Phase Contact Line Research Articles

Flow structure near three phase contact line of low-contact-angle evaporating droplets

Flow structure near three phase contact line (TPCL) of evaporating liquids plays a significant role in liquid wetting and dewetting, liquid film evaporation, and boiling. Despite the wide focus it receives, the interacting mechanisms therein remain elusive and in specific cases, controversial. Here, we reveal the profile of internal flow and elucidate the dominating mechanisms near TPCL of evaporating droplets, using mathematical modeling, trajectory analysis, and infrared thermography. We indicate that for less volatile liquids such as butanol, the flow pattern is dominated by capillary flow. With increasing liquid volatility, e.g., alcohol, the effect of evaporation cooling, under conditions, induces interfacial temperature gradient with cold droplet apex and warm edge. The temperature gradient leads to Marangoni flow that competes with outwarding capillary flow, resulting in the reversal of interfacial flow and the formation of a stagnation point near TPCL. The spatiotemporal variations of capillary velocity and Marangoni velocity are further quantified by mathematically decomposing the tangential velocity of interfacial flow. The conclusions can serve as a theoretical base for explaining deposition patterns from colloidal suspensions and can be utilized as a benchmark in analyzing more complex liquid systems.

Bubble-particle detachment behavior during bubble coalescence: Role of bubble size

Studies have reported that bubble coalescence causes particle–bubble detachment in the flotation pulp and foam phases. Most coalescence experiments have been conducted using bubble pairs with the same diameter; however, this is not the case in real flotation. In this study, particle–bubble detachment behavior during the coalescence of two bubbles with different sizes was investigated using a high–speed camera, and the variation of the coalescing bubble area was fitted to a damped oscillatory equation and analyzed. To explore the intrinsic detachment mechanism of the bubble size effect, the flow field variation in the bubble periphery was simulated using COMSOL 6.1. Results show that the particle–bubble detachment probability decreased with increasing bubble size difference. The released energy is greatest when the two equal bubbles coalesced, thus leading to the strongest oscillation and highest detachment probability. The simulation results show that turbulent kinetic energy affects particle-bubble stability and is an important reason for inducing particle-bubble detachment. Notably, particle–bubble detachment did not occur at the maximum turbulent energy, because there was a delay due to the time required for the sliding contraction of the three–phase contact line. The research finding provides new insights into the mechanism of particle–bubble detachment.

Structure and migration mechanism of thin liquid film in vicinity of advancing contact line

Thin liquid film near the gas-liquid-solid three phase contact line is the core area of oil and gas production, phase-change heat transfer, and material synthesis systems. Although there are many experimental studies on fluid dynamics in the contact line region, the prediction of contact angle is still difficult, and the bottleneck lies in the special structure of thin liquid film in the contact line region. Because the microstructure of thin liquid film is not well understood, the prediction of dynamic contact angle is always controversial. At present, the main controversial points focus on whether the microscopic contact angle changes with speed, and whether the microscopic contact angle is the same as the macroscopic contact angle. Therefore, it is crucial to monitor the dynamic process of the microscopic contact angle in the thin liquid film region of the contact line. In this work, the wetting system of 50 nm liquid droplets on different solid surfaces is constructed by molecular dynamics simulation, and the structure and migration mechanism of thin liquid film are studied. The structure of the precursor liquid film in the completely wetting droplet advancing contact line region and the nanoscale convex structure in the partially wetting droplet advancing contact line region are obtained. The precursor liquid film is 2–3 molecular layers in thickness, leading the droplet to move forward. However, there is no precursor liquid film in a partially wetting system, and the convex nano-bending larger than 10 nm is formed in the wetting process, resulting in the microscopic contact angle. By comparing the difference between the absolute smooth surface dynamic wetting process and the actual solid surface dynamic wetting process, the dynamic evolution law of the micro contact angle and the macro contact angle with time are obtained for the first time in the simulation. The liquid molecules in the contact line region are tracked and statistically analyzed by means of particle tracer. It is revealed that the liquid molecules in thin liquid film change from sliding mode to rolling mode with speed increasing under the action of solid surface friction, and then the air entrainment at the bottom of the contact line leads to slip and sputtering. The research results are expected to provide theoretical guidance for the following three directions: 1) improving heat transfer efficiency of micro and nano device based on wettability control; 2) improving the imbibition displacement efficiency of shale oil micro-nano matrix based on wettability regulation; 3) constructing universal contact angle prediction model.

Transients of Marangoni and Stefan advection dynamics during generic sessile droplet evaporation

We probe the transient evolution of Marangoni thermo-hydrodynamics in the liquid domain and the Stefan advection in the gaseous domain during evaporation of sessile droplets with generic contact line dynamics [both constant contact radius (CCR) and constant contact angle (CCA) modes]. A transient arbitrary Lagrangian–Eulerian framework was considered to computationally model the evaporation phenomenon over the droplet lifetime. The governing equations corresponding to the transport processes in both liquid and gaseous domains are simulated in a fully coupled manner, while precisely tracing the liquid–vapor interface and three phase contact line. The effects of the wetting state and contact line dynamics during CCR and CCA modes were explored, and good agreement with experimental observations is noted. The results show that the non-uniformity in an internal temperature field due to evaporation leads to formation of multi-vortex Marangoni patterns in the flow field at initial periods. At the quasi-stable state, the temperature variation becomes monotonic, thereby resulting in a single recirculation vortex in both liquid and gaseous domains. For the CCR mode, the strength of these advection fields is solely governed by a critical contact angle of ∼32°, which is determined to correspond to the critical Marangoni number. Beyond this critical point, viscous action becomes significant, and the fluid motion mitigates progressively with the formation of twin vortices at final stages due to localized heat advection near the contact line. For the CCA mode, the strength of initial vortices augments with progressing time due to amplified evaporative fluxes at smaller contact radius. The internal thermofluidic patterns and evaporative modes in turn modulate the external Stefan flow fields and neighborhood temperature fields. These findings may hold strong implications for efficient functioning of practical droplet based processes involving transport, mixing, and deposition of dissolved particles.

Efficient defrosting on hybrid surfaces with heterogeneous wettability

Frosting behavior and dynamic defrosting characteristics of horizontally oriented hybrid surfaces with heterogeneous wettability were experimentally investigated. The developed hybrid surfaces with superhydrophobic patterns built on superhydrophilic background integrated the properties of frost retardation under frosting conditions and fast surface cleaning of residual water upon defrosting. Four types of hybrid surfaces with different pattern spacings were tested in this work. Hybrid surfaces exhibited superior anti-frosting performance compared with that of a bare copper surface but lower than a complete superhydrophobic surface. During defrosting process, surface energy gradient and Laplace pressure gradient enabled by heterogeneous wettability on hybrid surfaces could drive the mobile slush composites on superhydrophobic regions move to superhydrophilic areas to achieve quick cleaning even in the absence of gravity force. The proportion of surface clean time of one full cycle duration on hybrid surfaces was as low as 32.2%–41.5%. Compared to complete superhydrophobic and bare copper surfaces, hybrid surfaces exhibited a significant enhancement on defrost efficiency due to larger three phase contact line length on evaporation-mediated surface cleaning performance, especially the SSH-3 surface, achieving the largest defrost efficiency within the present frost mass range.

Studying the effect of geometry of micro-cavity on pool boiling by LBM

Pool boiling heat transfer from structured surface is simulated numerically with a 3D OTRT (optimal two relaxation time) Lattice Boltzmann method. This work shows in detail that multiple bubbles grow and coalesce over hydrophilic (θ = 50°) surfaces in 3D view, heat flux transfers from heater surface to fluid, and temperature of heater surface varies with time. Specifically, four types of geometry in microstructure surfaces are examined and compared. It is found that heat flux of S5 is the highest and its wall temperature is the lowest. When compared with S0, the heat flux of S5~S7 increased a lot due to the easier formation of vapor blanket, and cubic shaped cavity alleviates largely this deterioration. Next, the large quantity of heat from the three phase contact line in the vicinity of side wall accounts for bubble nucleation and energy from the evaporation of thin liquid between bubbles and superheated wall helps bubbles to grow further. Besides, it is found that S5 increases nucleate site density, reduces boiling incipience superheat, and enhances remarkably heat transfer performance.

Relation between triple phase contact line and vapor groove width for enhancing thermal performance of a loop heat pipe evaporator

• The effects of changing vapor groove width of a porous wick and improving wettability of a LHP evaporator on heat transfer performances were evaluated experimentally and theoretically. • The micro-grooves processed on the heating plate improved heat transfer performances regardless of the vapor grooves width. • The micro-grooves increased heat transfer performances more greatly as the vapor grooves width increased. • Numerical model explained that the length of triple phase contact line has a great influence on the evaporative heat transfer coefficient. In this study, the effects of an increased evaporation area known as the triple-phase contact line (TPCL), of the porous wick and improved evaporator wettability on the loop heat pipe (LHP) heat transfer performance were evaluated experimentally and theoretically. An infrared camera and a microscope were used to observe the thermo-fluid behavior of porous wicks with different vapor grooves widths and evaporator heating plates with different inner wall structures in the experiment. The porous wick's vapor groove widths were 1.0 mm, 0.5 mm, and 0.2 mm. A normal heating plate and a micro-grooved heating plate were used as the evaporator case. As a result, it was clarified that processing the micro-grooves on the heating plate improved the evaporative heat transfer coefficient and maximum heat flux, regardless of the vapor grooves width of the porous wick. Furthermore, it was proposed that both of them increased significantly as the vapor grooves width increased. The thermal-hydraulic numerical model that predicted the heat transfer coefficients for each case was developed. The calculation results showed a significant increase in the heat transfer coefficient as the TPCL appearance rate, which expresses how much the TPCL appears in the micro-grooves, increased, and this increasing tendency was in good agreement with the experimental results. Furthermore, it was proposed that the TPCL appearance rate at a high heat flux was reduced as the vapor grooves width decreased. The results indicate a new promising approach for improving the heat transfer performance of LHP evaporators.

Controllable depositing behaviors and deposited morphologies of inkjet droplets on high energy surface

The high energy surface (HES) could realize a super-spreading process for droplet. In this work, a facile method was applied to fabricate HES by hydrothermally treating aluminum foil. The inkjet ink is obtained by dissolving poly acrylic acid (PAA) in ethanol. The depositing behaviors of inkjet droplet was investigated and controlled with pinned three phase contact lines. And the influence of coffee ring effect on the depositing behavior of inkjet droplet could be regulated to generate a variety of deposited morphologies, including super-spreading structure, ring structure, and homogeneous structure. With the inkjet printed pattern of PAA solution ink on the HES, a patterned wettability surface with high energy area and low energy area could be fabricated by modifying the surface with fluoro-alkyl silanes and removing the inkjet printed PAA with deionized water, which could transport water from bottom to up with a high wettability contrast. This work presented a systematic study in controllable depositing behaviors and deposited morphologies of the inkjet droplets on high energy surface. It has a great potential for the development of material patterning, 3D printing as well as related interface researching.

Cloaking Transition of Droplets on Lubricated Brushes.

We study the equilibrium properties and the wetting behavior of a simple liquid on a polymer brush, with and without the presence of lubricant by multibody Dissipative Particle Dynamics simulations. The lubricant is modeled as a polymeric liquid consisting of short chains that are chemically identical with the brush polymers. We investigate the behavior of the brush in terms of the grafting density and the amount of lubricant present. Regarding the wetting behavior, we study a sessile droplet on top of the brush. The droplet consists of nonbonded particles that form a dense phase. Our model and choice of parameters result in the formation of a wetting ridge and in the cloaking of the droplet by the lubricant; i.e., the lubricant chains creep up onto the droplet and eventually cover its surface completely. Cloaking is a phenomenon that is observed experimentally and is of integral importance to the dynamics of sliding droplets. We quantify the cloaking in terms of its thickness, which increases with the amount of lubricant present. The analysis reveals a well-defined transition point where the cloaking sets in. We propose a thermodynamic theory to explain this behavior. In addition, we investigate the dependence of the contact angles on the size of the droplet and the possible effect of line tension. We quantify the variation of the contact angle with the curvature of the contact line on a lubricant free brush and find a negative value for the line tension. Finally we investigate the effect of cloaking/lubrication on the contact angles and the wetting ridge. We find that lubrication and cloaking reduce the contact angles by a couple of degrees. The effect on the wetting ridge is a reduction in the extension of the brush chains near the three phase contact line, an effect that was also observed in experiments of droplets on cross-linked gels.

Pinning forces of sliding drops at defects

Wetting of surfaces depends critically on defects which alter the shape of the drop. However, no experimental verification of forces owing to the three phase contact line deformation at single defects is available. We imaged the contact line of sliding drops on hydrophobic surfaces by video microscopy. From the deformation of the contact line, we calculate the force acting on a sliding drop using an equation going back to Joanny and de Gennes (J. Chem. Phys., 81 (1984) 554). The calculated forces quantitatively agree with directly measured forces acting between model defects and water drops. In addition, both forces quantitatively match with the force calculated by contact angle differences between the defect and the surface. The quantitative agreement even holds for defects reaching a size of of the drop diameter. Our validation for drop’s pinning forces at single defects is an important step towards a general understanding of contact line motion on heterogeneous surfaces.

Effect of inorganic cations on enhancing graphite/kerosene adsorption and reducing carbon emission in graphite flotation

Understanding the effect of inorganic cations on the adsorption of kerosene droplet at graphite surface is a prerequisite to predict the graphite flotation. Using a high-speed motion acquisition system, the contact angle, kerosene droplet size and three phase contact line (TPC line) were explored. The equivalent diameter of the kerosene droplet increased until 10-2 mol/L and then decreased slightly with increasing the concentration of NaCl and MgCl2. On contrary, the equivalent diameter showed an opposite trend in the presence of AlCl3. The final TPC line followed the order: AlCl3 < MgCl2 < NaCl at an ion concentration 10-2 mol/L. Through the simulation of radial distribution function (RDF) via the Material studio software, the oxygen atom was more easily attracted than the hydrogen atom by Na+, resulting in the smallest kerosene droplet-graphite block contact angle in the presence of NaCl. Furthermore, NaCl and MgCl2 presented an opposite trend to AlCl3 in the solution/kerosene interfacial tension. Our results matched the cation hydration at different pH. The subsequently conducted graphite flotation showed that the recovery of clean graphite was enhanced by 5.11% (NaCl) and 3.31% (MgCl2) at 10-2 mol/L, respectively, while gradually decreased by the addition of AlCl3. Moreover, the discussion on increasing the graphite recovery by 1% showed that 1.9 mmol/L Na+ was equivalent to 3.0 mmol/L Mg2+, 18.3 J energy input, 7 mg/L 2-octyl alcohol and 0.9 mg/L diesel, respectively. It indicated that the addition of NaCl and MgCl2 is of great significance for reducing carbon emission and cleaning flotation process. Our results can provide a valuable insight into the development of technology for surfactant adsorption and mineral flotation, especially for reducing carbon emission.

Spreading behavior of dodecane-oleic acid collector mixture in low-rank coal flotation

Spreading of water-insoluble collectors on the mineral surface is important in flotation. In this study, the spreading behavior of dodecane (D), oleic acid (OA), and dodecane-oleic acid (D-OA) mixture in low-rank coal flotation was investigated. The viscosity and oil/water interfacial tension was measured to calculate the spreading coefficient and speed. The relaxation of coal-oil–water contact angle and the movement of three- phase contact line during the collector droplet spreading process were interpreted using the molecular kinetic (MK) model. It was found that the order of absolute values of spreading coefficient were D-OA < OA < D, and the spreading speeds were in the order of OA < D-OA < D. D-OA had the smallest coal-oil–water contact angle and the longest contact line length. The addition of OA can enhance the interaction between D and the low-rank coal surface, but at the same time reduce the spreading speed. This was mainly because OA not only increased the spreading force of the droplet but also increased the spreading resistance. MK model fitting results showed that the length of molecular displacement increased in the order of D < D-OA < OA, indicating that the hydrophobic sites were more dense than hydrophilic ones on the coal surface and D-OA interacted with both sites simultaneously. The molecular substitution frequency and the free energy of wetting activation had an opposite order. High molecular substitution frequency meant fast-spreading velocity, and thus the MK model fitting parameters were consistent with the contact angle relaxation results.

Understanding multiscale assembly mechanism in evaporative droplet of gold nanorods

Using in-situ contact angle measurement and ex-situ scanning electron microscopy, we present a direct correlation of the drying profile of CTAB coated AuNRs suspension with observed deposition pattern on hydrophilic silicon substrate. The droplet evaporation reveals the formation of surface pattern that primarily exhibits three different regions of assembly. Region 1, the exterior of droplet's triple phase contact line (TPCL), consists of small arrays of AuNR cluster followed by the much observed multi-layered coffee-ring deposit, comprising of AuNRs assembled in smectic phase. The transient TPCL depinning during the initial stage of evaporation due to autophobic effect results in formation of region 1. The increase in AuNR concentration due to outward capillary flow leads to pinned TPCL and coffee-ring deposit in region 2. The depletion mediated interparticle interaction due to nanoparticle stagnation at TPCL results in surfactant expulsion. The expelled CTAB creates surfactant-induced Marangoni flow and results in the formation of depletion region 3. Further, we will discuss the plasmonic application of the deposit pattern in determination of surface-enhanced Raman scattering signal. The SERS signal enhancement of Rhodamine B analyte, by factor of ~7.6 ∗ 105 and detection limit to concentration as low as ~10−8M has been achieved using the ordered arrays of gold nanorods as substrates. The AuNR assembly can be further explored for fabrication of optical sensors and other application based studies.

Numerical simulation of phase change and contact lines on unstructured grids: towards simulation of nucleate boiling

Numerical simulation of phase change and contact lines on unstructured grids: towards simulation of nucleate boiling

Validation of the mechano-bactericidal mechanism of nanostructured surfaces with finite element simulation

The mechano-bactericidal property of nanostructured surfaces has become the focus of intensive research toward the development of a new generation of antibacterial surfaces, especially in the current era of spreading antibiotic resistance. However, the mechanisms underlying nanostructured surfaces mechanically damaging bacteria remain unclear, which ultimately limits translational potential toward real-world applications. Using finite element simulation technique, we developed the three-dimensional thin wall with turgor pressure finite element model (3D-TWTP-FEM) of bacterial cell and verified the reliability of this model by the AFM indentation experiment simulation of the cell, and the cell model is able to simulate suspended bacterial cell and the process of cell adhering to the flat and nanopillar surfaces. Since bacterial cells suffer greater stress and deformation on the nanopillar surfaces, a two-stage model of the elastic and creep deformation stage of the cells on the nanostructured surfaces was developed. The calculations show that the location of the maximum stress/strain on the cells adhered to the nanopillar surfaces is at the liquid-cell-nanopillar three phase contact line. The computational results confirmed the ability of nanostructured surfaces to mechanically lyse bacteria and gave the effect of nanopillar geometry on the efficiency and speed of bacterial cell rupture. This study provides fundamental physical insights into how nanopillar surfaces can serve as effective and fast mechanical antimicrobial materials.

The Effect of Patterned Micro-Structure on the Apparent Contact Angle and Three-Dimensional Contact Line

The measurement of the apparent contact angle on structured surfaces is much more difficult to obtain than on smooth surfaces because the pinning of liquid to the roughness has a tremendous influence on the three phase contact line. The results presented here clearly show an apparent contact angle variation along the three phase contact line. Accordingly, not only one value for the apparent contact angle can be provided, but a contact angle distribution or an interval has to be given to characterize the wetting behavior. For measuring the apparent contact angle distribution on regularly structured surfaces, namely micrometric pillars and grooves, an experimental approach is presented and the results are provided. A short introduction into the manufacturing process of such structured surfaces, which is a combination of Direct LASER Writing (DLW) lithography, electroforming and hot embossing shows the high quality standard of the used surfaces.

Effect of surface chemical heterogeneity on kinetics of three phase contact formation

Bubble–particle interaction is a major focus for froth flotation research that has widespread use in mineral separation and concentration. The formation of a stable three phase contact (TPC) line is key to successful flotation. In industrial flotation processes, nearly all surfaces of particles are heterogeneous. Thus, the investigation of the influence of surface heterogeneity on the kinetics of TPC formation is important for understanding these processes. In this study, four types of heterogeneous surfaces were prepared by hydrophobization of glass slides followed by partial coverage with different mesh grids and oxidization with UV light. Interactions between bouncing bubbles and heterogeneous surfaces were investigated using a high-speed video camera. The results showed that the interval times between consecutive collisions with the patterned slide surface (before rupture) are almost independent of the surface. However, the behavior of the TPC line differed on various heterogeneous surfaces after bubble rupture. The terminal diameter was measured on different heterogeneous surfaces. It was found that the terminal diameter increased with the decrease in the mesh spacing of the grid. The slope of each curve is used to characterize the TPC line expansion velocity. The TPC line initial expansion velocity is inversely correlated with the grid mesh spacing. The surface heterogeneity had insignificant effect on the collision interaction between the bubble and the surface before the bubble rupture. However, after bubble rupture, the behavior of the expansion of TPC line was affected by the surface heterogeneity.

Lifshitz theory of wetting films at three phase coexistence: The case of ice nucleation on Silver Iodide (AgI)

HypothesisAs a fluid approaches three phase coexistence, adsorption may take place by the successive formation of two intervening wetting films. The equilibrium thickness of these wetting layers is the result of a delicate balance of intermolecular forces, as dictated by an underlying interface potential. The van der Waals forces for the two variable adsorption layers may be formulated exactly from Dzyaloshinskii-Lifshitz-Pitaevskii theory, and analytical approximations may be derived that extent well beyond the validity of conventional Hamaker theory. CalculationsWe consider the adsorption equilibrium of water vapor on Silver Iodide where both ice and a water layers can form simultaneously and compete for the vapor as the triple point is approached. We perform numerical calculations of Lifshitz theory for this complex system and work out analytical approximations which provide quantitative agreement with the numerical results. FindingsAt the three phase contact line between AgI/water/air, surface forces promote growth of ice both on the AgI/air and the water/vapor interfaces, lending support to a contact nucleation mode of AgI in the atmosphere. Our approach provides a framework for the description of adsorption at three phase coexistence, and allows for the study of ice nucleation efficiency on atmospheric aerosols.

Nanoparticles deposition patterns in evaporating nanofluid droplets on smooth heated hydrophilic substrates: A 2D immersed boundary-lattice Boltzmann simulation

Nanoparticles deposition dynamics and deposition patterns in evaporating nanofluid droplets on a smooth hydrophilic heated substrate in a vapor environment (0.9Tc) under zero gravity are investigated numerically by a 2D immersed boundary-lattice Boltzmann method in combination of the non-isothermal Gong-Cheng liquid-vapor phase change model. The Marangoni flow along droplet interface is found to be the dominated transportation mechanism of nanoparticles inside an evaporating nanofluid droplet when droplet contact line is freely moving. It is demonstrated that the pinning of the triple phase contact line on the substrate having a small contact angle (θ=51°) is a required condition for a ring-like deposition pattern after a nanofluid droplet evaporation. On the other hand, on a substrate with a larger contact angle (θ=74°) where the triple contact line is not pinned, the upward Marangoni flow along droplet interface has a greater strength to resist nanoparticles moving toward the edge of the heated substrate, which result in bump-like deposition patterns after a nanofluid droplet evaporation. A regime map, showing effects of substrate contact angle and substrate temperature on nanoparticle deposition patterns after droplet evaporation, is presented. It is shown that the ring-like deposition pattern occurs when the triple line is strongly pinned (at small contact angle) and the Marangoni flow is weak (small contact angle and low substrate temperature). The bump deposition pattern occurs when the droplet contact line is not pinned (at high contact angle) and the Marangoni flow is strong (large contact angle and high temperature).

Impact of substrate elasticity on contact angle saturation in electrowetting.

The electrostatically assisted wettability enhancement of dielectric solid surfaces, commonly termed as electrowetting-on-dielectric (EWOD), facilitates many microfluidic applications due to simplicity and energy efficiency. The application of a voltage difference between a conductive droplet and an insulated electrode substrate, where the droplet sits, is enough for realizing a considerable contact angle change. The contact angle modification is fast and almost reversible; however it is limited by the well-known saturation phenomenon which sets in at sufficiently high voltages. In this work, we experimentally show and computationally support the effect of elasticity and thickness of the dielectric on the onset of contact angle saturation. We found that the effect of elasticity is important especially for dielectric thickness smaller than 10 μm and becomes negligible for thickness above 20 μm. We attribute our findings on the effect of the dielectric thickness on the electric field, as well as on the induced electric stresses distribution, in the vicinity of the three phase contact line. Electric field and electric stresses distribution are numerically computed and support our findings which are of significant importance for the design of soft materials based microfluidic devices.