A Level-Set Method for the Direct Numerical Simulation of Particle Motion in Droplet Evaporation

A sharp-interface level-set (LS) method is presented for direct numerical simulation (DNS) of particle motion in droplet evaporation. The LS formulation for liquid–gas flows is extended to liquid–gas–solid flows by treating the moving solid region as a high-viscosity fluid phase. The evaporation effect is accurately implemented by imposing the coupled temperature and vapor fraction conditions at the interface. The LS method is tested through computations of particle sedimentation in single-phase and two-phase fluids. The DNS of particle motion in droplet evaporation demonstrates the pinning phenomena of the liquid–gas–solid contact line.     

Numerical investigation of heat and mass transfer from an evaporating meniscus in a heated open groove

The process of evaporation from a meniscus into air is more complicated than in enclosed chambers filled with pure vapor. The vapor pressure at the liquid–gas interface depends on both of the evaporation and the vapor transport in the gas environment. Heat and mass transport from an evaporating meniscus in an open heated V-groove is numerically investigated and the results are compared to experiments. The evaporation is coupled to the vapor transport in the gas domain. Conjugate heat transfer is considered in the solid walls, and the liquid and gas domains. The flow induced in the liquid due to Marangoni effects, as well as natural convection in the gas due to thermal expansivity and vapor concentration gradients are simulated. The calculated evaporation rates are found to agree reasonably well with experimentally measured values. The convection in the gas domain has a significant influence on the overall heat transfer and the wall temperature distribution. The evaporation rate near the contact lines on either end of the meniscus is high. Heat transfer through the thin liquid film near the heated wall is found to be very efficient. A small temperature valley is obtained at the contact line which is consistent with the experimental observation.     

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.     

Slip and micro flow characteristics near a wall of evaporating thin films in a micro channel

The microscopic liquid flow and heat transfer characteristics near the solid–liquid interface in the evaporating thin film region of a mini channel were investigated based on the augmented Young–Laplace equation and kinetic theory. A physical model using the boundary layer approximation and a constant slip length was developed to obtain the solid–liquid interfacial thermal resistances and interfacial temperatures. The results show that the ordered micro layer and micro flow near the wall reduce the effective liquid superheat and the liquid pressure difference mainly due to the reduced capillary pressure gradient. The solid–liquid interfacial thermal resistances and U‐shaped temperature drops tend to reduce the thin film spreading and heat transfer. The effects of the solid–liquid interfacial thermal resistances on the thin film evaporation outweigh the effects of the thermal conductivity enhancement due to the liquid ordering. The concepts of the micro flow and ordered adsorbed flowing micro layer are clarified to express the Kapitza resistance analytically in terms of the slip length and micro layer thickness. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; 39(7): 460–474, 2010; Published online 3 June 2010 in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/htj.20310     

Effects of functional surface on performance of a micro heat pipe

The effect of a functional surface with the axial ladder contact angle distribution on the thermal performance of a triangular micro heat pipe has been analyzed based on a one-dimensional steady-state model. Compared with the traditional micro heat pipe (MHP) with a uniform contact angle distribution on its surface, the simulation results show that a MHP with a functional surface can remove a greater amount of heat under the same condition. The increase in thermal performance is more obvious with the increase in the ladder difference of the contact angles between the adjacent sections of the MHP. The increased thermal performance associated with the functional surface can be attributed to the increase of the liquid capillary force as well as the no obvious increase of the liquid shearing force provided by the functional surface, which also brings about the increase in condensate mass flow rate through the adiabatic section–evaporation section interface. It is also found that for the traditional MHP with uniform contact angle surface, there is an optimal contact angle leading to the maximum heat input. The deviation of the optimal value will decrease the capillary force and thermal performance of the MHP.     

Physical mechanisms of heat transfer during single bubble nucleate boiling of FC-72 under saturation conditions-I. Experimental investigation

This paper is the first of a two-part study concerning the dynamics of heat transfer during nucleation process of saturated FC-72 liquid. Experimental results discussed in this paper provide new physical insight on the nature of heat transfer events at the nucleation site during the nucleate boiling process. The thermal field underneath a bubble during the boiling of FC-72 was measured with a spatial resolution of 22--40 μm. The time period of activation, area of influence, and magnitude of three different mechanisms of heat transfer active at the nucleation site were determined. These mechanisms consisted of: (1) microlayer evaporation following the rapid bubble expansion, (2) transient conduction due to rewetting of the surface during bubble departure, and (3) microconvection in the region external to the bubble/surface contact area. The area of influence of the transient conduction mechanism was found to be limited to the bubble/surface contact area, with most of the heat transfer occurring prior to the bubble detachment from the surface. The microconvection heat transfer mechanism was localized primarily outside the contact area and was found to be steady in nature. All three mechanisms of heat transfer were found to make significant contributions to the total surface heat transfer. The second part of this study provides the theoretical analysis of the results.     

A microscale model for thin-film evaporation in capillary wick structures

A numerical model is developed for the evaporating liquid meniscus in wick microstructures under saturated vapor conditions. Four different wick geometries representing common wicks used in heat pipes, viz., wire mesh, rectangular grooves, sintered wicks and vertical microwires, are modeled and compared for evaporative performance. The solid–liquid combination considered is copper–water. Steady evaporation is modeled and the liquid–vapor interface shape is assumed to be static during evaporation. Liquid–vapor interface shapes in different geometries are obtained by solving the Young–Laplace equation using Surface Evolver. Mass, momentum and energy equations are solved numerically in the liquid domain, with the vapor assumed to be saturated. Evaporation at the interface is modeled by using heat and mass transfer rates obtained from kinetic theory. Thermocapillary convection due to non-isothermal conditions at the interface is modeled for all geometries and its role in heat transfer enhancement from the interface is quantified for both low and high superheats. More than 80% of the evaporation heat transfer is noted to occur from the thin-film region of the liquid meniscus. The very small Capillary and Weber numbers resulting from the small fluid velocities near the interface for low superheats validate the assumption of a static liquid meniscus shape during evaporation. Solid–liquid contact angle, wick porosity, solid–vapor superheat and liquid level in the wick pore are varied to study their effects on evaporation from the liquid meniscus.     

A numerical investigation on the influence of liquid properties and interfacial heat transfer during microdroplet deposition onto a glass substrate

This work investigates the impingement of a liquid microdroplet onto a glass substrate at different temperatures. A finite-element model is applied to simulate the transient fluid dynamics and heat transfer during the process. Results for impingement under both isothermal and non-isothermal conditions are presented for four liquids: isopropanol, water, dielectric fluid (FC-72) and eutectic tin–lead solder (63Sn–37Pb). The objective of the work is to select liquids for a combined numerical and experimental study involving a high resolution, laser-based interfacial temperature measurement to measure interfacial heat transfer during microdroplet deposition. Applications include spray cooling, micro-manufacturing and coating processes, and electronics packaging. The initial droplet diameter and impact velocity are 80 μm and 5 m/s, respectively. For isothermal impact, our simulations with water and isopropanol show very good agreement with experiments. The magnitude and rates of spreading for all four liquids are shown and compared. For non-isothermal impacts, the transient drop and substrate temperatures are expressed in a non-dimensional way. The influence of imperfect thermal contact at the interface between the drop and the substrate is assessed for a realistic range of interfacial Biot numbers. We discuss the coupled influence of interfacial Biot numbers and hydrodynamics on the initiation of phase change.     

Evaporation heat transfer characteristics of a grooved heat pipe with micro-trapezoidal grooves

A detailed mathematical model predicting the effect of contact angle on the meniscus radius, thin film profile and heat flux distribution occurring in the micro-trapezoidal grooves of a heat pipe has been presented. The model can be used to determine the maximum evaporating heat transfer rate in the evaporator including the effects of disjoining pressure and surface tension. The equation of meniscus radii calculation in the evaporator at given heat load based on the liquid wicks configuration has been put forward. The numerical results show that while the capillary limitation governs the maximum heat transport capability in a grooved heat pipe, the thin film evaporation determines the effective thermal conductivity in a grooved heat pipe. The ratio of the heat transfer through the thin film region to the total heat transfer through the wall to the vapor phase decreases when the contact angle increases. The superheat effects on the heat flux distribution in the thin film region also have been conducted and the results show that the disjoining pressure plays an important role in this region. The current investigation will result in a better understanding of thin film evaporation and its effect on the effective thermal conductivity in a grooved heat pipe.     

Convective Heat Transfer from a Thick Hemispherical Plate during Free Liquid Jet Impingement

Convective heat transfer during free liquid jet impingement on a hemispherical solid plate of finite thickness has been examined. The model included the entire fluid region (impinging jet and flow spreading out over the hemispherical surface) and solid plate as a conjugate problem. Solution was done for both isothermal and constant heat flux boundary conditions at the inner surface of the hemispherical plate. Computations were done for jet Reynolds number (Re _j ) ranging from 500 to 2,000, dimensionless nozzle-to-target spacing ratio (β) from 0.75 to 3, and for various dimensionless plate thicknesse-to-nozzle diameter ratios (b/d _n ) from 0.08 to 1.5. Results are presented for local Nusselt number using water (H₂O), flouroinert (FC-77), and oil (MIL-7808) as working fluids, and aluminum, Constantan, copper, silicon, and silver as solid materials. It was observed that plate materials with higher thermal conductivity maintained a more uniform temperature distribution at the solid–fluid interface. A higher Reynolds number increased the Nusselt number over the entire solid–fluid interface.     

Theoretical model for annular flow condensation in rectangular micro-channels

This study examines the pressure drop and heat transfer characteristics of annular condensation in rectangular micro-channels with three-sided cooling walls. A theoretical control-volume-based model is proposed based on the assumptions of smooth interface between the annular liquid film and vapor core, and uniform film thickness around the channel’s circumference. Mass and momentum conservation are applied to control volumes encompassing the liquid film and the vapor core separately. The model accounts for interfacial suppression of turbulent eddies due to surface tension with the aid of a new eddy diffusivity model specifically tailored to shear-driven turbulent films. The model predictions are compared with experimental pressure drop and heat transfer data for annular condensation of FC-72 along 1 × 1 mm² parallel channels. The condensation is achieved by rejecting heat to a counterflow of water. The data span FC-72 mass velocities of 248–367 kg/m² s, saturation temperatures of 57.8–62.3 °C, qualities of 0.23–1.0, and water mass flow rates of 3–6 g/s. The data are also compared to predictions of previous separated flow mini/micro-channel and macro-channel correlations. While some of the previous correlations do provide good predictions of the average heat transfer coefficient, they fail to capture axial variation of the local heat transfer coefficient along the channel. The new model accurately captures the pressure drop and heat transfer coefficient data in both magnitude and trend, evidenced by mean absolute error values of 3.6% and 9.3%, respectively.     

Interfacial temperature measurements,high-speed visualization and finite-element simulations of droplet impact and evaporation on a solid surface

The objective of this work is to investigate the coupling of fluid dynamics, heat transfer and mass transfer during the impact and evaporation of droplets on a heated solid substrate. A laser-based thermoreflectance method is used to measure the temperature at the solid–liquid interface, with a time and space resolution of 100 μs and 20 μm, respectively. Isopropanol droplets with micro- and nanoliter volumes are considered. A finite-element model is used to simulate the transient fluid dynamics and heat transfer during the droplet deposition process, considering the dynamics of wetting as well as Laplace and Marangoni stresses on the liquid–gas boundary. For cases involving evaporation, the diffusion of vapor in the atmosphere is solved numerically, providing an exact boundary condition for the evaporative flux at the droplet–air interface. High-speed visualizations are performed to provide matching parameters for the wetting model used in the simulations. Numerical and experimental results are compared for the transient heat transfer and the fluid dynamics involved during the droplet deposition. Our results describe and explain temperature oscillations at the drop–substrate interface during the early stages of impact. For the first time, a full simulation of the impact and subsequent evaporation of a drop on a heated surface is performed, and excellent agreement is found with the experimental results. Our results also shed light on the influence of wetting on the heat transfer during evaporation.     

Experimental investigation of water drop evaporation under moist air or saturated vapour conditions

Majority of studies on the drop evaporation phenomena have been realized in air atmosphere environment. Through the present experimental study, we attempt to underline the influence of the gas surrounding the drop during its evaporation in order to give some new physical elements for the modelling of drops or meniscus evaporation. This study has been motivated by the application of two-phase closed systems (heat pipes, loop heat pipes, pulsating heat pipes …), into which liquid and vapour phases are close to the saturation equilibrium state. A silicon wafer substrate, whose roughness does not exceed 3 nm, was selected for the water drop base in order to focus on the gas environment effect on the drop evaporation while reducing the roughness effect. The evaporation of a water drop put on a plane and horizontal silicon surface has been experimentally studied under atmospheric moist air and under saturated vapour conditions at 23 °C. The results show two different behaviours according to surrounding conditions, as well for the contact angle at the equilibrium state, than for the dynamic contact angle during the drop evaporation.     

Non-isothermal Evaporation of Salt Solutions on a Microstructured Surface

Heat transfer of a droplet and layer during evaporation of aqueous solutions of salts has been studied. The behavior of salt solutions on a smooth and microstructured surface is compared here. Evaporation rate of aqueous salt solutions is greater for a microstructured surface than for a smooth wall. The behavior of heat transfer coefficient α can be described by two time regimes: quasi-constant values of α and significant increase in heat transfer at a multiple decrease in the liquid layer height. Measurements made with application of the particle image velocimetry showed that the structured surface increases liquid speed inside the sessile drop. The largest value of the heat transfer coefficient α on the structured surface corresponds to water for the final stage of evaporation. For salt solutions, the heat transfer coefficient is lower than that for water in the entire period of evaporation on the structured surface. The maximal excess (20–30%) of α of the structured wall above the smooth surface corresponds to the maximal height of the liquid layer at the beginning of evaporation. With increasing time, the excess is reduced. A drop of heat transfer intensification with a decrease in the layer height relates to suppression of free convection (a multiple decrease in the average velocity in the drop).     

The experimental and numerical investigation of a grooved vapor chamber

An effective thermal spreader can achieve more uniform heat flux distribution and thus enhance heat dissipation of heat sinks. Vapor chamber is one of highly effective thermal spreaders. In this paper, a novel grooved vapor chamber was designed. The grooved structure of the vapor chamber can improve its axial and radial heat transfer and also can form the capillary loop between condensation and evaporation surfaces. The effect of heat flux, filling amount and gravity to the performance of this vapor chamber is studied by experiment. From experiment, we also obtained the best filling amount of this grooved vapor chamber. By comparing the thermal resistance of a solid copper plate with that of the vapor chamber, it is suggested that the critical heat flux condition should be maintained to use vapor chamber as efficient thermal spreaders for electronics cooling. A two-dimensional heat and mass transfer model for the grooved vapor chamber is developed. The numerical simulation results show the thickness distribution of liquid film in the grooves is not uniform. The temperature and velocity field in vapor chamber are obtained. The thickness of the liquid film in groove is mainly influenced by pressure of vapor and liquid beside liquid–vapor interface. The thin liquid film in heat source region can enhance the performance of vapor chamber, but if the starting point of liquid film is backward beyond the heat source region, the vapor chamber will dry out easily. The optimal filling ratio should maintain steady thin liquid film in heat source region of vapor chamber. The vapor condenses on whole condensation surface, so that the condensation surface achieves great uniform temperature distribution. By comparing the experimental results with numerical simulation results, the reliability of the numerical model can be verified.     

Comprehensive experimental and theoretical study of fluid flow and heat transfer in a microscopic evaporating meniscus in a miniature heat exchanger

The complex physicochemical phenomena occurring in the contact line region of an evaporating meniscus are described using a unique combination of high-resolution experimental data and three complementary models. The following were used: (1) high-resolution experimental liquid profile data (thickness, slope, curvature and curvature gradient) to obtain the pressure gradient in the evaporating pentane meniscus in a vertical constrained vapor bubble (VCVB); (2) macroscopic outside surface temperature profile data; (3) a finite element model to obtain the two-dimensional heat conduction profile in the solid substrate wall (macro-model) and the solid–liquid interfacial temperature profile in the evaporating meniscus region; (4) a continuum fluid-dynamics model (micro-model) to obtain the liquid–vapor interfacial temperature, mass flow rate, Marangoni stresses, and evaporative heat flux profiles along the length of the evaporating meniscus; and (5) the Kelvin–Clapeyron model to obtain the vapor temperature profile (liquid–vapor interfacial temperature jump) in the evaporating meniscus region.The retarded dispersion constant and high-resolution thickness, slope, curvature and curvature gradient profiles were obtained from the experimental reflectivity profiles. There was a substantial increase in the measured curvature in the transition region, where the evaporation rate and flux are a maximum. To obtain numerical closure between the three complementary models, the continuum fluid dynamics model (micro-model) required slip at the solid–liquid interface to support the observed high mass flow rates in the evaporating pentane meniscus. Mass flow rates due to Marangoni stresses, capillary pressure and disjoining pressure are compared. Depending on the liquid thickness, Marangoni stresses can either enhance or hinder fluid flow towards the contact line for the evaporating pure pentane meniscus. Due to the high heat removal rate by the evaporating pentane meniscus in the transition region, dips in the vapor, liquid–vapor and solid–liquid interface temperature were obtained. The results demonstrate and describe the sensitivity and complexity of the phase change process in micro-regions.     

Numerical Simulation of Evaporation-Induced Particle Line Formation on a Moving Substrate

Numerical simulations are performed for evaporation-induced particle line formation on a moving substrate by solving the conservation equations of mass, momentum, energy, vapor concentration, and particle concentration in the liquid–gas phases. The liquid–gas interface and the liquid–gas–solid contact line are tracked by using a level-set method, which is modified to include the effects of contact line, phase change, and particle concentration. The numerical results for liquid evaporation and particle deposition in confined convective coating between two parallel plates showed that the substrate velocity is a key parameter determining the particle deposition pattern and the particle line formation can be controlled by varying the substrate velocity.     

Internal flow in evaporating droplet on heated solid surface

This work numerically studies the evaporation process of a liquid droplet on a heated solid surface using a comprehensive model. The internal flow within the evaporating liquid droplet is elucidated, while considering the effects of buoyancy force, thermocapillary force, and viscous resistance. The evaporation process is modeled by simultaneously solving the Navier–Stokes equations and energy equation for the liquid domain and the heat conduction equation for the solid domain, while assuming the liquid–vapor interface is a free surface. Three dimensionless parameters are utilized to describe the contribution of individual driving forces to internal flow. Evolutions of the thermal and internal flows during evaporation are discussed. The volume evolution and experimental data are in good agreement.     

A Level-Set Method for Analysis of Particle Motion in an Evaporating Microdroplet

A sharp-interface level-set (LS) method is presented for computing particle motion in an evaporating microdroplet. The LS formulation for incompressible two-phase flow is extended to include the effects of evaporation, mass transfer, heat transfer, and dynamic contact angles. A numerical technique for the conservation of particle concentration is incorporated into the LS method, and calculation procedures are also developed and tested for reducing the numerical errors caused in the computation of interface curvature and liquid–gas velocity jump. The improved LS method is applied to the simulation of particle distribution in microdroplet evaporation on a solid surface.     

Contact line behavior for a highly wetting fluid under superheated conditions

The contact line behavior of a highly wetting, dielectric liquid (FC-72) droplet under superheated conditions is investigated. Relatively large macroscopic contact angles atypical of FC-72 droplets were observed under superheated conditions. The addition of a non-condensable dissolved gases in the system increased the contact angle at a given superheat. Numerical simulations of the transport phenomena near the microscopic three phase contact line were performed that show how the macroscopic contact angle is related to the superheat and thickness of the adsorbed film ahead of the contact line. The use of a macroscopic contact angle that is a function of superheat in established models for bubble departure diameter and the onset of nucleate boiling enhanced the ability of those models to describe the behavior of highly wetting fluids.