Steady-state Evaporation Research Articles

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.

Saturated and unsaturated salt transport in peat from a constructed fen

Abstract. The underlying processes governing solute transport in peat from an experimentally constructed fen peatland were analyzed by performing saturated and unsaturated solute breakthrough experiments using Na+ and Cl− as reactive and non-reactive solutes, respectively. We tested the performance of three solute transport models, including the classical equilibrium convection–dispersion equation (CDE), a chemical non-equilibrium one-site adsorption model (OSA) and a model to account for physical non-equilibrium, the mobile–immobile (MIM) phases. The selection was motivated by the fact that the applicability of the MIM in peat soils finds a wide consensus. However, results from inverse modeling and a robust statistical evaluation of this peat provide evidence that the measured breakthrough of the conservative tracer, Cl−, could be simulated well using the CDE. Furthermore, the very high Damköhler number (which approaches infinity) suggests instantaneous equilibration between the mobile and immobile phases underscoring the redundancy of the MIM approach for this particular peat. Scanning electron microscope images of the peat show the typical multi-pore size distribution structures have been homogenized sufficiently by decomposition, such that physical non-equilibrium solute transport no longer governs the transport process. This result is corroborated by the fact the soil hydraulic properties were adequately described using a unimodal van Genuchten–Mualem model between saturation and a pressure head of ∼-1000 cm of water. Hence, MIM was not the most suitable choice, and the long tailing of the Na+ breakthrough curve was caused by chemical non-equilibrium. Successful description was possible using the OSA model. To test our results for the unsaturated case, we conducted an unsaturated steady-state evaporation experiment to drive Na+ and Cl− transport. Using the parameterized transport models from the saturated experiments, we could numerically simulate the unsaturated transport using Hydrus-1-D. The simulation showed a good prediction of observed values, confirming the suitability of the parameters for use in a slightly unsaturated transport simulation. The findings improve the understanding of solute redistribution in the constructed fen and imply that MIM should not be automatically assumed for solute transport in peat but rather should be evidence based.

Molecular simulation of steady-state evaporation and condensation in the presence of a non-condensable gas.

Using molecular dynamics simulations, we study evaporation and condensation of fluid Ar in the presence of a non-condensable Ne gas in a nanochannel. The evaporation and condensation are driven by the temperature difference, ΔTL, between the evaporating and condensing liquid surfaces. The steady-state evaporation and condensation fluxes (JMD) are also affected by the Ne concentration, ρNe, and the nanochannel length. We find that across a wide range of ΔTL and ρNe, JMD is in good agreement with the prediction from Stefan's law and from Schrage relationships. Furthermore, for ΔTL less than ∼20% of the absolute average temperature, we find that both steady-state heat and mass fluxes are proportional to ΔTL. This allows us to determine the interfacial resistance to the heat and mass transfer and compare it with the corresponding resistances in the gas phase. In this context, we derive an analytical expression for the effective thermal conductivity of the gas region in the nanochannel and the mass transport interfacial resistance equivalent length, i.e., the length of the nanochannel for which the resistance to the mass flow is the same as the interfacial resistance to the mass flow.

Stable Hydrothermal Waves at Steady State Evaporating Droplet Surface

Stable hydrothermal waves (HTWs) are found at a sessile ethanol droplet surface under the steady state evaporation. It is different from those which greatly decrease with the evaporation time in the transient droplet drying process. This study removes the possible effect of shrinking droplet on HTWs. An analysis of the dimensionless numbers indicates the increasingly enhanced role of thermocapillary instabilities upon raising the substrate temperature. The onset HTWs can be continuously maintained under the steady state evaporation conditions. Interestingly, the stable number of HTWs follows a linear fitting with the dimensionless factor incorporating the normalized temperature difference between the substrate and the surroundings and the droplet aspect ratio. The temperature heterogeneity of HTWs is intensified by increasing the substrate temperature. The stable HTWs exhibit the “one source-to-one sink” propagation at lower substrate temperatures. However, such directional traveling, normally presented in the transient HTWs in the drying droplet, is changed at the higher substrate temperatures due to the newly emerged sources and sinks under the steady state conditions.

Experimental investigation of the effect of natural convection on the evaporation characteristics of small fuel droplets at moderately elevated temperature and pressure

The role of natural convection in droplet evaporation is experimentally investigated for a range of micro-sized alkane fuel droplets at moderately elevated pressure and temperature. This paper assesses the impact of buoyant mass transfer from two perspectives; the resulting variation in steady-state evaporation rate, and the potential relation to non-linear temporal d2 profiles. The steady-state evaporation rate is found to increase linearly with initial droplet diameter at all tested conditions, where the relative improvement in evaporation rate depends upon the fuel type, pressure, and temperature. In addition to modifying the steady-state evaporation rate, the various environmental conditions also impact the occurrence and timing of d2 deviation, which manifests as a strong reduction in evaporation rate near the end of a droplet’s lifetime. Pressure tends to encourage the appearance of d2 deviation for both heptane and decane by increasing the proportion of evaporation for which natural convection is responsible. The effect of temperature depends upon the droplet volatility, and the results differ between the two test fuels. Overall, the relative importance of natural convection, as compared to pure molecular diffusion, appears to govern both the expected improvement in, and potential deviation from, steady-state evaporation. Proposed Grashof correlations justify the above hypothesis.

Fuel vaporization: Effect of droplet size and turbulence at elevated temperature and pressure

This paper presents an extensive experimental study regarding the effect of turbulence and droplet size on the evaporation rate of suspended monocomponent alkane droplets at elevated temperature and pressure conditions of up to 100 °C and 10 bar, respectively. Individual droplets of n-heptane and n-decane were suspended at the intersection of two crossed micro-fibers in the center of a fan-stirred spherical vessel. The droplet size was varied in the range between 110 and 730 µm. Eight axial fans generated a controlled turbulent flow field with quasi-zero mean velocity and turbulence intensity up to 1.5 m/s. The results reveal a linear relationship between the initial droplet size and its turbulent steady-state evaporation rate, where larger droplets evaporate at a faster rate than their smaller counterparts at all elevated temperature and pressure conditions. The normalized turbulent evaporation rate increases with pressure, whereas elevated temperature produces the opposite effect. The ratio of the Kolmogorov length scale to initial droplet diameter is shown to be of paramount importance for interpreting the effect of turbulence, as the normalized evaporation rate increases dramatically at lower values of this ratio under all test conditions. However, the ability of turbulence to enhance the vaporization rate vanishes when this ratio approaches unity, suggesting that only droplets which are initially larger than the smallest turbulent eddies experience enhanced evaporation. In addition, the widespread belief that turbulence enhances less volatile fuels more than their high volatility counterparts also depends on the ambient pressure and initial droplet size. The ability of turbulence to generate small-scale structures and, subsequently, the interaction of these eddies with the available fuel concentration gradient at the surface of the droplet governs the relationship between fuel type, initial droplet size, and ambient temperature and pressure. A turbulent Reynolds number or a vaporization Damköhler number is used to correlate turbulent droplet evaporation rates at all explored test conditions.

Calculation of Steady-State Evaporation for an Arbitrary Matric Potential at Bare Ground Surface

Evaporation from soil columns in the presence of a water table is a long lasting subject that has received great attention for many decades. Available analytical studies on the subject often involve an assumption that the potential evaporation rate is much less than the saturated hydraulic conductivity of the soil. In this study, we develop a new semi-analytical method to estimate the evaporation rate for an arbitrary matric potential head at bare soil surface without assuming that the potential evaporation rate is much less than the saturated hydraulic conductivity of the soil. The results show that the evaporation rates calculated by the new solutions fit well with the HYDRUS-1D simulation. The new solutions also can reproduce the results of potential evaporation rate calculated from previous equations under the special condition of an infinite matric potential head at bare soil surface. The developed new solutions expand our present knowledge of evaporation estimation at bare ground surface to more general field conditions.

Isotopic ratio of evaporated ions, critical ionization distances, and ionization regions in the process of the field evaporation of molybdenum at high temperatures

A magnetic mass spectrometer with a field ion source has been used to study the steady-state field evaporation of molybdenum at a temperature of 1000–2000 K. Ions of all seven molybdenum isotopes have been observed in the process of evaporation; only low-charge ions Mo+2 and Mo+ have been detected. The critical ionization distances and ionization regions for single- and double-charge Mo ions have been identified based on the measured ion energies and the experimentally determined intensity of the evaporation field. It has been demonstrated that ions are produced in the process of field evaporation of surface atoms at certain distances from the emitter surface in a very narrow spatial region.

Molecular simulation of steady-state evaporation and condensation: Validity of the Schrage relationships

The accuracy, or even the validity, of the Schrage relationships expressing the rate of evaporation and condensation in terms of local interfacial thermodynamics properties and the mass accommodation coefficient is a subject of significant discussion. In this work, we carry out molecular dynamics (MD) simulations of evaporation and condensation of fluid Ar in a nanochannel. By adjusting the temperature difference, ΔT, between the evaporating and condensing surfaces, we control the steady-state evaporation and condensation fluxes (JMD). We find that across a wide ΔT range studied, JMD is always in excellent agreement with the prediction from the exact Schrage relationships. Furthermore, if the temperature difference between the two liquid surfaces in the nanochannel is less than ∼20% of the average absolute temperature, we find that both energy and mass fluxes at the interface are proportional to ΔT. Our analysis indicates that in the case of steady-state evaporation and condensation processes, the exact Schrage relationships satisfy the conservation of mass, momentum and energy, and provides accurate predictions of the rates of the associated processes.

Hydraulic conductivity of stratified unsaturated soils: Effects of random variability and layering

For simulating flow in heterogeneous porous media it is computationally more efficient to define an equivalent effective (i.e., upscaled) medium rather than considering detailed spatial heterogeneities. In this paper, the effective unsaturated hydraulic conductivity (K) of soils exhibiting random variability, layering, or both is calculated based on numerical simulations of steady-state evaporation from a shallow water table. It is demonstrated that the effective K of randomly-varied coarse-textured soils generally falls between the harmonic and geometric means of the unsaturated hydraulic conductivities of the constituting soils. Layering and random variability when occurring concurrently magnify each other’s effects on effective K. As a result, the higher the degree of heterogeneity, the lower the effective K. Therefore, neglecting either random spatial variability or layering in numerical simulations can lead to significant overestimation of water flow in soils.

Direct Hydraulic Parameter and Function Estimation for Diverse Soil Types Under Infiltration and Evaporation

A new computationally efficient direct method is applied to estimating unsaturated hydraulic properties during steady-state infiltration and evaporation at soil surface. For different soil types with homogeneous and layered heterogeneity, soil hydraulic parameters and unsaturated conductivities are estimated. Unlike the traditional indirect inversion method, the direct method does not require forward simulations to assess the measurement-to-model fit; thus, the knowledge of model boundary conditions (BC) is not required. Instead, the method employs a set of local approximate solutions to impose continuity of pressure head and soil water fluxes throughout the inversion domain, while measurements act to condition these solutions. Given sufficient measurements, it yields a well-posed system of nonlinear equations that can be solved with optimization in a single step and is thus computationally efficient. For both Gardner’s and van Genuchten’s soil water models, unsaturated hydraulic conductivities and pressure heads (including the unknown BC) can be accurately recovered. When increasing measurement errors are imposed, inversion becomes less accurate, but the solution is stable, i.e., estimation errors remain bounded. Moreover, when the unsaturated conductivity model is known, inversion can recover its parameters; if it is unknown, inversion can recover a nonparametric, piecewise continuous function to which soil parameters can be obtained via fitting. Overall, inversion accuracy of the direct method is influenced by (1) measurement density and errors; (2) rate of infiltration or evaporation; (3) variation of the unsaturated conductivity; (4) flow direction; (5) the number of soil layers.

Modeling of the evaporation of liquids and condensation of their vapor during distillation

This paper considers the evaporation process in an evaporator–connecting tube–condenser system under conditions such that the evaporation rate is determined by the evaporation and condensation mechanisms and the hydraulic resistances of the evaporation and condensation compartments and connecting tube. We present a mathematical model and numerical simulation results that demonstrate quantitative patterns of a steady-state evaporation process in a closed evaporation–condensation system. For a particular example of selenium vacuum distillation, we have determined the evaporation coefficient of selenium from experimental data on the temperature dependences of the selenium evaporation rate and saturated vapor pressure.

Determination of the critical ionization distance and ionization zone during high-temperature field evaporation of molybdenum

Steady-state field evaporation of molybdenum at high emitter temperatures (T ∼ 2000 K) has been studied using a magnetic mass spectrometer equipped with a field ion source. Only low-charge ions (Mo+2 and Mo+) have been observed in the course of evaporation. The measured ion energies and evaporating field strengths (Fev) were used to determine the critical ionization distances (xcr) and ionization zones (Δ) for singly and doubly charged ions. The obtained xcr and Δ values show that the formation of ions takes place at a certain distance from the emitter surface.

Steady-state droplet evaporation: Contact angle influence on the evaporation efficiency

Steady-state water droplet evaporation on a heated substrate is investigated to systematically correlate the effects of a droplet’s contact angle on the evaporation rate. Experiments are performed on laser-patterned polymer substrates, using a syringe-pump fluid supply methodology – in combination with in situ infrared thermography and visible-image microscopy – to pin/fix the contact line and facilitate steady-state operation with controlled substrate surface temperatures and contact angles ranging between 22°C≲TS≲70°C and 80°≲θ≲110° respectively. The results affirm that (1) the effects of substrate cooling (also referred to as evaporative cooling) cannot be neglected for evaporation on low thermal conductivity polymer surfaces and (2) the evaporative mass flux (φLG) scales inversely with contact angle (i.e., φLG∝θ−1) with maximum values of φLG near the triple-line. We also find – via mass transfer calculations based on the kinetic theory of gases – that the evaporation coefficient (∊e, also referred to as the evaporation efficiency or the accommodation coefficient for evaporation) scales inversely with contact angle (i.e., ∊e∝θ−1); yielding values for ∊e within 0.52×10−3≳∊e≳0.18×10−3 for 80°≲θ≲110°, respectively.

Investigating the heat transfer on the top side of inclined printed circuit boards during vapour phase soldering

In this paper, heat transfer and condensate layer formation was investigated by numerical simulations on the top side of inclined printed circuit boards during vapour phase soldering. The phase change on the inclined surface and the transfer mechanisms in the condensate layer were embedded in a three-dimensional model. Steady-state and saturated vapour conditions were applied as boundary conditions in order to study the pure effect of the inclination. Due to the electronic component and circuit board structures during soldering only moderate inclination angles were studied between 0° and 10°. It was found that a moderate inclination of the printed circuit board has considerable effects on the formation of condensate layer and consequently on heat transfer. Compared to the default horizontal orientation of the board, the thickness differences of the condensate layer can be decreased with an optimised inclination of the printed circuit board. This effect homogenizes heat transfer during the process, enabling improved solder joint quality, with reduced overall soldering failure count.

An Excel®-based visualization tool of 2-D soil gas concentration profiles in petroleum vapor intrusion.

In this study we present a petroleum vapor intrusion tool implemented in Microsoft® Excel® using Visual Basic for Applications (VBA) and integrated within a graphical interface. The latter helps users easily visualize two-dimensional soil gas concentration profiles and indoor concentrations as a function of site-specific conditions such as source strength and depth, biodegradation reaction rate constant, soil characteristics and building features. This tool is based on a two-dimensional explicit analytical model that combines steady-state diffusion-dominated vapor transport in a homogeneous soil with a piecewise first-order aerobic biodegradation model, in which rate is limited by oxygen availability. As recommended in the recently released United States Environmental Protection Agency's final Petroleum Vapor Intrusion guidance, a sensitivity analysis and a simplified Monte Carlo uncertainty analysis are also included in the spreadsheet.

Role of the source to building lateral separation distance in petroleum vapor intrusion

The adoption of source to building separation distances to screen sites that need further field investigation is becoming a common practice for the evaluation of the vapor intrusion pathway at sites contaminated by petroleum hydrocarbons. Namely, for the source to building vertical distance, the screening criteria for petroleum vapor intrusion have been deeply investigated in the recent literature and fully addressed in the recent guidelines issued by ITRC and U.S.EPA. Conversely, due to the lack of field and modeling studies, the source to building lateral distance received relatively low attention. To address this issue, in this work we present a steady-state vapor intrusion analytical model incorporating a piecewise first-order aerobic biodegradation limited by oxygen availability that accounts for lateral source to building separation. The developed model can be used to evaluate the role and relevance of lateral vapor attenuation as well as to provide a site-specific assessment of the lateral screening distances needed to attenuate vapor concentrations to risk-based values. The simulation outcomes showed to be consistent with field data and 3-D numerical modeling results reported in previous studies and, for shallow sources, with the screening criteria recommended by U.S.EPA for the vertical separation distance. Indeed, although petroleum vapors can cover maximum lateral distances up to 25–30m, as highlighted by the comparison of model outputs with field evidences of vapor migration in the subsurface, simulation results by this new model indicated that, regardless of the source concentration and depth, 6m and 7m lateral distances are sufficient to attenuate petroleum vapors below risk-based values for groundwater and soil sources, respectively. However, for deep sources (>5m) and for low to moderate source concentrations (benzene concentrations lower than 5mg/L in groundwater and 0.5mg/kg in soil) the above criteria were found extremely conservative as the model results indicated that for such scenarios the lateral screening distance may be set equal to zero.

Effects of Inhomogeneities on Heat and Mass Transport Phenomena in Thermal Bridges

The interest of calculating the effects of thermal bridges in buildings energy consumption is growing, due to recent energy saving regulations applied in different countries. The widespread use of insulating materials to reduce energy requirements of buildings, often employed for intermediate insulation of the building envelope, makes thermal bridges a crucial point in the energy analysis of building envelopes. Furthermore, heat losses through thermal bridges often lead to building pathologies due to moisture condensation. Therefore, thermal bridges need to be correctly characterized in the building design stage in order to reduce heat losses and avoid materials degradation. The authors numerically simulate, by using finite elements, the steady-state and dynamic three-dimensional (3D) heat and vapor transport in inhomogeneous thermal bridges and building envelopes. The aim of the present work is to show the importance of taking into account the presence of inhomogeneities (i.e., metal stud) in building materials for the calculation of actual heat losses and water condensation in 3D thermal bridges. The obtained heat transfer results are verified against the reference data of the technical standard UNI EN ISO 10211. The proposed microscopic approach is essential to calculate the actual heat losses of three-dimensional thermal bridges and building envelopes and to overcome condensation problems.

One-dimensional analytical approach to modelling evaporation and heating of deformed drops

A general analytical solution for the steady-state evaporation from deformed liquid drops is proposed. The solution is applicable to classes of drop shapes for which 1-D solution exists. The method is used to find the evaporation rate and local vapour and heat fluxes for general ellipsoidal drops, extending previous available results on spheroids. A direct dependence of the local vapour flux on the surface Gaussian curvature is evidenced. A quantitative evaluation of the effect of drop deformation on the total evaporation rate and the local vapour flux is reported.

Steady State Vapor Bubble in Pool Boiling.

Boiling, a dynamic and multiscale process, has been studied for several decades; however, a comprehensive understanding of the process is still lacking. The bubble ebullition cycle, which occurs over millisecond time-span, makes it extremely challenging to study near-surface interfacial characteristics of a single bubble. Here, we create a steady-state vapor bubble that can remain stable for hours in a pool of sub-cooled water using a femtosecond laser source. The stability of the bubble allows us to measure the contact-angle and perform in-situ imaging of the contact-line region and the microlayer, on hydrophilic and hydrophobic surfaces and in both degassed and regular (with dissolved air) water. The early growth stage of vapor bubble in degassed water shows a completely wetted bubble base with the microlayer, and the bubble does not depart from the surface due to reduced liquid pressure in the microlayer. Using experimental data and numerical simulations, we obtain permissible range of maximum heat transfer coefficient possible in nucleate boiling and the width of the evaporating layer in the contact-line region. This technique of creating and measuring fundamental characteristics of a stable vapor bubble will facilitate rational design of nanostructures for boiling enhancement and advance thermal management in electronics.