Triple Line Motion Research Articles

Reactive pressure infiltration of Cu-46at.pct. Si into carbon

We explore how reaction at the interface between a solid porous ceramic and an infiltrating molten metal influences wetting in pressure infiltration, wetting being characterized by a drainage curve that plots the metal saturation versus the applied metal pressure. Specifically, we infiltrate Cu-46at.pct. Si into graphite preforms at 1050 °C, 1100 °C, 1150 °C or 1200 °C. The Si in the copper alloy reacts with the graphite to form SiC, which is better wetted by the alloy compared to the initial graphite. We show that, unlike what is observed in non-reactive systems, at fixed applied pressure reaction prevents stabilization of the metal saturation and causes the metal to continuously flow into the preform. Interpreting the data under the assumption that the applied pressure influences the local rate of thermally activated triple line motion as does the applied stress the rate of thermally activated motion of dislocations, measured infiltration velocities can be exploited to deduce both an activation volume and an activation energy for the interfacial process that governs reaction-driven motion of the triple line in this system. The resulting activation volume is on the order of one to a few 100 nm3, leading to estimated activation energy values of a few times 100 kJmol. Both are realistic for a process that is limited by the rate of SiC growth along the metal/graphite interface.

The role of surface energy in heterogeneous bubble growth on ideal surface

An analytical model for heterogeneous bubble growth during nucleate boiling with variable wettability on an ideal smooth surface has been developed. We analyzed the growth of bubbles in terms of the motion of the triple line, and three stages of bubble growth were identified based on the triple line motion. The transition points between these stages were modelled using a free-energy analysis and force-balance of the bubble growth system. We considered two bubble-growth pathways: one with a constant angle between the liquid–vapor interface and the surface, and one with a constant base (i.e., constant triple line), and the two paths are linked during a bubble growth. It is hypothesized that the transition from a regime to another is linked to the less expansive energy path. To confirm this, a bubble growth was experimentally observed on various different wettability surfaces, and the results of these experiments were compared with the analytical model. In general, a larger contact angle (i.e., a more hydrophobic surface) resulted in bubble growth with a larger triple line, and hence a larger base diameter and a larger departing bubble diameter.

(In)compressibility and parameter identification in phase field models for capillary flows

Phase field (diffuse interface) models accommodate diffusive triple line motion with variable contact angle, thus allowing for the no-slip boundary condition without the stress singularities. We consider two commonly used classes of phase field models: the compositionally compressible (CC) model with compressibility limited to the fluid mix within the diffuse interface, and the incompressible (IC) model. First, we show that the CC model applied to fluids with dissimilar mass densities exhibits the computational instability leading to the breakup of the triple line. We provide a qualitative physical explanation of this instability and argue that the compositional compressibility within the diffuse interface is inconsistent with the global incompressible flow. Second, we derive the IC model as a systematic approximation to the CC model, based on a suitable choice of continuum velocity field. Third, we benchmark the IC model against sharp interface theory and experimental kinetics. The triple line kinetics is well represented by the triple line mobility parameter. Finally, we investigate the effects of the bulk phase field diffusional mobility parameter on the kinetics of the wetting process and find that within a wide range of magnitudes the bulk mobility does not affect the flow.

The spreading simulation of molten Al alloy on Q235 steel in the first cycle of cold metal transfer process

The volume of fluid and the solidification-melting models were used for the study of the wetting of Q235 steel by molten Al alloy in the first cycle of cold metal transfer process. Together with the consideration of the welding temperature field and the solidification process, the effect of welding temperature field (corresponding to the different wire feed speeds) on solidification, final wettability, and wetting behavior were discussed, respectively. The results showed that the molten Al alloy primarily began to solidify at the triple line, which is consistent with the distribution of temperature field; partial solidified metal blocked the motion of triple line to a certain extent; good wettability of Q235 steel plate by molten Al alloy can be observed with the increase of wire feed speed, and the advance of triple line was controlled by capillary force.

Wetting of carbide ceramics (B4C, SiC, TiC and ZrC) by molten Ni at 1753 K

Wetting of carbide ceramics (B4C, SiC, TiC and ZrC) by molten Ni was investigated by using an improved sessile drop method at 1753 K. Due to the partial metallic bonds in metallic ceramics (TiC and ZrC), the intrinsic wettability of them is better than the predominantly covalent ceramics (B4C and SiC). The smaller density of solid causes that the dissolution is more incline to the vertical direction, which also causes limited improvement of wettability. The final wettability for specific systems (Ni/carbide ceramic systems) is related to the dissolved solute from substrate, the recrystallized phases and the characteristics of interfacial structures. The spreading dynamics for the dissolutive wetting can be described by molecular dynamic model, and then the main energy barrier for the triple line motion may come from the dissolution.

High-precision drop shape analysis (HPDSA) of quasistatic contact angles on silanized silicon wafers with different surface topographies during inclining-plate measurements: Influence of the surface roughness on the contact line dynamics

Contact angles and wetting of solid surfaces are strongly influenced by the physical and chemical properties of the surfaces. These influence quantities are difficult to distinguish from each other if contact angle measurements are performed by measuring only the advancing θa and the receding θr contact angle. In this regard, time-dependent water contact angles are measured on two hydrophobic modified silicon wafers with different physical surface topographies. The first surface is nearly atomically flat while the second surface is patterned (alternating flat and nanoscale rough patterns) which is synthesized by a photolithography and etching procedure. The different surface topographies are characterized with atomic force microscopy (AFM), Fourier transform infrared reflection absorption spectroscopy (FTIRRAS) and Fourier transform infrared attenuated total reflection spectroscopy (FTIR-ATR). The resulting set of contact angle data obtained by the high-precision drop shape analysis approach is further analyzed by a Gompertzian fitting procedure and a statistical counting procedure in dependence on the triple line velocity. The Gompertzian fit is used to analyze overall properties of the surface and dependencies between the motion on the front and the back edge of the droplets. The statistical counting procedure results in the calculation of expectation values E(p) and standard deviations σ(p) for the inclination angle φ, contact angle θ, triple line velocity vel and the covered distance of the triple line dis relative to the first boundary points XB,10. Therefore, sessile drops during the inclination of the sample surface are video recorded and different specific contact angle events in dependence on the acceleration/deceleration of the triple line motion are analyzed. This procedure results in characteristically density distributions in dependence on the surface properties. The used procedures lead to the possibility to investigate influences on contact angles more in detail.

Nano/microstructured polyhedral oligomeric silsesquioxanes-based hybrid copolymers: Morphology evolution and surface characterization

Unique “micro-bean sprouts” with “nano-tails” were electrohydrodynamically prepared from poly[(propylmethacryl-heptaisobutyl-polyhedral oligomeric silsesquioxane)-co-(methylmethacrylate)] (POSS-MMA). The nano/microstructured POSS-MMA substrates reveal superhydrophobic nature, with contact angles >160°. Contact angle versus time plots show that water droplet evaporation from the substrates with “micro-bean sprouts” falls into two stages: the initial stage, marked by steadily decreasing contact angles and the later stage, marked by rapidly decreasing contact angles. The turning point differentiating these two stages occurs at ∼120°–130°. The substrates consisting of “micro-bean sprouts” with larger “heads” experience pinned triple-line phase during the early stage of droplet evaporation. In contrast, the triple line for a droplet placed on “micro-bean sprouts” with smaller “heads” can move easily, leading to a rapid decrease in contact diameter. Meanwhile, the contact angle decreases only slightly during the rapidly moving triple-line phase. The contact angles of the fibrous substrates measured during the initial stage of water droplet evaporation are much lower than those of “micro-bean sprouts”, even though the time period of the initial stage is extended. Both the architectures and the sizes of these POSS-MMA nano/microstructures were shown to affect the energy barrier for the triple-line motion during water droplet evaporation and therefore the contact angle hysteresis.

The effect of evaporation kinetics on nanoparticle structuring within contact line deposits of volatile drops

This paper deals with the evaporation behaviour of nano-suspensions. An investigation of the relationship between reduced environmental pressure and the ring-stain formation mechanism is presented. Monodisperse, nanosuspension sessile drops formed a variety of patterns, at the macro-scale, consisting of sets of rings, concentric rings and irregularly distributed stains. “Stick-slip” motion of the triple line (TL), constantly pinned TL and very rapid evolution of the evaporation were the reasons for each of the observed patterns respectively. At the particle level (nano-scale), the promotion of close-packed, hexagonal particle structures was observed as a result of the enhanced evaporation rate and hence increased particle velocity. Beyond an optimal/critical pressure, a combination of further enhanced particle velocity with very limited space (for particles to find their most thermodynamically favourable positions) led to the formation of a disordered region at the exterior region and, as expected, to more defects. Lastly, inside the rings, particles formed random groups of particle aggregates, resembling branches, following TL motion during the “slip” phase. On the other hand, particle structures resembling ripples formed on top of a particle monolayer with increasing surface coverage as pressure was reduced. This was a direct result of fluid flow being too weak to reach the TL but strong enough to carry particles over smaller distances during the last stages of the evaporation process.

Pressure drop and dynamic contact angle of triple-line motion in a hydrophobic microchannel

Surface wettability influences flow configuration in many cases, such as pool boiling, flow boiling, and adiabatic flow regime. In mini and microchannels, the flow regime of a two-phase flow is also influenced by surface wettability. In particular, slug flow in a two-phase flow regime varies according to surface wettability. In hydrophilic microchannels, slugs are generated with liquid films, but in hydrophobic microchannels, they are generated with triple-lines instead of liquid films. Moreover, a slug with a triple-line exhibits a higher pressure drop than a slug with a liquid film, due to the motion of the triple line. Previous researches have observed that the pressure drop of a triple-line is affected by the dynamic contact angle, channel diameter, and fluid properties. Furthermore, the dynamic contact angle is affected by velocity, static contact angle, and fluid properties. To understand the pressure drop of a triple-line, we measured the pressure drops of slugs with triple-lines for various diameters (0.546, 0.763, 1.018, 1555 and 2.075mm), several fluids (DI water, DI water-1%, 5%, 10% ethanol), and a range of velocities (0.01–0.4m/s). Dynamic contact angles were calculated from an equation describing the pressure drop of a triple-line. Over the given experimental range, previous correlations have underestimated the dynamic contact angles in comparison with the experimental values. We suggest that the reason for this underestimation is that previous correlations were developed solely in a dynamic contact angle regime in which inertial forces were not considered. Accordingly, we propose a new dynamic contact angle correlation for a regime in which inertial forces are considered.

Modeling the early stages of reactive wetting

Recent experimental studies of molten metal droplets wetting high-temperature reactive substrates have established that the majority of triple-line motion occurs when inertial effects are dominant. In light of these studies, this paper investigates wetting and spreading on reactive substrates when inertial effects are dominant using a thermodynamically derived diffuse interface model of a binary three-phase material. The liquid-vapor transition is modeled using a van der Waals diffuse interface approach, while the solid-fluid transition is modeled using a phase field approach. The results from the simulations demonstrate an O(t(-1/2)) spreading rate during the inertial regime and oscillations in the triple-line position when the metal droplet transitions from inertial to diffusive spreading. It is found that the spreading extent is reduced by enhancing dissolution by manipulating the initial liquid composition. The results from the model exhibit good qualitative and quantitative agreement with a number of recent experimental studies of high-temperature droplet spreading, particularly experiments of copper droplets spreading on silicon substrates. Analysis of the numerical data from the model suggests that the extent and rate of spreading are regulated by the spreading coefficient calculated from a force balance based on a plausible definition of the instantaneous interface energies. A number of contemporary publications have discussed the likely dissipation mechanism in spreading droplets. Thus, we examine the dissipation mechanism using the entropy-production field and determine that dissipation primarily occurs in the locality of the triple-line region during the inertial stage but extends along the solid-liquid interface region during the diffusive stage.

Spreading and dynamics of liquid drops involving nanometric deformations on soft substrates

When a liquid spreads spontaneously on a rigid solid, a dynamic equilibrium is set up in which the non-equilibrated Young force causes triple line motion. Most solids may be considered as rigid when submitted to capillary forces. With soft solids, however, a ‘wetting ridge’ is formed as the wetting front advances or recedes. This ridge accompanies the motion leading to energy dissipation due to the hysteretic nature of the soft substrate and the strain cycle undergone. It has been established that the wetting ridge (of the order of tens of nanometers in height on silicone rubbers) can be so important in its consequences that viscous dissipation within the liquid becomes negligible. We propose to review the impact of solid deformation in the kinetics of spreading of liquids on soft materials, in wetting and dewetting modes, and we will consider also liquid drop motion due to gravity. In this last case, liquid drops running down a rubber plane move at a speed largely determined by the shear modulus of the polymer. The possibility of tailoring wetting, dewetting or draining kinetics on soft materials to a specific need is clearly evidenced.

Viscoelastic Braking of a Running Drop

Wetting or dewetting on soft elastomeric surfaces is largely controlled by the dissipative properties (viscoelasticity) of the substrate. The component of liquid surface tension acting perpendicularly to the solid causes a deformation, or “wetting ridge”, which must be displaced with the triple line. Previously, triple line motion due to capillary imbalance has been studied, whereas in the present work, we consider liquid motion due to gravity. Liquid drops running down an elastomeric plane move at a speed largely determined by the properties of the polymer. Results obtained agree well with the theory and demonstrate how motion depends on the state of the polymer, the angle of inclination of the plane, and drop volume.

Surfactant-induced wetting singularities in confined solid-liquid-liquid systems: kinetic and dynamic aspects

The paper reports some wetting singularities related to surfactant adsorption at solid-liquid 1-liquid 2 interfaces which are specifically driven by the time evolution of the concentration C(t) around the triple line as the surfactant diffuses freely from a localized source. Two model systems have been considered: a hydrophobic methyl-terminated surface and a hydrophilic glass plate, both in contact with a squalane drop and surrounded by external bulk water. On the hydrophobic surface, an intermediate plateau was observed over a certain concentration range in the kinetics of the drop parameters [contact angle (t) and radius R(t)]. This singularity is shown to arise from the overlap of the linear domains in the individual kinetics γ[C(t)] at the different interfaces. On the hydrophilic plate, an earlier spreading at low concentration is observed before the drop starts to recede as the local concentration around the triple line increases. This inversion in triple line motion, driven by the bilayer adsorption transition at the glass-water interface, combines with the buoyancy in the late stage, leading to the neck rupture of the confined drop.

Grain rotation in thin films of gold

We present transmission electron microscope observations of microstructural development in thin, fine-grained, columnar, 〈111〉 textured films of gold. In a sequential annealing experiment, we find that individual grains constantly rotate about the film normal in apparently random, and randomly changing directions. This contributes to the rearrangement of grain boundaries by allowing their individual energies to vary, thus promoting triple-line motion. We perform an analysis of the kinetics of grain rotation: assuming that its rate is limited by grain boundary diffusion, we obtain very good agreement between the observed and predicted rates and the rotation rate is predicted to be very sensitive to the grain size. A simple computer model is developed to investigate the structural consequences of grain rotation, which include reduction in the total grain boundary energy in a specimen, and changes in the populations of the various CSL-related boundaries.

Strange Spreading Behavior of Tricresyl Phosphate

The spreading of a sessile drop can be explained by a dynamic energy balance in which released excess capillary energy causes triple-line motion while wetting front speed is moderated by viscous dissipation within the liquid. This energy balance leads to a well-known relationship between dynamic and equilibrium contact angles and spreading speed. Experiments conducted with a silicone oil, poly(dimethylsiloxane), confirmed the validity of this equation. Similar experiments of spreading of tricresyl phosphate (TCP) on the same three substrates, glass, Halar (polyethylene−chlorotrifluoroethylene), and polypropylene, led to anomalous behavior: among other observations, we noted that the (apparent) spreading force needed for a given spreading speed was too high. Here, we suggest a tentative theory involving molecular orientation or conformation of the asymmetrical liquid molecules after they have been “laid down” on the solid substrates during spreading. As TCP molecules orientate near the triple line, the li...

Effect of Cross-Linking on the Dewetting of an Elastomeric Surface

It has been shown over the last few years how the wetting (or dewetting) of a soft, elastomeric substrate can be markedly affected by local deformation of the solid near the triple line, due to the component of liquid surface tension acting perpendicularly to the (undeformed) solid surface, i.e., the “wetting ridge.” Since the degree of cross-linking of an elastomer affects its mechanical properties, we have undertaken a study of the influence of cross-linking on (de)wetting behavior. Using a silicone rubber in four states of cross-linking, we have observed that triple-line motion of tricresyl phosphate increases in speed with degree of cross-linking. Two principal factors influence this behavior, both being directly linked to average intercross-link molecular weight,Mc. A decrease inMcincreases elastic modulus and therefore decreases the importance of the wetting ridge, whilst also lowering the dissipative properties of the polymer. The combined effects lead, in the case studied, to a linear relationship between dewetting speed and elastomeric elastic modulus to the power 10/3.