Steady-state Evaporation Research Articles

Microdroplet evaporation under increasing temperature conditions: Experiments and modelling

This paper compares predictions of droplet evaporation processes of the widely used infinite conductivity model to experimental data of microdroplets evaporating under an increasing temperature condition. Near complete droplet histories of <100μm sized droplets of dodecane, decane and nonane are convected at low Reynolds number through a reactor with a dominantly increasing gas temperature. This produces a prolonged heating period up to the peak temperature condition. This differs from previous studies which make use of a fixed temperature condition. Results show that while evaporation rates at the peak temperature condition are generally well predicted, during the prolonged expansion phase, evaporation rates are over predicted, while during the transitional heating phase, rates are under predicted. Similar to a steady state evaporation process, experimental evaporation rates were found to be almost linearly dependent on gas temperature once evaporation dominates expansion processes.

Fate of nitrogen during volume reduction of human urine using an on-site volume reduction system

This study was carried to assess the effect of a mixture of salts, urea and creatinine on water evaporation from urine using an on-site volume reduction system in long-term experiments. Subsequently, the fate of nitrogen during volume reduction of urine was also assessed. The water evaporation rate, salt accumulation in the gauze sheet, concentrations of urea and ammonia-N, and pH of urine were measured periodically. Based on the results, a mass balance of nitrogen in concentrated urine was calculated for a moderate evaporating condition. The results revealed that steady-state evaporation was observed throughout the experiment period without any inhibition due to salt accumulation. Salt concentration in the gauze sheet reached steady-state illustrating the possibility of salt falling back to the tank from the sheet. No significant reduction of urea was observed for a moderate evaporating condition, which indicates inhibition of urea hydrolysis by the high concentration of the mixture of salts, urea and creatinine in the urine. In contrast, for a low evaporating condition, the pH of the urine increased to 8.9, which indicates early urea hydrolysis, causing an offensive odour and ammonia loss to the air. In simple storage experiments, a mixture of salts, urea and creatinine amounting to 227–334 g L−1 in urine inhibited urea hydrolysis, even with faecal contamination, at 25°C, while urine samples containing a mixture of salts, urea and creatinine at less than 227 g L−1 did not provide strong inhibition of hydrolysis.

Kinetics of the steady-state evaporation of single-component liquids into an inert gas

The effect of a driving force on steady-state evaporation in open and closed systems is studied.

Visualization and evaporator resistance measurement in heat pipes charged with water, methanol or acetone

The evaporation process in the wick of an operating flat-plate heat pipe was studied for three different working fluids having widely different figures of merit: deionized water, methanol and acetone. A sintered two-layer 100 + 200 mesh copper wick was adopted. Uniform heating was applied to the copper base plate near one end, and cooling with a water jacket at the other end. The evaporator resistance was determined using the temperature difference between the copper plate and the vapor respectively under and above the evaporator center. While the steady-state evaporation process was visualized through the upper glass plate of the heat pipe, the evaporator resistances were measured simultaneously. The maximum heat loads for water are far greater than those of methanol and acetone, with their values correlating well with their figures of merit. The minimum evaporator resistances for the three working fluids differ slightly in spite of the large differences in their properties. The differences can be mainly attributed to the different average thicknesses of the evaporating liquid layers, according to visualization. While nucleate boiling was not observed for water, very weak and localized nucleate boiling was observed for methanol near the maximum heat loads, beyond which local dryout began. For acetone, slow, periodic up-and-down motion of the liquid layer as a result of nucleate boiling was observed near the maximum heat loads over a significant portion of the evaporator. Beyond the maximum heat loads, nucleate boiling was again suppressed.

Modeling of vapor intrusion from hydrocarbon-contaminated sources accounting for aerobic and anaerobic biodegradation

A one-dimensional steady state vapor intrusion model including both anaerobic and oxygen-limited aerobic biodegradation was developed. The aerobic and anaerobic layer thickness are calculated by stoichiometrically coupling the reactive transport of vapors with oxygen transport and consumption. The model accounts for the different oxygen demand in the subsurface required to sustain the aerobic biodegradation of the compound(s) of concern and for the baseline soil oxygen respiration. In the case of anaerobic reaction under methanogenic conditions, the model accounts for the generation of methane which leads to a further oxygen demand, due to methane oxidation, in the aerobic zone. The model was solved analytically and applied, using representative parameter ranges and values, to identify under which site conditions the attenuation of hydrocarbons migrating into indoor environments is likely to be significant. Simulations were performed assuming a soil contaminated by toluene only, by a BTEX mixture, by Fresh Gasoline and by Weathered Gasoline. The obtained results have shown that for several site conditions oxygen concentration below the building is sufficient to sustain aerobic biodegradation. For these scenarios the aerobic biodegradation is the primary mechanism of attenuation, i.e. anaerobic contribution is negligible and a model accounting just for aerobic biodegradation can be used. On the contrary, in all cases where oxygen is not sufficient to sustain aerobic biodegradation alone (e.g. highly contaminated sources), anaerobic biodegradation can significantly contribute to the overall attenuation depending on the site specific conditions.

Reply to comment by N. Shokri and D. Or on “A simple model for describing hydraulic conductivity in unsaturated porous media accounting for film and capillary flow”

Reply to comment by N. Shokri and D. Or on “A simple model for describing hydraulic conductivity in unsaturated porous media accounting for film and capillary flow”

Statistical Rate Theory Examination of Ethanol Evaporation

A series of low-temperature (246 < T(I)(L) < 267 K) steady-state ethanol evaporation experiments have been conducted to determine the saturation vapor pressure of metastable ethanol. The measured interfacial conditions have been used with statistical rate theory (SRT) to develop an expression for the saturation vapor pressure as a function of temperature, f(srt)(eth). This expression is shown to be thermodynamically consistent because it gives predictions of both the evaporative latent heat and the liquid constant-pressure specific heat that are in agreement with independent measurements of these properties. In each experiment, the interfacial vapor temperature was measured to be greater than the interfacial liquid temperature, [triple bond]DeltaT(I)(LV). When f(srt)(eth) is used in SRT to predict DeltaT(I)(LV), the results are shown to be consistent with the measurements. Other expressions for the saturation vapor pressure that are in the literature are examined and found to be thermodynamically inconsistent and do not lead to valid predictions of DeltaT(I)(LV).

The relationship between transepidermal water loss and skin permeability

Transepidermal water loss (TEWL) is a measure of the steady-state water vapour flux crossing the skin to the external environment and it has been used extensively to characterise skin barrier function. We have previously hypothesised that in vivo TEWL is directly related to the reciprocal of the diffusional permeation pathlength through the stratum corneum (SC). The aim of the present paper is to validate experimentally this hypothesis. Ninety volunteers were recruited and TEWL and corneocyte surface areas were measured for six anatomic sites. The number of cell layers in the SC was calculated for each anatomic site in order to estimate the geometric pathlength for water efflux. Significant anatomic site variability was found for both TEWL and corneocyte surface area which were inversely correlated. A direct reciprocal relationship between TEWL and pathlength was determined, with TEWL values tending to zero when corneocytes are infinitely large. In general, skin sites with smaller corneocytes have fewer cell layers, with shorter permeation pathlengths and higher TEWL values. The results confirm our previous hypothesis and suggest that TEWL may be used to characterise the permeation routes for different anatomic sites.

Droplet Image Feedback Control System in Evaporation Experiment

In order to realize the steady-state droplet evaporation, image feedback control system is designed based on DSP. The system has three main functions: to capture and store droplet images during the experiment; to calculate droplet geometrical and physical parameters such as volume, surface area, surface tension and evaporation velocity at a high-precision level; to keep the droplet volume constant. The DSP can drive an injection controller with the PID control to inject liquid so as to keep the droplet volume constant. The evaporation velocity of droplet can be calculated by measuring the injected volume during the evaporation. The structure of hardware and software of the control system, key processing methods such as contour fitting and experimental results are described.

Steady-state water and vapor flows in a porous medium

Stationary regimes of nonisothermal flow of a liquid and its vapor through a porous medium in the gravity field are investigated. Possible flow types are analyzed in the plane of the determining parameters. The analytical results obtained are used in discussing the possibility of finding the pressure and temperature in the interior of a geothermal system from the parameters of the liquid and vapor flow in its permeable surface formations.

Experimental verification of the Stefan-Maxwell equations

Analysis of the study by Carty and Schrodt is performed, and it is shown that the experimental data of the authors are in satisfactory agreement with the data calculated by the Stefan-Maxwell equations on the basis of an actual length of the diffusion channel. Equations for profiles of the concentrations of components in the diffusion channel are derived. The dynamics of steady-state evaporation of acetone and methanol into air at a temperature of 35°C is experimentally studied, and a satisfactory agreement is found between the values of fluxes measured in experiments and calculated by the Gilliland equations that are the solution of the Stefan-Maxwell equations for a ternary gas mixture.

Solute transport in sub-irrigated peat-based growing media

New legislation to reduce the amount of fertilizer leached into the environment by horticultural growers and the need to implement water-saving irrigation systems require an understanding of salt build-up and of nutrient cycles in order to develop efficient water-use strategies for growers. Solute transport in growing media is central to this process, but has received little attention thus far. The objectives of this study were to determine how solutes behave in sub-irrigated growing media and to assess a solute transport model for these media. A steady state evaporation (upward water flow) experiment was carried out with three different growing media in packed columns in the laboratory. Bromide, potassium and copper concentrations were determined using in-column pore water solution samplers and by sectioning the columns at the end of the experiment to obtain concentration profiles. The Hydrus-1D model was fitted to the solution sampler data assuming non-linear Freundlich adsorption, and then used to obtain favorable predictions of the measured concentration profiles. Independent adsorption isotherm results from batch experiments were found to be inadequate when used to predict solute movement and the results indicate that the preferred approach is an in-column evaluation of the transport parameters.Key words: Solute transport, sub-irrigation, peat, growing media

Role of molecular phonons and interfacial-temperature discontinuities in water evaporation

During steady-state water evaporation, when the vapor phase is heated electrically, the temperature on the vapor side of the interface has been reported to be as much as 27.83 degrees C greater than that on the liquid side. The reported interfacial temperatures were measured with thermocouple beads that were less than 50 microm in diameter and centered 35 microm from the interface in each phase. We examine the reliability of these measurements by using them with a theory of kinetics to predict the interfacial-liquid temperature. The predicted temperature discontinuities are found to be in agreement with those measured up to a temperature discontinuity of 15.69 degrees C , but larger discontinuities cannot be confirmed because of uncertainties in the vapor-phase pressure measurements. The theory of kinetics used in the analysis includes molecular phonons in the expression for the evaporation flux. We show it is essential to include these terms if the theory is to be used to predict the temperature discontinuities.

Estimating catchment evaporation and runoff using MODIS leaf area index and the Penman‐Monteith equation

This paper shows the feasibility of using steady state water balances of gauged catchments to calibrate a spatially explicit evaporation model and then applying this to estimate mean annual runoff for 120 gauged catchments in the Murray‐Darling Basin (MDB) of Australia from 2001 to 2005. We used remotely sensed leaf area indices from the Moderate Resolution Imaging Spectrometer (MODIS) mounted on the polar‐orbiting Terra satellite with the Penman‐Monteith equation, gridded meteorology, and a two‐parameter biophysical model for surface conductance (Gs) to estimate 8‐day average evaporation at 1‐km resolution. Parameters for the Gs model were optimized using steady state water balance estimates (precipitation minus runoff) in the gauged catchments in three precipitation zones of the MDB, and the calibrated evaporation model was then used to estimate evaporation (ERS) and runoff from gauged and ungauged catchments in the MDB. Mean annual calibrated estimates of ERS compared well with water balance estimates, indicated by a root‐mean‐square error (RMSE) of 78.6 mm/a and the Nash‐Sutcliffe coefficient of efficiency (CE) of 0.68. Reasonable agreement was obtained between the estimated mean annual runoff (RRS) (rainfall minus ERS), and the measured runoff (RMSE = 71.0 mm/a and CE = 0.75). Cross validation showed that estimated ERS and RRS were almost as good as the calibrated ones. Furthermore, RRS has an accuracy similar to that of a seven‐parameter conceptual rainfall‐runoff model in the gauged catchments. The results show that the evaporation model can be easily applied to estimate steady state evaporation and runoff and that ERS can be used with rainfall‐runoff models to improve accuracy of estimated runoff in ungauged catchments.

An analysis of the radial flow in the heterogeneous porous media based on fractal and constructal tree networks

In this paper, an analysis of the radial flow in the heterogeneous porous media based on fractal and constructal tree networks is presented. A dual-domain model is applied to simulate the heterogeneous porous media embedded with a constructal tree network based on the fractal distribution of pore space and tortuosity nature of flow paths. The analytical expressions for seepage velocity, pressure drop, local and global permeability of the network and binary system are derived, and the transport properties for the optimal branching structure are discussed. Notable is that the global permeability ( K n ) of the network and the volume fraction ( f n ) occupied by the network exhibit linear scaling law with the fractal dimension ( D p ) of channel diameter by log K n ∼ 0.46 D p and log f n ∼ 1.03 D p , respectively. Our analytical results are in good agreement with the available numerical results for steady-state soil vapor extraction and indicate that the fractal dimension for pore space has significant effect on the permeable properties of the media. The proposed dual-domain model may capture the characteristics of heterogeneous porous media and help understanding the transport mechanisms of the radial flow in the media.

Statistical Rate Theory Determination of Water Properties below the Triple Point

We report a new method for determining the saturation vapor pressure, Ps(T), of water at conditions below its triple point. Ps(T) appears as a parameter in the statistical rate theory (SRT) expression for the net evaporation flux. We use measurements of the interfacial conditions during steady-state evaporation and condensation experiments and SRT to determine the values of Ps(T) from 50 different experiments over a range of interfacial conditions. From these values of Ps(T), we develop an analytical expression and from it calculate the liquid-vapor latent heat, Llv(T), and the constant pressure specific heat, cp(L)(T). The calculated values of these properties are compared with those obtained from independent measurements. This comparison indicates the SRT expressions for Llv(T) and cp(L)(T) are consistent with the measurements over a range of temperatures.

Vapour density field of mixed-phase clouds

This work presents a theoretical model based on the electrostatic image charges method to calculate the steady-state water vapour density field for a population of supercooled cloud droplets and ice crystals. The model allows a determination of the vapour density among the cloud droplets and ice particles and obtains a representative vapour density of the system which is called the ambient vapour density of the mixed-phase cloud. The results show that the ambient vapour density is close to the saturated value over water in clouds where the cloud droplet concentration is much higher than the ice crystal concentration and close to the ice saturation value in glaciated clouds. A parameterization of the ambient vapour density is given as a function of the sizes and concentrations of the cloud droplets and ice crystals. In addition, the model is used to study the diffusional growth rate of ice crystals immersed in a mixed cloud. The results indicate that the growth of an ice crystal can be reduced by the presence of neighbouring crystals. A mass growth rate equation for diffusional growth was found, which incorporates effects of the ice crystal size, the cloud droplet radius, liquid water content, and ice crystal and droplet concentrations. These studies are of important to considerations in thunderstorm electrification processes, where the mechanism of charge transfer between colliding ice particles and graupel is influenced by growth rate.

Comprehensive investigation of numerical methods in simulating a steady-state vapor compression system

Computer simulation has become a required tool in the design phase of vapor compression systems; however with relatively few exceptions most simulations focus on the basic four component systems. With an increasing focus being placed on energy efficiency, the simulation of multi-component vapor compression systems (having multiple evaporators, condenser or compressors) will become essential to assist in the design of these more complicated systems. The implementation of a component-based framework will facilitate the simulation of multi-component systems. This paper describes three algorithms used to simulate a component-based vapor compression system. A test matrix of 6174 sample runs covering a wide range of operating conditions was constructed to determine the robustness and speed of each method when using three different types of nonlinear equation solvers. Each method was tested by simulating a basic four component cycle and a more advanced multiple evaporator system. The results are presented in such a format as to describe the reasons that contribute to any instability of the solvers and the computational efficiency of each method is discussed.

Surface thermal capacity and its effects on the boundary conditions at fluid-fluid interfaces

We have formulated a generalization of the energy boundary condition for fluid-fluid interfaces that includes the transport of the Gibbs excess internal energy. A newly measured surface property - the surface thermal capacity c(sigma) - appears in the result, and couples the temperature and velocity fields. If this term is not included in the energy boundary condition at liquid-vapor interfaces, the energy-conservation principle cannot be satisfied during steady-state evaporation of H(2)O(l) or D(2)O(l) . The c(sigma) term is possibly important in a number of other circumstances, and its importance can be determined from the magnitude of two nondimensional numbers.

Experimental and theoretical investigations on interfacial temperature jumps during evaporation

Experimental results are summarized on investigations of positive temperature jumps at water–vapor interfaces during steady-state evaporation under low-pressure. Steady-state evaporation of water experiments were carried out to measure the interfacial properties and to obtain the evaporation rate. The interfacial vapor temperature close to the interface was always found to be higher than the interfacial liquid temperature. To study the influence of the vapor side thermal boundary conditions on the temperature jump, the evaporation chamber was heated with the help of a heating wire mesh which was mounted in the vapor side plane above the evaporating free surface. It was astounding to the authors to find that the temperature jump at the liquid–vapor interface increases linearly with the heat flux from the vapor side. The maximum temperature jump across the water–vapor interface was measured as 15.68 °C in the presence of vapor phase heating. Still higher temperature jump values can be achieved by applying higher vapor side heat fluxes close to the water–vapor interface. It was attempted to explain these unique experimental results using existing theories of evaporation. Kinetic theory of gases (KTG) predicts the temperature jumps, but the magnitude is 10–20 times smaller than the experimentally obtained temperature jumps. The linearized statistical rate theory yields the evaporation mass flux expression which is same as the KTG expression with evaporation and condensation coefficients of unity. Only non-equilibrium thermodynamics using phenomenological equations appear to predict the magnitude of the temperature jump measured in the experimental study. However, more theoretical work needs to be done to fully understand the new experimental findings reported here.