Fingering instability of partially wetting evaporating liquids

A numerical study of the fingering instability of the leading edge of a film of evaporating partially wetting liquid flowing down an inclined solid substrate is presented. The effects of capillarity, gravity, disjoining pressure, and evaporation are included in the formulation of our lubrication-type model. The disjoining pressure is assumed to be a linear combination of two components to account for both van der Waals forces and electrostatic effects. Consistent with previously published results, evaporation has a stabilizing effect on fingering instability and can completely suppress the instability if the evaporation number, a nondimensional measure of evaporation intensity, is above a critical value. The critical evaporation number decreases as the inclination angle is decreased. Increasing the apparent contact angle by suitable changes in the disjoining pressure parameters, has a destabilizing influence on the contact line. Also investigated is the length of the fingers in the regime when the instability develops, and it is found that this length decreases as the evaporation number is increased.     

The relation of steady evaporating drops fed by an influx and freely evaporating drops

We discuss a thin film evolution equation for a wetting evaporating liquid on a smooth solid substrate. The model is valid for slowly evaporating small sessile droplets when thermal effects are insignificant, while wettability and capillarity play a major role. The model is first employed to study steady evaporating drops that are fed locally through the substrate. An asymptotic analysis focuses on the precursor film and the transition region towards the bulk drop and a numerical continuation of steady drops determines their fully non-linear profiles. Following this, we study the time evolution of freely evaporating drops without influx for several initial drop shapes. As a result we find that drops initially spread if their initial contact angle is larger than the apparent contact angle of large steady evaporating drops with influx. Otherwise they recede right from the beginning.     

Influence of fluorinated self-assembled monolayer on wetting dynamics during evaporation of refrigerant–oil mixture on metal surface

Reducing wettability of a metal surface is a promising method for enhancing boiling heat transfer of refrigerant–oil mixture on the metal. As fluorinated self-assembled monolayer (F-SAM) coating is effective for wettability reduction, its influence on wetting dynamics including meniscus shape, contact angle, contact line velocity and rising liquid height during evaporation of refrigerant–oil mixture on metal surface were experimentally investigated. The refrigerant–oil mixture was prepared by R141b and NM56, the oil mass fraction ranged from 0 to 10 wt%, and the surface roughness ranged from 0.028 to 1.166 µm. The results show that during evaporation of refrigerant–oil mixture, the presence of F-SAM changes the evaporation mode to be constant contact line velocity followed by both constant contact angle and contact line velocity, while decreases the rising liquid height. The results suggest that larger surface roughness and higher oil mass fraction are preferred when using F-SAM to reduce surface wettability.     

Vapor-Liquid Steady Meniscus at a Superheated Wall: Asymptotics in an Intermediate Zone Near the Contact Line

The study concerns steady configurations of a perfectly wetting liquid in contact with its pure vapor and a superheated substrate/wall maintained at a constant temperature. Despite the perfect wetting, the system is characterized by a finite apparent contact angle formed at a microscale, within a steady microstructure of the contact line, the finiteness owing itself to an actually dynamic situation caused by the evaporation process. The angle is assumed to be small here, which is the case for sufficiently small superheats. When macroscopically treating a steady meniscus, one typically implies that the wall is met at the contact angle given by the microstructure. This remains somewhat an intuitive, heuristic approach unless a more rigorous asymptotic matching is carried out between the meniscus and the microstructure, which is accomplished in the present paper by studying an intermediate zone connecting these two regions. The analysis, based upon a standard one-sided planar model of an evaporating liquid layer in the lubrication approximation, confirms the validity of the mentioned approach. A possible uncertainty in the definition of the contact angle is shown to be small given that the macroscopic curvature (i.e. that of the meniscus and of the wall) is small on the scale of the contact line microstructure.     

A new experiment for investigating evaporation and condensation of cryogenic propellants

Passive and active technologies have been used to control propellant boil-off, but the current state of understanding of cryogenic evaporation and condensation in microgravity is insufficient for designing large cryogenic depots critical to the long-term space exploration missions. One of the key factors limiting the ability to design such systems is the uncertainty in the accommodation coefficients (evaporation and condensation), which are inputs for kinetic modeling of phase change.A novel, combined experimental and computational approach is being used to determine the accommodation coefficients for liquid hydrogen and liquid methane. The experimental effort utilizes the Neutron Imaging Facility located at the National Institute of Standards and Technology (NIST) in Gaithersburg, Maryland to image evaporation and condensation of hydrogenated propellants inside of metallic containers. The computational effort includes numerical solution of a model for phase change in the contact line and thin film regions as well as an CFD effort for determining the appropriate thermal boundary conditions for the numerical solution of the evaporating and condensing liquid. Using all three methods, there is the possibility of extracting the accommodation coefficients from the experimental observations. The experiments are the first known observation of a liquid hydrogen menisci condensing and evaporating inside aluminum and stainless steel cylinders. The experimental technique, complimentary computational thermal model and meniscus shape determination are reported. The computational thermal model has been shown to accurately track the transient thermal response of the test cells. The meniscus shape determination suggests the presence of a finite contact angle, albeit very small, between liquid hydrogen and aluminum oxide.     

Effects of nonuniform heating and thermocapillarity in evaporating films falling down an inclined plate

Summary. The dynamics of a thin evaporating liquid film falling down an inclined plate is studied in the cases of both uniformly and nonuniformly heated plates. The film flow is influenced by gravity, mean surface tension, thermocapillary force and mass loss. The dynamics of the two-dimensional evaporating film is studied by the use of long-wavelength theory. Numerical solution of the evolution equation indicates that the evaporation has a strong stabilizing effect on the film instability and that a sequence of instability, stability and then instability of the falling film during its evaporation exists. The effect of nonuniform heating is dominant prior to film disappearance and it enforces film rupture. Due to the joint action of thermocapillarity and evaporating mass loss, the film evolution exhibits the formation of multi-hump structures, the downstream propagation of which is suppressed. When the nonuniformities in the imposed temperature differences are increased, large deformations of the liquid-vapor interface occur that lead to an enhancement of the heat transfer processes.     

The Effect of Wave Formation and Wetting Angle on the Thermocapillary Breakdown of a Falling Liquid Film

An experimental investigation is performed of the breakdown of a liquid film flowing down a vertical plate with a heater sized 150×150 mm. The main parameters which are varied in the experiment are the Reynolds number Re = 0.47 to 331 and the heat flux q = 0 to 1.92 W/cm². It is found that the effect of the heat flux on the wave motion of the liquid film causes the formation of a jet flow. Dry spots are formed in the region of thin film between the jets. For the purpose of investigating the effect of wave formation on the film breakdown, the distance between the nozzle and heater is varied from 41.5 to 200 mm. It is found that the distance between the nozzle and heater defines the hydrodynamics of the liquid at relatively low heat fluxes, but has no appreciable effect on the heat flux at which the film breakdown occurs. Different working liquids and coatings of the working surface are used in the experiments to investigate the effect of the wetting angle on the film breakdown. The equilibrium wetting angle is measured by the "bubble" method. No effect of the equilibrium wetting angle on the nonisothermal breakdown of the film was revealed.     

Condensation of steam on a vertical tube in a granulated material

The heat transfer enhancement was studied during condensation of steam on a chilled vertical surface of a tube packed into a granulated material with different contact angles of wetting. The dimensionless values of heat transfer at condensation on a surface in filling, obtained for a vertical tube in the range of Reynolds numbers from 70 up to 400, exceed Nu* values for a smooth tube by the factor of 2–3. The intensification of heat transfer on a vertical tube, housed in a granulated layer, is conditioned by the several interdependent phenomena: 1 — capillary ascent of some liquid near the meniscuses, and as a consequence, reduction of the mean film thickness; 2 — burble of a film at the points of sphere contact with a surface of condensation at Re>10; 3 — removal of some film liquid by a granulated layer; accompanied by simultaneous film burble at the points of sphere contact with a cooling surface at Re>83. Results of the current research can be used for the development of heat exchanging devices under the conditions of microgravitation.     

Marangoni-induced deformation of evaporating liquid films on composite substrates

Marangoni convection plays an important role in hydrodynamics of evaporating liquid films and sessile drops. Evaporation of liquid films induces unsteady nonuniform temperature distribution across the liquid layer and in a substrate. If the substrate is composed of parts with different thermal properties, the interface temperature distribution becomes non-uniform, leading to appearance of Marangoni stresses, convective vortices, and film deformation. In this article, a model describing evaporation, Marangoni effect and interface dynamics of liquid films on composite substrates is developed. The film dynamics is described in the framework of long-wave theory. The unsteady heat conduction in the substrate is described using the Laplace transform method for semi-infinite substrates and using the separation of variables technique for substrates of finite thickness. The non-uniformity of substrate thermal properties has a pronounced effect on film dynamics.     

Heat transfer and wave characteristics of a binary freon film flowing over a three-dimensional textured surface

The results of the study of heat transfer, crisis phenomena, and wave characteristics of laminar-wavy liquid films falling over a vertical three-dimensional texture surface have been considered. The R21/R114 freon mixture is served as a working fluid. Some peculiarities of heat transfer, hydrodynamics, and development of crisis phenomena in a binary liquid film falling over heat-releasing surfaces of different geometry have been revealed. The dependence of the heat-transfer coefficient on the flow rate for a three-dimensional texture surface in the regime of evaporation is shown to be similar to the dependence for a smooth surface with slightly intensified heat transfer in the region of inlet film Reynolds numbers of 100–500. The heat transfer coefficients of nucleate boiling on the studied types of structured surfaces are much lower than for a smooth tube. In the regime of undeveloped nucleate boiling, the critical heat flux for all surface types is deter-mined by the dependence obtained by considering the appearance of the heat transfer crisis in an evaporating wave liquid film.     

Bubble behaviors in subcooled boiling of wetting surface under low gravity

Stainless steel plate with 30mm in length, 1 mm in width and 0.1 mm in thickness is employed for a heating surface in subcooled quasi-pool boiling of water under low gravity performed by a parabolic flight. Testing liquid subcooling is about 10K at atmospheric pressure. The wetting heating surfaces are coated with ceramics materials which have been developed by a certain glass company. DC power is applied directly into the test heating surface and the bubble behaviors are observed by a high-speed video camera. Contact angle of water droplet is about 77–96 degree for the stainless surface and 30 degree or less for the wetting surface. In the ground experiment, the size of detaching bubbles from the wetting surface is smaller than those of stainless surface and the detaching period is shorter at same heating power. The burnout heat fluxes of wetting surfaces are about 50 percent higher those of stainless surfaces. In the low gravity experiment, DC power is applied into the surface at 10 second before start of low gravity and increases slightly until burnout. A single large bubble grows on the stainless surface and finally, the surface is burned out in a short period. For wetting surface, several large coalescing bubbles appear and they move rapidly on the surface, then one of the large bubbles grows and the burnout occurs. The burnout heat fluxes are higher than those of stainless surface. The wetting ceramics surface is considered to accelerate the liquid supply and the bubble moving.     

Asymmetric distribution of falling film solution flowing on hydrophilic horizontal round tube

A two-dimension two phase flow model was established to simulate the falling film flow of LiBr solution on a horizontal hydrophilic tube with different solution sprinkle density and tube surface wettability, and the latter has been an overlook factor. The transient characteristics of solution spreading as well as steady film thickness were analyzed. The results show that a continuous film can only be obtained at sufficiently greater sprinkle density with real surface wettability, the liquid coverage of tube surface increases with the increase of sprinkle density or the decrease of static contact angle. The obvious asymmetric distributions of film thickness and film velocity over the horizontal tube surface are demonstrated in a steady state. The thinnest film thickness or maximum film velocity takes place at circumferential angle around 120°. A modified Nusselt equation for predicting the film thickness is suggested and verified by available both simulation and experimental data.     

Evaporation heat and mass transfer in natural convection pipe flow

Abstract

A numerical analysis has been performed to examine film evaporation on natural convection heat and mass transfer in a vertical pipe. Coupled governing equations for liquid film and induced gas flow were simultaneously solved by the implicit finite difference method. Results for interfacial heat and mass transfer coefficients are specifically presented for ethanol film and water film vaporization. The predicted results indicate that the heat transfer from gas‐liquid interface to the gas flow is predominated by the transport of latent heat in association with film evaporation. The results are also contrasted with those of zero film thickness and show that the assumption of extremely thin film thickness made by Chang et al. [5] and Yan and Lin [19] is only valid for a system with a low liquid Reynolds number Re _l1. But as the liquid Reynolds number is high, the assumption becomes inappropriate.     

Wetting and evaporation behaviors of molten Mg–Al alloy drops on partially oxidized α-SiC substrates

The wetting and evaporation behaviors of Mg–Al alloys over a full composition range on partially oxidized polycrystalline α-SiC substrates were studied in a flowing Ar atmosphere using an improved sessile drop method. The time dependence of the changes in contact angle and drop geometry was monitored and representative wetting stages were identified. The initial contact angles at 1173 K were 100° for pure Al and 76° for pure Mg, with the maximum value of 106° for the 7.6 mol.% Mg–Al alloy. The interfacial reaction and the evaporation of Mg led to the decrease in the apparent contact angle in the spreading stage and their respective contribution was evaluated. After the pinning of the triple line, the decrease in the contact angle resulted from the diminishing drop volume as a consequence of the Mg evaporation. The effects of Mg concentration on the wetting and evaporation behaviors were discussed. A mechanism for the time-dependent diminishing drop volume was proposed in light of the competition between the Mg evaporation and its diffusion from the drop bulk to the surface. Finally, the interfacial reaction was analyzed based on thermodynamic considerations.     

Study of Evaporative Convection in an Open Cavity under Shear Stress Flow

When a layer of volatile liquid is exposed to a shear flow of inert gas, thermal patterns, in the form of interfacial ripples and bulk plumes, are created by the combined action of evaporative, shear-driven and surface-tension-driven instabilities. The topology of the interfacial thermal patterns is mainly influenced by the geometry of the evaporating surface, the thickness of the evaporating layer, the intensity of the shear flow and by the physic-chemical properties of the working fluid. In this paper, by means of numerical simulations, we focused our attention on the dynamics of the interfacial thermal patterns for different working fluids and thicknesses of the volatile liquid layer. This study has been performed in the frame of the ESA sponsored Space Program on heat and mass transfer CIMEX-1. The choice of the fluids—ethyl alcohol and FC72 (n-perfluorohexane)—the reference values for the inert gas flow rate, the thickness of the liquid layer as well as the geometrical features of the computational domain correspond exactly to the ones foreseen for the CIMEX-1 experiment. However, the main conclusions can be considered of more general validity.     

Effect of Surface Excess Energy Transport on the Rupture of an Evaporating Film

In most of existing works on the instabilities of an evaporating film, the energy boundary condition only takes into account contributions of the evaporation latent heat and the heat conduction in the liquid. We use a new generalized energy boundary condition at the evaporating liquid-vapor interface, in which the contribution of the transport of the Gibbs excess energy is included. We have derived the long-wave equations in which the thickness of film and the interfacial temperature are coupled to describe the dynamics of an evaporating thin film. The results of our computation show that the transport of the Gibbs excess internal energy delay the rupture of thin films due to van de Waals force, evaporating effect and vapor recoil.     

The wave characteristics of a nonisothermal film of liquid under conditions of jets forming on its surface

An eight-channel capacitive sensor is used for the first time, which enables one to investigate the dynamics of three-dimensional wave flows and the variation of the transverse profile of a nonisothermal film of liquid during formation of jets. Measurements are performed of the wave characteristics of the flow of a film of water on a vertical plate with a heater 150 × 150 mm in size. During the heating of falling liquid, the thermocapillary forces cause the formation of jets and of a thin film between them. The film thickness and wave amplitude in the interjet region decrease with increasing heat flux. Two ranges of the effect of the heat flux on the characteristics of wave flow are identified. Under conditions of low heat fluxes, the film flow hardly differs from isothermal. Under significant heat loads, an intensive formation of jets occurs. Three-dimensional waves propagate over the jet crests, where the film thickness and wave amplitude increase with increasing heat flux. In the interjet region of the film being heated, the average relative amplitude of waves increases with decreasing average thickness, and in the isothermal region this amplitude decreases. Comparison of the obtained results with experimental data for isothermal film reveals that the values of relative amplitude differ significantly in the interjet region at high densities of heat fluxes. Transverse temperature gradients cause a decrease in the liquid film thickness, and longitudinal gradients cause an increase in the relative amplitude of waves compared to isothermal flows. In the end, this leads to the emergence of dry spots and breakdown of film. The relative amplitude of waves on the jet surface decreases with increasing heat flux; this is true of isothermal film flows.     

Photothermal Study of the Formation Dynamics of Fumed Silica Thin Films

In this work the formation of thin films by evaporation of liquid mixtures of agglomerated amorphous untreated fumed silicon dioxide nanoparticles is analyzed. Fumed silica is a material that has been used as a thickening agent due to the fact that it has chain-like particle morphology. When mixed with a liquid, the chains bond together and increase the viscosity. The experiments were performed on samples deposited on a metallic substrate. Thermal waves were generated by sending a modulated laser beam at constant frequency onto the substrate. These waves are propagated to the evaporating solution allowing the monitoring of the film formation. It is shown that the last stage of the film formation is strongly affected by the formation of cracks and migration of the material to the lateral surface of the container. The experimental data are compared with predictions of effective thermal property models.     

Mathematical modeling of moving contact lines in heat transfer applications

We provide an overview of research on the mathematical modeling of apparent contact lines in non-isothermal systems conducted over the past several decades and report a number of recent developments in the field. The latter involve developing mathematical models of evaporating liquid droplets that account not only for liquid flow and evaporation, but also for unsteady heat conduction in the substrate. The droplet is placed on a flat heated solid substrate and is assumed to be in contact with a saturated vapor. Furthermore, we discuss a careful comparison between mathematical models and experimental work that involves simultaneous measurement of shapes of evaporating droplets and temperature profiles in the solid substrate. The latter is accomplished using thermochromic liquid crystals. Applications to new research areas, such as studies of the effect of evaporation on fingering instabilities in gravity-driven liquid films, are also discussed.