Three-phase Contact Line Region Research Articles

Mesoscopic Model for Disjoining Pressure Effects in Nanoscale Thin Liquid Films and Evaporating Extended Meniscuses.

Disjoining pressure effect is the key to describe contact line dynamics, micro/nanoscale liquid-vapor phase change heat transfer, and liquid transport in nanopores. In this paper, by combining a mesoscopic approach for nanoscale liquid-vapor interfacial transport and a mean-field approximation of the long-range solid-fluid molecular interaction, a mesoscopic model for the disjoining pressure effect in nanoscale thin liquid films is proposed. The capability of this model to delineate the disjoining pressure effect is validated. We demonstrate that the Hamaker constant determined from our model agrees very well with molecular dynamics (MD) simulation and that the transient evaporation/condensation mass flux predicted by this mesoscopic model is also consistent with the kinetic theory. Using this model, we investigate the characteristics of the evaporating extended meniscus in a nanochannel. The nonevaporating film region, the evaporating thin-film region, and the intrinsic meniscus region are successfully captured by our model. Our results suggest that the apparent contact angle and thickness of the nonevaporating liquid film are self-tuned according to the evaporation rate, and a higher evaporation rate results a in larger apparent contact angle and thinner nonevaporating liquid film. We also show that disjoining pressure plays a dominant role in the nonevaporating film region and suppresses the evaporation in this region, while capillary pressure dominates the intrinsic meniscus region. Strong evaporation takes place in the thin-film region, and both the disjoining pressure and capillary pressure contribute to the total pressure difference that delivers the liquid from the intrinsic meniscus region to the evaporating thin-film region, compensating for the liquid mass loss due to strong evaporation. Our work provides a new avenue for investigating thin liquid film spreading, liquid transport in nanopores, and microscopic liquid-vapor phase change heat/mass transfer mechanisms near the three-phase contact line region.

Molecular dynamics simulation of Wenzel-state nanodroplets: Evaporation on heated substrates with different rough structures

Droplet evaporation on rough substrates is ubiquitous in nature and has numerous technological applications, such as coating. To study the evaporation characteristics of nanodroplets on substrates with different rough structures, molecular dynamics simulations have been performed. Based on the Wenzel wetting model, three systems with different rough structures were constructed, in which the ratios of contact area (RCA) between substrates and nanodroplets were 33.3%, 50%, and 66.6%, respectively. The results indicate that the evaporation pattern of the nanodroplet in the system with RCA = 33.3% is the mixed mode, the evaporation pattern of the nanodroplet in the system with RCA = 50% is the constant-contact-radius mode, and the evaporation pattern of the nanodroplet in the system with RCA = 66.6% is the constant-contact-angle mode. Meanwhile, when the temperature of substrates (T) is suddenly raised from 0.67 to 0.83 ε/kB, followed by a corresponding rise in the temperature of nanodroplets, we find that temperature and evaporation rates of the nanodroplets increase with the increase in RCA in this period. Changes in RCA that lead to the changes in substrate wettability affect the heat transfer between nanodroplets and substrates. In particular, the more the substrate wettability, the higher the heat transfer efficiency. Moreover, the wettability of the substrate in the systems with RCA = 50% and 66.6% promotes the heat and mass transfer in the three-phase contact line region of the nanodroplets during the evaporation process, while the non-wettability of the substrate in the system with RCA = 33.3% suppresses the local heat and mass transfer. This work offers further knowledge of droplet evaporation on rough substrates, which, in turn, provides a reference for the process optimization of its technological applications.

Dynamic Wetting of Ionic Liquid Drops on Hydrophobic Microstructures.

Ionic liquids (ILs)─salts in a liquid state─play a crucial role in various applications, such as green solvents for chemical synthesis and catalysis, lubricants, especially for micro- and nanoelectromechanical systems, and electrolytes in solar cells. These applications critically rely on unique or tunable bulk properties of ionic liquids, such as viscosity, density, and surface tension. Furthermore, their interactions with different solid surfaces of various roughness and structures may uphold other promising applications, such as combustion, cooling, and coating. However, only a few systematic studies of IL wetting and interactions with solid surfaces exist. Here, we experimentally and theoretically investigate the dynamic wetting and contact angles (CA) of water and three kinds of ionic liquid droplets on hydrophobic microstructures of surface roughness (r = 2.61) and packing fraction (ϕ = 0.47) formed by micropillars arranged in a periodic pattern. The results show that, except for water, higher-viscosity ionic liquids have greater advancing and receding contact angles with increasing contact line velocity. Water drops initially form a gas-trapping, CB wetting state, whereas all three ionic liquid drops are in a Wenzel wetting state, where liquids penetrate and completely wet the microstructures. We find that an existing model comparing the global surface energies between a CB and a Wenzel state agrees well with the observed wetting states. In addition, a molecular dynamic model well predicts the experimental data and is used to explain the observed dynamic wetting for the ILs and superhydrophobic substrate. Our results further show that energy dissipation occurs more significantly in the three-phase contact line region than in the liquid bulk.

Research on heat transfer capability of liquid film in three-phase contact line area

• Heat transfer studies were carried out in the three-phase contact line region using the TDTR method with high spatial and temporal resolution. • The experimentally measured results of the overall heat transfer coefficient of the n-octane liquid film in the evaporating thin-film region can reach 439 kW/(m 2 ·K). • A bidirectional heat transfer model for the TDTR experiment was built during data processing. • The usability of the TDTR method in microscopic liquid film heat transfer studies is demonstrated by numerical calculation. The three-phase contact line area plays a vital role in the heat dissipation of micro-devices due to its intense heat transfer capacity. However, the scale of the three-phase contact line area is small, and experimental studies are mainly used to observe the film profile. Few experiments can characterize this area with high spatial resolution, making it a well-known challenge to make a quantitative assessment of the limit of heat transfer capacity. In this work, we use the time-domain thermoreflectance system to measure the liquid film heat transfer capacity in the contact line region. The effective thermal conductivity of the liquid film obtained from the experiment can well reflect the heat transfer capacity of the liquid film at different positions and can be used to calculate the evaporating heat flux and the overall heat transfer coefficient of the liquid film. We also established a theoretical model and performed numerical calculations compared with the experimental results. The results show that the liquid film has the most vital heat transfer capacity in the evaporating thin-film region. The overall heat transfer coefficient can reach ∼439 kW/(m 2 ·K), and the evaporating heat flux of the liquid film can reach ∼1.8 × 10 6 W/m 2 . This work provides a new idea for the experimental study of the three-phase contact line area, offers experimental support for theoretical research, and lays a foundation for revealing the heat and mass transport mechanism in the three-phase contact line area.

Lattice Boltzmann Modeling of Condensation Heat Transfer on Downward-Facing Surfaces with Different Wettabilities.

The model of vapor condensation heat transfer on downward-facing surfaces with different wettabilities is built by a two-dimensional (2D) lattice Boltzmann method. Dynamic evolution of condensate microdroplets on different wettability surfaces is simulated and the influence on heat transfer performance is analyzed. Moreover, the mechanism of a heterogeneous wettability surface enhancing condensation heat transfer is explored by investigating the condensate behaviors in the process of condensation. The numerical results indicate that as the contact angle of the homogeneous wettability surface increases, the initial nucleation time of the condensate is prolonged, while the departure time of the condensate is reduced significantly. The temperature adjacent to the gas-liquid interface, especially in the three-phase contact line region, is much higher than elsewhere due to the release of latent heat during condensation. Coalescence and detachment behaviors of condensate droplets cause the average heat flux to fluctuate locally with time. For the hybrid wettability surface, if the proportion of hydrophobic regions is small, the condensation heat transfer performance will be deteriorated. However, increasing the hydrophobic-hydrophilic ratio has a positive effect on enhancing heat transfer. It is found that a critical hydrophobic-hydrophilic ratio exists to optimize the heat transfer performance. For the gradient wettability surface, directional migration induced by capillary force facilitates the removal of condensate droplets, thereby enhancing the condensation heat transfer. Furthermore, a larger wetting gradient benefits to further improve the heat transfer performance. The results are valuable for optimally designing the heat transfer enhancement of vapor condensation on functionalized surfaces with heterogeneous wettability.

An experimental investigation into the spread and heat transfer dynamics of a train of two concentric impinging droplets over a heated surface

Extensive studies of two concentric droplets consecutively impinging over a thin heated foil surface are carried out to compare the spread and heat transfer dynamics of a single drop, and drop-on-drop configurations using high speed imaging and infrared thermography. Millimeter-sized deionized water droplets (2.80 ± 0.04 mm) are impinged upon a heated Inconel surface (thickness of 25 μm) from a fixed height corresponding to a Weber number (We) of 50 ± 2 and Reynolds number (Re) of 3180 ± 90 with a flow rate of 20 droplets per minute. Surface temperature is chosen as a parameter, and is varied from 22 °C (non-heated) to 175 °C. Temperature and heat flux distributions associated with droplet-surface interactions are obtained, and the outcomes of the process are measured in terms of spread diameter, droplet input heat transfer, dynamic contact angle, and surface mean temperature. A decline in the droplet heat transfer for drop-on-drop impingement is observed for all temperatures investigated in the present work. This is attributed to the surface pre-cooling by the initial droplet and also to the reduced surface area-to-volume ratio i.e., increased spreading film thickness. High heat transfer rates are observed around the three-phase contact line region, especially during the receding phase of the droplet, for both configurations, confirming the significance of contact line evaporation in droplet-hot wall interactions. Theoretical models predicting the maximum spread factor and corresponding input heat transfer into the droplet are identified from the literature, and found to be in good agreement with present experimental observations.

Simultaneous reflectometry and interferometry for measuring thin-film thickness and curvature.

A coupled reflectometer-interferometer apparatus is described for thin-film thickness and curvature characterization in the three-phase contact line region of evaporating fluids. Validation reflectometry studies are provided for Au, Ge, and Si substrates and thin-film coatings of SiO2 and hydrogel/Ti/SiO2. For interferometry, liquid/air and solid/air interferences are studied, where the solid/air samples consisted of glass/air/glass wedges, cylindrical lenses, and molded polydimethylsiloxane lenses. The liquid/air studies are based on steady-state evaporation experiments of water and isooctane on Si and SiO2/Ti/SiO2 wafers. The liquid thin-films facilitate characterization of both (i) the nano-scale thickness of the absorbed fluid layer and (ii) the macro-scale liquid meniscus thickness, curvature, and curvature gradient profiles. For our validation studies with commercial lenses, the apparatus is shown to measure thickness profiles within 4.1%-10.8% error.

Direct Numerical Simulation of the Microscale Fluid Flow and Heat Transfer in the Three-Phase Contact Line Region During Evaporation

The heat and mass transfer close to the apparent three-phase contact line is of tremendous importance in many evaporation processes. Despite the extremely small dimensions of this region referred to as the microregion compared to the macroscopic length scale of a boiling process, a considerable fraction of heat can be transferred in this region. Due to its small characteristic length scale, physical phenomena are relevant in the microregion, which are completely negligible on the macroscopic scale, including the action of adhesion forces and the interfacial heat resistance. In the past, models have been developed taking these effects into account. However, so far these models are based on the assumption of one-dimensional (1D) heat conduction, and the flow within the thin liquid film forming the microregion near the apparent three-phase contact line is modeled utilizing the lubrication approximation. Hence, the application of existing models is restricted to small apparent contact angles. Moreover, the effects of surface structures or roughness are not included in these lubrication models. To overcome these limitations, a direct numerical simulation (DNS) of the liquid flow and heat transfer within the microregion is presented in this paper. The DNS is employed for validation of the existing lubrication model and for investigation of the influence of surface nanostructures on the apparent contact angle and in particular on the heat transfer within the microregion.

Experimental study of the heated contact line region for a pure fluid and binary fluid mixture in microgravity

Understanding the dynamics of phase change heat and mass transfer in the three-phase contact line region is a critical step toward improving the efficiency of phase change processes. Phase change becomes especially complicated when a fluid mixture is used. In this paper, a wickless heat pipe was operated on the International Space Station (ISS) to study the contact line dynamics of a pentane/isohexane mixture. Different interfacial regions were identified, compared, and studied. Using high resolution (50×), interference images, we calculated the curvature gradient of the liquid-vapor interface at the contact line region along the edges of the heat pipe. We found that the curvature gradient in the evaporation region increases with increasing heat flux magnitude and decreasing pentane concentration. The curvature gradient for the mixture case is larger than for the pure pentane case. The difference between the two cases increases as pentane concentration decreases. Our data showed that the curvature gradient profile within the evaporation section is separated into two regions with the boundary between the two corresponding to the location of a thick, liquid, “central drop” region at the point of maximum internal local heat flux. We found that the curvature gradients at the central drop and on the flat surfaces where condensation begins are one order of magnitude smaller than the gradients in the corner meniscus indicating the driving forces for fluid flow are much larger in the corners.

Two-dimensional mesoscale simulations of saturated pool boiling from rough surfaces. Part I: Bubble nucleation in a single cavity at low superheats

Bubble nucleation, growth and departure from a single cavity on the top of a uniformly hydrophilic heater and a uniformly hydrophobic heater at low superheats are investigated numerically based on a recently developed liquid–vapor phase-change lattice Boltzmann method. A conjugate 2D heat transfer problem, including heat conduction in the heated plate with a finite thickness, is considered in this paper. It is found that bubble nucleation starts in the central part of a hydrophilic cavity and at corners of a hydrophobic cavity. In addition, the bubble departure diameter from the single cavity increases with the increase of the contact angle on a uniform wettability surface. It is also found that there is little effect on bubble behaviors if the cavity depth is small, but there is a sudden jump in bubble departure frequency from a hydrophilic cavity when the cavity depth reaches a critical value, causing the formation of a residual bubble in the hydrophilic cavity. There also exists a critical cavity width, beyond which the bubble departure diameter and bubble departure frequency increase with the increase of cavity width, and therefore enhancing boiling heat flux. The three-phase contact line region exhibits the highest local heat flux and lowest local temperature along the rough heating surface, and its location greatly affects the direction of heat transfer on the vertical side walls of the cavity. The three-phase contact line is pinned at the cavity mouth on a uniformly hydrophilic rough surface while it is expanded to outside of the cavity mouth on a uniformly hydrophobic rough surface. For a mixed wettability rough surface with a hydrophobic cavity on a hydrophilic surface, it is shown that the hydrophobic cavity promotes bubble nucleation at low wall superheats while the hydrophilic surface prevents the forward expansion of the three-phase contact line outside of the cavity mouth.

Microtiter plate tests for segregation of bioluminescent bacteria

It has been recently shown that bioluminescence imaging can be usefully applied to provide new insights into bacterial self-organization. In this work we employ bioluminescence imaging to record images of nutrient rich liquid cultures of the lux-gene reporter Escherichia coli in microtiter plate wells. The images show that patterns of inhomogenous bioluminescence form along the three-phase contact lines. The paper analyzes the dependencies of the average number of luminous aggregates (clouds) on various environmental factors. In particular, our results show that optimal (neutral) pH and high aeration rates determine the highest mean number of clouds, and that spatiotemporal patterns do not form in the pH buffered suspensions. In addition, a sigmoidal (switch-like) dependence of the number of aggregates on the rate of aeration was observed. The obtained bioluminescence imaging data was interpreted by employing the Keller-Segel-Fisher (KSF) model of chemotaxis and logistic growth, adapted to systems of metabolically flexible (two-state) bacteria. The modified KSF model successfully simulated the observed switch-like responses. The results of the microtiter plate tests and their simulations indicate that the segregation of bacteria with different activities proceeds in the three-phase contact line region.

Lattice Boltzmann simulations for surface wettability effects in saturated pool boiling heat transfer

Effects of wettability on saturated pool boiling heat transfer from a smooth superheated substrate, with a finite thickness at constant wall temperatures at the bottom, are investigated based on a recently developed liquid–vapor phase-change lattice Boltzmann method. For a hydrophilic surface, it is shown that bubble departure diameter and bubble departure frequency increase with the increase of contact angle and superheat, and the whole bubble departs from the surface with a waiting period in the ebullition cycle. A microlayer of liquid exists between the bubble and the heated hydrophilic surface and this region exhibits a high local heat flux during bubble growth period. On the other hand, a residual bubble will be left on the surface when bubble departs from a hydrophobic surface and hence no waiting period exists. No microlayer exists on the heated hydrophobic surface, and the three-phase contact line region has the highest local heat flux and lowest local temperature. Time histories of the wall temperature on the top of a hydrophilic substrate and a hydrophobic substrate as well as the associated heat flux are studied in details during the nucleate boiling process. Effects of wettability, superheat and heater size on number of nucleation sites in saturated pool boiling are investigated. Saturated boiling curves (from onset of nucleate boiling to critical heat flux, to transition boiling to stable film boiling) for hydrophilic and hydrophobic heating surfaces are obtained by numerical simulation for the first time.

Assessment of Water Droplet Evaporation Mechanisms on Hydrophobic and Superhydrophobic Substrates

Evaporation rates are predicted and important transport mechanisms identified for evaporation of water droplets on hydrophobic (contact angle ~110°) and superhydrophobic (contact angle ~160°) substrates. Analytical models for droplet evaporation in the literature are usually simplified to include only vapor diffusion in the gas domain, and the system is assumed to be isothermal. In the comprehensive model developed in this study, evaporative cooling of the interface is accounted for, and vapor concentration is coupled to local temperature at the interface. Conjugate heat and mass transfer are solved in the solid substrate, liquid droplet, and surrounding gas. Buoyancy-driven convective flows in the droplet and vapor domains are also simulated. The influences of evaporative cooling and convection on the evaporation characteristics are determined quantitatively. The liquid-vapor interface temperature drop induced by evaporative cooling suppresses evaporation, while gas-phase natural convection acts to enhance evaporation. While the effects of these competing transport mechanisms are observed to counterbalance for evaporation on a hydrophobic surface, the stronger influence of evaporative cooling on a superhydrophobic surface accounts for an overprediction of experimental evaporation rates by ~20% with vapor diffusion-based models. The local evaporation fluxes along the liquid-vapor interface for both hydrophobic and superhydrophobic substrates are investigated. The highest local evaporation flux occurs at the three-phase contact line region due to proximity to the higher temperature substrate, rather than at the relatively colder droplet top; vapor diffusion-based models predict the opposite. The numerically calculated evaporation rates agree with experimental results to within 2% for superhydrophobic substrates and 3% for hydrophobic substrates. The large deviations between past analytical models and the experimental data are therefore reconciled with the comprehensive model developed here.

The effect of three-phase contact line speed on local evaporative heat transfer: Experimental and numerical investigations

In pool boiling or flow boiling devices or e.g. during meniscus evaporation within capillary structures the local heat flux and evaporation rate at the position where the liquid–vapor interface meets the solid wall can be extremely high. This three-phase contact line region is characterized by a thin liquid film with a very low heat resistance. Depending on the application the contact line can move with velocities of several meters per second, either in receding (dewetting) or in advancing (wetting) direction. In this paper, experimental and numerical results on the influence of three-phase contact line speed on the local heat transfer in the contact line region during pool boiling and during meniscus evaporation are presented and analyzed. It is shown that the local heat flux can be one or more orders of magnitude higher than the mean heat flux supplied to the system. This local heat transfer peak is almost independent of the contact line speed in the case of a receding contact line while it significantly increases with contact line speed for an advancing contact line. This behavior could be observed in different evaporation configurations and with different fluids. Experimental and numerical results agree well and allow a characterization of the transient heat transfer phenomena in the contact line region during evaporation.

Discussion notes on “Disjoining pressure of planar adsorbed films”, by J.R. Henderson

Discussion notes on “Disjoining pressure of planar adsorbed films”, by J.R. Henderson

Instability of the three-phase contact region and its effect on contact angle relaxation

Contact angle relaxation was measured for captive air bubbles placed on solid surfaces of varying degrees of heterogeneity, roughness, and stability, in water. The experimental results indicate that both advancing and receding contact angles undergo slow relaxation in these water-air-solid systems, due to instabilities of the three-phase contact line region. It is shown that the advancing contact angle decreases and the receding contact angle increases for many systems over a period of a few hours. Also, examples of reverse progressions are reported. Additionally, in extreme cases, the contact angle oscillates down and up, over and over again, preventing the system from stabilization/equilibration. Four different mechanisms are proposed to explain the contact angle relaxation. These include (i) pinning of the three-phase contact line and its slow evolution; (ii) the formation of microdroplets on the solid surface and their coalescence with the base of the gas bubble, which causes dynamic behavior of the three-phase contact line; (iii) deformation of the solid surface and its effect on the apparent contact angle; and (iv) chemical instability of the solid.