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.     

A molecular dynamics investigation on evaporation of thin liquid films

Understanding of evaporation process of thin liquid film is important for studying heat transfer near the triple-phase contact line. In the present work, equilibrium molecular dynamics (EMD) and non-equilibrium molecular dynamics (NEMD) were employed to investigate the evaporation of thin liquid films in a nanoscale triple-phase system. The simulation domain was a cuboid, which consisted of an upper and a lower platinum wall, with argon fluid in between. The solid walls were first set at the same temperature and EMD was employed to achieve an equilibrium state. Then the walls were set at different temperatures and NEMD was employed to simulate the non-equilibrium state. Evaporation and condensation of thin liquid films were observed. The evolution of the film thickness as well as the net mass flux was obtained for the evaporating thin film. Interfacial accommodation coefficient was analyzed and the measured evaporation mass flux was compared with Hertz–Knudsen–Schrage equation which is based on kinetic theory of gases (KTG). Non-evaporating layer due to strong intermolecular forces was obtained and compared with theoretical models.     

Evaporative heat transfer characteristics of a water spray on micro-structured silicon surfaces

Experiments were performed to evaluate the evaporative heat transfer characteristics of spray cooling of water on plain and micro-structured silicon surfaces at very low spray mass fluxes. The textured surface is made of an array of square micro-studs. It was found that the Bond number of the microstructures is the primary factor responsible for the heat transfer enhancement of evaporative spray cooling on micro-structured silicon surface in the present study. A qualitative study of evaporation of a single water droplet on plain and textured silicon surface shows that the capillary force within the microstructures is effective in spreading the deposited liquid film, thus increasing the evaporation rates. Four distinct heat transfer regimes, which are the flooded, thin film, partial dryout, and dryout regimes, were identified for evaporative spray cooling on micro-structured silicon surfaces. The microstructures provided better cooling performance in the thin film and partial dryout regime and higher liquid film breakup heat flux, because more water was retained on the heat transfer surface due to the capillary force. Heat transfer coefficient and temperature stability deteriorated greatly once the liquid film breakup occurred. The liquid film breakup heat flux increases with the Bond number. Effects of surface material, system orientation and spray mass flux were also addressed in this study.     

Effects of radius and heat transfer on the profile of evaporating thin liquid film and meniscus in capillary tubes

The physical and mathematical models are established to account for the formation of evaporating thin liquid film and meniscus in capillary tubes. The core vapor flow is due to gradient of vapor pressure, which is mainly contributed by the shear stress at vapor-liquid interface. The liquid film flow is owing to gradients of capillary pressure and disjoining pressure. The heat transfer is composed of liquid film conduction and evaporation at vapor-liquid interface. The mass balance of vapor flow is considered to obtain the vapor velocity, this can evade directly solving the rarefied gas velocity field.In regard to the capillary tubes of micron scale, the calculation results show that, the bigger the inner radius or the smaller the heat flow, the longer the evaporating interfacial region will be. There only exists meniscus near the wall, and nearby the axial center is flat interface. While as to the capillary tubes of scale about 100 μm, the evaporating interfacial region will increase with heat flux. Compared with capillaries of micron scale, the meniscus region will extend to the center of capillary axis. These can be tentatively explained as strong influence of the thin liquid film.For the capillary tubes of radius about 100 μm, the experimental results indicate that the apparent contact angles and meniscus profiles can almost coincide with those of the theoretical values.     

Capillary-assisted flow and evaporation inside circumferential rectangular micro groove

To introduce capillary-assisted evaporation from micro-size fields to normal-size fields, an inclined circumferential micro groove with rectangular cross sections is investigated analytically and a systematic mathematical model is developed. The model is composed of five sub-models: a natural convection model, a liquid axial flow model, a heat transfer model in and below the intrinsic meniscus, an evaporation thin film region model and an adsorbed region model. In this model, for the extended meniscuses formed at groove cross sections, both the intrinsic meniscus and evaporation thin film region are considered when calculating heat absorbing. Through solving the model, the influences of dynamic contact angle on the heat absorbing in the intrinsic meniscus and evaporation thin film region are investigated. Moreover, the factors affecting the whole-groove equivalent heat transfer coefficient have been investigated.     

Effects of inlet conditions on film evaporation along an inclined plate

The evaporation of falling water liquid film in air flow is used in different solar energy applications as drying, distillation and desalination, and desiccant systems. The good understanding of the hydrodynamics and heat exchange in falling liquid film and gas flow, with interfacial heat and mass transfer, can be applied in improving solar systems performance. The solar system performance is dependent on the operating conditions, system conception and related to several physical parameters, where the effects of some of these parameters are not completely clarified. In the present numerical study, we examine the effects of inlet conditions on the evaporation processes along the gas–liquid interface. The liquid film streams over an inclined plate subjected to different thermal conditions. Liquid and gas flows are approached by two coupled laminar boundary-layers. The numerical solution is obtained by utilizing an implicit finite-difference box method. In this analysis an air–water system is considered and the coupled effects of inclination, inlet liquid mass flow rate and gas velocity are examined. The results show that, for imposed heat flux or uniform wall temperature, the effect of inclination is highly dependent on the liquid mass flow rate and gas velocity. An increase in the liquid mass flow rate causes an enhancement of the effect of inclination on the heat and mass transfer. The inclination affects the heat and mass transfer, especially at lower gas velocities. In the range of inclination angles of 0–10°, an increase in the inclination improves the evaporation by increasing the vapor mass flow rate. The maximum effect of inclination is nearly achieved at an inclination angle of 10°.     

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.     

A sharp-interface level-set method for analysis of Marangoni effect on microdroplet evaporation

A level-set method is presented for computation of microdroplet evaporation including not only the effects of heat and mass transfer, phase change and contact line dynamics but also the Marangoni effect, which is a key parameter affecting the internal flow of the droplet and the particle deposition pattern. A sharp-interface formulation of the Marangoni force is derived and tested for two-phase Marangoni convection in a cavity. The computed results show good convergence in both the liquid and gas regions and are in excellent agreement with the analytical solutions. The level-set formulation is applied to microdroplet evaporation on a solid surface to investigate the Marangoni effect.     

Contact angles and interface behavior during rapid evaporation of liquid on a heated surface

Photographic observations of the boiling phenomena have played an important role in gaining insight into the boiling mechanism. This paper presents a brief historical review of the available literature on the photographic studies in pool and flow boiling. This is followed by the results of the photographic studies conducted in the authors' laboratory on liquid droplets impinging on a heated surface. Liquid-vapor interface and contact line movements are observed through a high speed camera at high resolution. The effect of surface roughness and surface temperature on dynamic advancing and receding contact angles has been studied. In addition, the effects of rapid evaporation on advancing and receding contact angles, liquid-vapor interface motion, and the dryout front propagation have been investigated.     

Effects of film evaporation on laminar mixed convection heat and mass transfer in a vertical channel

A numerical study of finite liquid film evaporation on laminar mixed convection heat and mass transfer in a vertical parallel plate channel is presented. The influences of the inlet liquid mass flow rate and the imposed wall heat flux on the film vaporization and the associated heat and mass transfer characteristics were examined for air-water and air-ethanol systems. Predicted results obtained by including transport in the liquid film are contrasted with those where liquid film transport is neglected, showing that the assumption of an extremely thin film made by Tsay and Yan (Wärme- und Stoffübertragung 26, 23–31 (1990)) is only valid for a system with a small liquid mass flow rate. Additionally, it is found that the heat transfer between the interface and gas stream is dominated by the transport of latent heat associated with film evaporation. The magnitude of the evaporative latent heat flux may be five times greater than that of sensible heat flux.     

Experimental evidences of distinct heat transfer regimes in pulsating heat pipes (PHP)

Various experiments were conducted on two full-size pulsating heat pipes (PHP) which differed from their diameter, number of turns, and working fluid. The analysis of the experimental results showed two kind of operating curves (overall thermal resistance vs. heat rate): for low heat fluxes, the curve is irregular and the PHP performance is sensitive to the orientation. For high heat fluxes, the operating curve is smooth and independent from the orientation. To contribute to the analysis of these results, experiments were conducted at the scale of a single branch of a PHP. An oscillating motion was imposed to a single liquid plug surrounded by two vapour slugs in a capillary tube and high speed visualizations were performed. The test section was either adiabatic or heated. The adiabatic experiments brought to the fore the importance of dynamic contact angles in the flow and the dissymmetry between the advancing and receding contact angle. The non-adiabatic experiments showed that at low flux, the flow is disturbed by bubble nucleation, while at high heat flux, the main heat transfer mechanism is thin film evaporation, with a completely different thermal and hydrodynamic behaviour.     

Effect of surface wettability and electric field on transition of film boiling to nucleate boiling

Abstract

The phenomena of liquid–solid contact during film boiling due to the effect of surface-wettability have been focused in the present study. The numerical simulations during film boiling exhibit the collapse of vapor layer when the surface-wettability is sufficiently high, that is, for the hydrophilic surface. Vapor film collapse results in contact of liquid with the heated surface, which transforms the boiling mode more toward the nucleate regime. The contact area of liquid increases with time. However, such transition is not observed in the case of hydrophobic surface or the surface with higher contact angles. When a sufficiently strong electric field is applied across the liquid-vapor interface, the vapor film collapses and results in similar transition from film boiling to nucleate boiling. The required intensity of electric field at which the vapor film collapses increases with the increase in surface-superheat.     

Lateral wetting angle of falling film in dense fluid

An investigation of the wetting ability of a liquid-falling film on vertical steel and glass surfaces is performed by measuring the thickness and the width of the water falling film at 313 K up to 27 MPa. An attempt to reconstruct the two-dimensional cross-section of the falling film was made. The cross-section of the falling film is assumed to have the shape of a circular segment.The falling film wetting angle is compared with the sessile drop contact angle. The sessile drop contact angle represents the upper limit of the film wetting angle. A continuous increase in the mass flow at a constant pressure causes the spreading of the film. This happens when the force balance between the interfacial tensions and the dynamic forces, which deform the film geometry, is exceeded. However, if the pressure increases, the wettability goes down. This is partly due to the accumulation of liquid mass, which is caused by a larger buoyancy.The critical mass flow, that is, the minimum mass flow needed to guarantee a wide covering film is reported. The disintegration point of a liquid film is directly affected by its wettability.     

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.     

Falling film evaporation of ternary mixture under three different modes of heating

This numerical study deals with heat and mass transfer by evaporation under mixed convection in three different configurations of a ternary liquid film in a vertical channel. The ternary liquid mixture water-methanol-benzene falls along the right plate of channel while the other plate is kept thermally insulated. In the first configuration, a heat flux density is applied to the wall carrying the trickle film, while in the other configurations this same amount of heat is used to preheat the liquid film or the air at the inlet of the channel. The implicit finite difference scheme is used to solve the system of equations in both liquid and vapor phases. According to this study, it was observed that the evaporation efficiency is high when the mass fraction of volatile components is high or in the preheating state of ternary film.     

Numerical investigation on the evaporation of droplets depositing on heated surfaces at low Weber numbers

The evaporation of water droplets, impinging with low Weber number and gently depositing on heated surfaces of stainless steel is studied numerically using a combination of fluid flow and heat transfer models. The coupled problem of heat transfer between the surrounding air, the droplet and the wall together with the liquid vaporisation from the droplet’s free surface is predicted using a modified VOF methodology accounting for phase-change and variable liquid properties. The surface cooling during droplet’s evaporation is predicted by solving simultaneously with the fluid flow and heat transfer equations, the heat conduction equation within the solid wall. The droplet’s evaporation rate is predicted using a model from the kinetic theory of gases coupled with the Spalding mass transfer model, for different initial contact angles and substrate’s temperatures, which have been varied between 20–90° and 60–100 °C, respectively. Additionally, results from a simplified and computationally less demanding simulation methodology, accounting only for the heat transfer and vaporisation processes using a time-dependent but pre-described droplet shape while neglecting fluid flow are compared with those from the full solution. The numerical results are compared against experiments for the droplet volume regression, life time and droplet shape change, showing a good agreement.     

Thermal protection with liquid film in turbulent mixed convection channel flows

In this numerical study, a channel flow of turbulent mixed convection of heat and mass transfer with film evaporation has been conducted. The turbulent hot air flows downward of the vertical channel and is cooled by the laminar liquid film on both sides of the channel with thermally insulated walls. The effect of gas–liquid phase coupling, variable thermophysical properties and film vaporization are considered in the analysis. In the air stream, the k–ε turbulent model has been utilized to formulate the turbulent flow. Parameters used in this study are the mass flow rate of the liquid film B, Reynolds number Re, and the free stream temperature of the hot air T_o. Results show that the heat flux was dramatically increases due to the evaporation of liquid water film. The heat transfer increases as the mass flow rate of the liquid film decreases, while the Reynolds number and inlet temperature increase, and the influences of the Re and T_o are more significant than that of the liquid flow rate. It is also found that liquid film helps lowering the heat and mass transfer rate from the hot gas in the turbulent channel, especially at the downstream.     

Mixed convection heat transfer enhancement through film evaporation in inclined square ducts

The investigation of mixed convection heat transfer enhancement through film evaporation in inclined square ducts has been numerically examined in detail. The main parameters discussed in this work include the inclined angle, the wetted wall temperature and the relative humidity of the moist air mixture. The numerical results of the local friction factor, Nusselt number and Sherwood number are presented for moist air mixture system. Attention was particular paid to the effects of latent heat transport on the heat transfer enhancement. Results show that the latent heat transport with film evaporation augments tremendously the heat transfer rate. The heat transfer rate can be enhanced to be 10 times of that without mass transfer, especially for a system with a lower temperature. Besides, better heat and mass transfer rates related with film evaporation are found for case with a higher wetted wall temperature. The increase in the relative humidity of moist air in the ambient causes the decrease in heat transfer enhancement.     

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.     

Shear-driven flows of locally heated liquid films

This paper considers the flow of a liquid film sheared by gas flow in a channel with a heater placed at the bottom wall. A one-sided 2D model is considered for weakly heated films. The heat and mass transfer problem is also investigated in the framework of a two-sided model. The exact solution to the problem of heat transfer is obtained for a linear velocity profile. The double effect of Marangoni forces is demonstrated by the formation of a liquid bump in the vicinity of the heater’s upper edge and film thinning in the vicinity of the lower edge. The criterion determining the occurrence of “ripples” on the film surface upstream from the bump is found. Numerical analysis reveals that evaporation dramatically changes the temperature distribution, and hence, thermocapillary forces on the gas–liquid interface. All transport phenomena (convection to liquid and gas, evaporation) are found to be important for relatively thin films, and the thermal entry length is a determining factor for heaters of finite length. The thermal entry length depends on film thickness, which can be regulated by gas flow rate or channel height. The influence of the convective heat transfer mechanism is much more prominent for relatively high values of the liquid Reynolds number. The liquid–gas interface Biot number is shown to be a sectional-hyperbolic function of a longitudinal axis variable. Some qualitative and quantitative comparisons with experimental results are presented.