass and energy equations under the applied criterion of the minimum of total energy. That allows to determine the minimum thickness of isothermal, thin liquid film created by impinging two-phase jet on a solid surface. The mechanical energy of the system consists of kinetic energy of liquid film and surface energy of all physical surfaces consisting for the control surface. An analytical expression for the minimum thickness of such liquid film is derived. The liquid film thickness at the breakdown is a function of the contact angle and shear stresses on the liquid–gas interface. Some comparisons with the experimental data are shown exhibiting a good performance of the postulated model.

The profile of a capillary liquid bridge between solid surfaces

Scanning force microscopy, such as atomic force microscopy (AFM) is complicated by the capillary force of a water meniscus formed in air between the probe tip and the sample. This small liquid bridge between the hydrophilic sample and the sharp AFM tip can be formed by capillary condensation from the vapor phase. We present an analytical model that describes the shape of the meniscus in which the pressure difference across the curved liquid air interface is taken into account. The analysis is based on a minimization of the liquid surface energy, together with the boundary condition of a given pressure drop across the surface as determined by the relative humidity of the vapor. The capillary forces that the wetting liquid exerts on the AFM tip are derived from the model. The resulting expressions can be used to describe arbitrary axial symmetric liquid air interfaces with nonzero total curvature, such as fluid bridges between two surfaces and droplets under a uniform force. The model illustrates some of the basic concepts of capillarity, such as surface tension forces and interfacial pressure drops.

Surface Energy and Wetting Behaviour of Plasma Etched Porous SiCOH Surfaces and Plasma Etch Residue Cleaning Solutions

The removal of plasma etch residues by wet cleaning is an alternative or additional process to plasma processes, which are known to degrade low-k and ultralow-k dielectric materials. Besides Cu/low-k compatibility wetting is an important issue for wet cleaning. Surface energy of solid and liquid is the key to understand the wetting behaviour. In this study we examined the energetic character of plasma etched/stripped solid surfaces, etch polymers and several cleaning solutions by contact angle measurements. The results show, that variations of the etching process can heavily change the energetic character of the solid. Calculating the surface energies of solid and liquid provides the possibility to make a prediction if a cleaning liquid will wet the surface which has to be cleaned.

Applications of a high temperature sessile drop device

The wettability of a liquid metal on a solid surface is of great technological interest for the industry (soldering, brazing, infiltration) as well as for fundamental research (diffusion, chemical reaction, intermetallic phases). The characterization of wetting is done by measuring the contact angle at the triple line of the liquid on the solid. A High Temperature Sessile Drop Device (HTSDD) was constructed and several applications were tested: (i) a wettability study of a copper-based brazing alloy (Cu-ABA®) on TiNx coatings with different stoichiometries. The data derived from the HTSDD show that the reduction of the nitrogen content in the TiN coating reduces the time for reaching the final contact angle. Also for substoichiometric TiC a similar behaviour is predicted in literature. (ii) The liquid surface energy of molten metals can be estimated from the curvature of flattened droplets due to the influence of gravity. Two models were used for the calculation of the liquid surface energy of different liquid metals. (iii) From the droplet radius vs. time curves it is possible to distinguish between two different reactive wetting regimes — the diffusion and the reaction controlled reactive wetting. The beginning of this research topic will be discussed.

Influence of gravity on narrow input forced drainage in 2D liquid foams

Liquid foam is a dense packing of gas bubbles in a small amount of liquid containing surfactants or other surface-active macromolecules, which is one of the highly organized materials and possesses hallmark rheological behaviour of soft matters. Forced foam drainage is the flow of constantly inputted liquid through the network of interstitial channels between bubbles under actions of gravity and capillarity. This process involves two mechanisms: minimal viscous flow dissipation of liquid and minimal surface energy of bubbles. For constant surfactant solution, viscous dissipation usually varies with gravity. This work reports simulations of 2D forced foam drainage with narrow input in a Hele-Shaw cell under 8 different gravities, g, ranging from 9.8 to 0 ms(-2). The spread of liquid both vertical due to gravity action, and horizontal due to capillary suction, is recorded over time. Positions of drainage wave fronts in both directions with time are found to be well described in the power law form, and the exponents are 0.536+5.29 x 10(-3)g and 0.479-7.27 x 10(-3)g, respectively, while the sum is close to a constant of 1.015 which is independent of gravity. For g=9.8 ms(-2), the calculated exponents are in good agreement with experimental results by Hutzler et al. and Wang.

Experimental determination of solid–liquid surface energy for Cd solid solution in Cd–Znliquid solutions

The equilibrated grain boundary groove shapes for the Cd solid solution in equilibrium withthe Cd–Zn liquid have been observed by rapid quenching. From the observed grain boundarygroove shapes, the Gibbs–Thomson coefficient and the solid–liquid surface energy for theCd solid solution in equilibrium with the Cd–Zn eutectic liquid have been determined to be(8.16 ± 0.65) × 10−8 K m and (121 ± 16) mJ m−2 with the numerical method and from the Gibbs–Thomson equation, respectively.The grain boundary energy for the same material has been calculated as(241 ± 30) mJ m−2 from the observed grain boundary groove shapes. The thermal conductivities of the solidand liquid phases for Cd–26.5% Zn and Cd–5% Zn alloys have also been measured.

Technologically significant capillary phenomena in high-temperature materials processing: Examples drawn from the aluminum industry

Examples of the impact of capillary phenomena on materials processing are drawn from the aluminum industry spanning aluminum smelting to recycling. The profound interaction of the oxides that form on molten aluminum is felt in many of the processes considered. Areas for improved understanding of wetting, spreading, infiltration, and Marangoni flow behavior are identified. Databases on liquid surface tension and solid surface energies need to be expanded to encompass commercial materials. Practical screening tests remain to be developed that provide realistic and scaleable rankings of interfacial behavior stemming from the interaction of complex solid microstructures and commercial aluminum alloys.

The percolation transition in filling a nanoporous body by a nonwetting liquid

The paper presents the results of an experimental study of the percolation transition in filling by nonwetting liquids of nanoporous bodies of various natures with different specific surface areas and mean pore and granule sizes. The liquid that we used was an aqueous solution of ethylene glycol. The hysteresis and non-outflow phenomena observed in this transition at various (known) surface energies of liquids were studied by varying the concentration of ethylene glycol. This helped us explain the mechanism of the percolation transition in filling nanoporous bodies with nonwetting liquids. It was shown that, to quantitatively describe the observed dependences in terms of percolation theory taking into account energy barriers to filling, we must use a non-scaling distribution function of clusters of accessible and filled pores that admits the formation of pore clusters of arbitrary dimensions.

A New Approach to Calculate Liquid-Vapor Surface Energy Using Sessile Droplet Test

In this work an applicable mathematical method is described in the analysis and description of the profile of the drop obtained in the sessile droplet test. The proposed method bases on the study of the differential geometry of surfaces and in the analysis of phenomena related with the creation, expansion and contraction of interfaces to calculate the surface tension of metals. Liquid vapor surface energy of tin and indium were calculated by using sessile droplet method. Tests were carried out at 280 and 350oC temperature over a titanium nitride substrate. Results showed a very good agreement between both methodologies. For example, Sn at 280oC presented a surface tension of 545 mN/m, which is closer to the value reported in the literature (550 mN/m).

Solid∕liquid two-phase structures in isolated nanometer-sized alloy particles

Solid∕liquid two-phase structures in isolated nanometer-sized alloy particles have been studied by transmission electron microscopy. The microstructure developed in the $\text{crystal}+\text{liquid}$ two-phase region was different between particles in the Au-Sn and Bi-Sn systems; namely, a core (crystal)-shell (liquid) structure appeared in the former system, whereas a simple two-phase structure with a planar interface separating the crystalline and liquid phases in the latter system. The reason for the difference between the two alloy systems is discussed in terms of the relative contributions of the surface energy of solid, the surface energy of liquid, and the inferface energy to the total Gibbs free energy of a particle.

Wetting of a liquid surface by another immiscible liquid in microgravity

The investigation of interfacial properties is essential to the development of new drugs either on earth or, particularly, in the absence of gravity. Under the reduced gravity conditions of parabolic flights, we have shown that, using an appropriate cell setup in order to control liquid surfaces, a liquid drop can be expanded onto and withdrawn from another immiscible liquid, which permits the measurement of the contact angle of this system. Surface energies of liquids being easily measurable, this technique allows a verification of numerous models used in interface science. During each parabola, 20 s of microgravity measurements permitted the acquisition of video pictures of these drops. Contact angles have been obtained from goniometric analysis of the recorded images. Generally, the drops obtained satisfied the equilibrium state predicted by Neumann's equations. However, unexpected long lasting metastable drops have also been observed on a curved unconfined liquid surface. The existence of a drop-sinking barrier, larger for a curved liquid surface, is proposed to explain this observation.

The effect of Sn additions on the semi-solid microstructure of an Al–7Si–0.3Mg alloy

The influence of Sn additions on both the binary Al–Si equilibrium phase diagram and the microstructural evolution of an Al7Si0.3Mg alloy (A356) having a solid/liquid ratio close to 0.5 were studied. Application of the THERMOCALC method showed that in the range 0.2–10.0 wt.%, Sn decreases all the L→S transformation temperatures. The microstructural evolution was studied by scanning electron microscopy (SEM), transmission electron microscopy (TEM) and by quantitative optical microscopy. Results showed that Sn additions decreased the rate of attainment of the equilibrium liquid fraction besides reducing the kinetics of particle spheroidisation and growth. This behaviour was attributed to a decrease of solid–liquid surface energy brought about by the presence of Sn as small globules within the Si or Al phases and at the Al–Si interface. This interpretation was supported by experimental measurements of particle contiguity and by dihedral angle calculations. The less accentuated effect observed on sample 2.0Sn, was explained by a different spatial distribution of the Sn globules.

Thermalfluctuations of thin liquid films

A surprising lowering of the surface energy of liquid surfaces wasrecently found in x-ray scattering experiments which enhancesthermal fluctuations of fluid interfaces at microscopic scales andcalls for a re-examination of small-scale interfacial processes.This reduction was predicted for microscopic undulations below a fewnm by density functional theory taking into account the long-rangeattraction of molecular interaction potentials. Here, aself-consistent theory is proposed for the fluctuation of fluidinterfaces in arbitrary potentials which can significantly alterthermodynamical and structural properties of liquid drops, thinfilms, or membranes near a substrate. The substrate-inducedhindrance of thermally excited capillary waves increasesconsiderably the thickness of thin liquid films, which cannot beneglected in the analysis of adsorption data. An explicitexpression for adsorption isotherms is given depending ontemperature, Hamaker constant A, and surface tension γwhich takes into account the influence of capillary waves on thethickness of the fluid film and removes reported discrepancies withthe Lifshitz theory of van der Waals forces. Also the stericrepulsion potential of a membrane at distance D from a hard wallcan be calculated self-consistently in excellent agreement withMonte Carlo simulations.

Method to estimate crystal/liquid surface energy by dissolution of subcritical nuclei

Within the framework of the classical nucleation theory (CNT) the nucleus–liquid surface energy ( σ) is one of the most important parameters to predict or analyze nucleation kinetics in undercooled liquids. However, the few methods proposed to determine σ are based on the direct use of nucleation rate data and, thus, do not allow an independent test of the theory. In the present paper, this parameter is estimated without direct use of nucleation rate data. Instead, we provide further experimental evidence for the dissolution of sub-critical nuclei at several development temperatures and use this effect to estimate the nucleus–liquid surface energy. The results of the present analysis demonstrate that, in agreement with a new approach for the description of nucleation processes, not only the surface energy but also the driving force for nucleation have quite different values from those of the evolving macrophases. The possible implications of this result for the understanding of crystal nucleation in liquids are discussed.

Solid–liquid surface energy of pivalic acid

The Gibbs–Thomson coefficient and the solid–liquid surface energy for pivalic acid have been measured by a direct method. The grain boundary energy of the pivalic acid also has been calculated from the observed grain boundary groove shapes.

Crystal–liquid surface energies from transient nucleation

A new method for the determination of the crystal–liquid surface energy, σ, from transient nucleation data is described and applied to lithium disilicate glasses (LS 2). The method is based upon the use of experimentally determined induction times, nucleation rates and free energy data in conjunction with the Shneidman expression for transient nucleation. Assuming homogeneous nucleation in LS 2, surface energies are obtained directly from this analysis using data from single-stage nucleation experiments. In order to extend the applicable temperature range for this method, two-stage nucleation data are also used. Results indicate an apparent positive temperature coefficient of σ. Values of surface energies are used to calculate nucleation rates, which are compared with measurements.