Equations For Evaporation Rate Research Articles

Analysis of the evaporation coefficients of water, heavy water, and methanol in a high vacuum environment

The evaporation coefficient of liquids is an important factor for many practical situations but has been poorly understood due to the complexity of the experiments and uncertainty in the measurements. Indeed, the lack of current knowledge about the nature of the evaporation coefficient prevents accurate confirmation of its value. We have determined the evaporation coefficients of three liquids, water, heavy water, and methanol, by fitting Knudsen's evaporation rate equation to past measurements of the temperature of droplet trains and liquid jets evaporating in a high-vacuumed environment. Analysis of available experimental data suggests the value of 1 for the evaporation coefficient (αe) of water, and 0.725 for that of heavy water. A small-jet methanol study predicts αe≈1; however, analysis of experimental data from a large-jet methanol study was an exception—indicating coefficients well over unity (1.5<αe<9). These exceed the suggested maximum theoretical value of unity. We found that considering αe=1 for water, and most of the test fluids, is a fair approximation in a high-vacuumed environment that presents minimal kinetic barriers to evaporation. These results confirm that water should not be considered an anomalous liquid with respect to evaporation. This study provides insight that will help improve the design and development of the many processes in which evaporation plays a key role.

An Experimental Validation Study on Ferrofluid Evaporation

The current research on the evaporation of ferrofluids mainly focuses on the characterization of ultra-low vapor pressure ferrofluids in vacuum and the theoretical analysis of the evaporation process. Few studies have focused on the experimental validation of the proposed evaporation rate equations and on the comparison of the differences in ferrofluid evaporation. In this study, based on the Bolotov’s model, an evaporation rate equation is deduced from the experimental model. The experimental study included a comparison of the evaporation, magnetic particle volume fraction, temperature, height of the fluid surface from the outlet, and magnetic field of a kerosene-based ferrofluid and its base carrier liquid. The prepared sample was evaporated in a test tube, and the evaporation rate was calculated by measuring the weight loss of the sample. The experimental results show that the evaporation rate of the base carrier liquid is higher than that of the ferrofluid. The smaller the volume fraction of the magnetic particles, the greater the evaporation rate. The magnetic particles play a key role in preventing evaporation of the base liquid. The higher the temperature, the smaller the deviation of the evaporation rate from the predicted value. The evaporation rates obtained by the two control groups at the height of the fluid surface from the outlet were lower than the predict value. The magnetic field had a certain promotional effect on the evaporation of the ferrofluid. The experimental results were consistent with the results obtained using Bolotov’s model. This research validates Bolotov’s model and shows that the model is somewhat biased but still responds well to different variables.

Efecto del secado en el rendimiento de la extracción de aceite esencial de Luma chequen (Molina) A. Gray

This work studies the effect of drying at 40 °C of the leaves and stems of the species Luma chequen (Molina) A. Gray on the extraction yield of its essential oil by steam distillation at a pilot scale. From the micromorphological evaluation at the moisture levels fresh state (72±1%), critical moisture (24±1%) and equilibrium moisture (8.2±0.5%), it is found that the tissues fold, the secretory cavities thin out, according to the lacunarity, the microstructure of the plant material exhibits greater uniformity at the critical moisture. For the extraction tests 18 levels of moisture were considered, keeping the packing factor at 54 Kg/m3. The maximum yield of 0.52 ± 0.01% (v/w) was reached when the moisture of the material was 22±1%, very close to the critical moisture. A first-order model provided a suitable fit to the extraction kinetic data for samples with different humidity levels. Based on the evaporation rate equation, a description of the microstructure of the material and the drying conditions, a model was developed which shows the evaporation mechanism to be dominant in both the drying process and in the extraction of essential oil.

Review for prediction of evaporation rate at natural convection

The aim of the present research is to analyse evaporation intensity induced by natural convection. Simultaneous heat and mass transfer is observed in the case of evaporation from open water tanks as well as during the evaporation of surface moisture when drying materials. Relationships to determine the evaporation rate at natural convection were collected within this work. The equations for evaporation rate from these studies are valid in different ranges of interpretation (different gas and liquid temperature, surface area) and under certain conditions, which reduces their usefulness. New measuring apparatus has been installed and equations for determination of evaporation rate were validated. As a result of the validation, the equations of Leven, Boelter et al. and Bower and Saylor proved to be the most precise (±5% deviation) and equations of Box showed ±10% deviation to our measurement results.

Two-Dimensional Description of Absorption in Humans after Dermal Exposure to Volatile Organic Compounds

A two-dimensional diffusion model was developed to predict the absorption of chemicals in humans following dermal contact. A first-order evaporation rate equation was applied to the skin surface while a perfect-sink boundary condition was imposed at the stratum corneum/viable epidermis interface. Initially, there was a certain amount of the substance present within the stratum corneum at the end of the exposure period. Laplace transform techniques were implemented to solve the governing equations and to derive an expression for the time elapsed before reaching 90% of the final amount of chemical absorbed by the body. This index was 0.43, 2.67, 6.91, and 36.9 h for ethanol, diphenylamine, p-nitroaniline, and benzyl butyl-phthalate, respectively. Simulations show that surface evaporation is important for highly volatile compounds. A large fraction of the amount of poorly volatile compounds, available in the skin after exposure, was absorbed into the bloodstream.

A simplified method on thermal performance capacity evaluation of counter flow cooling tower

Abstract The thermal performance capacity of a wet cooling tower is dominated by weather conditions, particularly ambient wet-bulb temperature. In this paper, the tower performance was predicted by a simplified model which was characterized by specification of a mass evaporation rate equation. The purpose of this study was to present a calculation that was accurate and simple to implement, and could be applied to evaluate acceptance tests for new towers, to monitor changes in tower performance as an aid in planning maintenance, and to predict tower performance under changed operating conditions. The results were validated and showed good agreement with experimental measurements. The results were also presented in simple formats that were easy to use and understand. These allowed reduction of test data and comparison of test results to design data. The method held a practical advantage for predicted tower thermal performance capability to which it was best suited when both flow rate and temperature of inlet water were near design conditions since it required neither the measurement of air flow rate nor the calculation of tower characteristic ( h mass A / L ) . The expected results of this study will make it possible to incorporate cooling tower design and simulation to evaluate and optimize the thermal performance of power plants for example.

Explanation of charged nanoparticle production from hot surfaces

The production of charged nanoparticles from hot surfaces like glowing wires was used earlier in connection with mobility classification, but the phenomenon was not understood. In the present paper, negative particle charge is explained by thermoemission of electrons and positive particle charge by surface ionization of impurity atoms with low ionization energy. Such impurities are inevitably present even in high-purity metals. A model based on Saha–Langmuir and Richardson equations for particle charging and Hertz–Knutsen and Clausius–Clapeyron equations for evaporation rate can be fitted to the experimental charge emission in a satisfactory manner. This applies to the charge attached to Ag and Pd nanoparticles forming from a glowing wire (this work) and to data on charge emission from hot surfaces in vacuum reported by Jeon et al. The charging probability of particles is proportional to their volume indicating that the charge was incorporated during the formation process.

Experimental and Theoretical Investigations of Porous Structure Formation in Electrospun Fibers

The development of internal microstructure in electrospun fibers has been investigated both experimentally and theoretically. Various morphologies such as tubes, beads, and porous structures have been observed experimentally during electrospinning from amorphous polymer solutions such as poly(methyl methacrylate)/methylene chloride and poly(styrene)/tetrahydrofuran. The dynamics of electrospinning is modeled based on multiple virtual strands of beads connected by Maxwell's elements in a cylindrical coordinate system. Concurrently, spatiotemporal growth of the porous structure is calculated in the framework of Cahn−Hilliard time-evolution equation under the quasi steady state assumption coupled with the solvent evaporation rate equation. The coarse-grain simulation reveals the real-time formation of pores along the spinline of the electrospun fiber as the concentration traverses across the phase diagram of the amorphous polymer solution.

Morphology development of main‐chain liquid crystalline polymer fibers during solvent evaporation

AbstractA nonequilibrium thermodynamic approach has been developed for describing the emergence of fiber morphologies from a liquid crystalline polymer solution undergoing solvent evaporation, including fibrillar structures, concentric rings, and spiral structures. We utilized Matsuyama–Kato free energy for main‐chain liquid crystalline polymer (MCLCP) solutions, which is an extension of Maier–Saupe theory for nematic ordering and incorporates a chain‐stiffening, combined with Flory‐Huggins free energy of mixing. Temporal evolution of the concentration and nematic order parameters pertaining to the above free energy density of liquid crystalline polymer solution was simulated in the context of time‐dependent Ginzburg–Landau theory coupled with the solvent evaporation rate equation under the quasi‐steady state assumption. The emerged morphological patterns are discussed in relation to the phase diagram of the MCLCP solution and the rate of solvent evaporation. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 429–435, 2007

Closed Form Equations for the Evaporation Rate and Droplet Size of Knudsen Droplets

The flux-matching method is reexamined and found to be a necessary but not a sufficient condition at the flux-matching surface. The equation of continuity in the quasi-stationary approximation requires, that the flux density also be continuous across the boundary surface. When both flux-matching and flux-density matching are considered, it is found that the traditional flux-matching equation of Fuchs is only valid for Kn « 1 where Kn is the Knudsen number. A new evaporation rate equation is developed valid for all Kn. The equation reduces to Maxwell's diffusional equation in the limit of small Kn. Under appropriate conditions in the limit of large Kn the equation reduces to the free molecule regime's standard rate of evaporation in a vacuum. When Kn and the droplet radius are small, the equation reduces to both Schafer's equation and Fuchs' equation. The evaporation rate equation is integrated to give a second closed form equation which describes droplet size as a function of time. This equation is also valid in the Knudsen regime and reduces, under appropriate conditions, to either the equation for the continuum or the free molecule regime. This second equation is applied to the DBS/N2 data of Davis and Ray (1978). Excellent agreement is found throughout the Knudsen regime of 0.07 Kn < 0.2, for which the data applied.

Sodium Vapor Deposition, on Simulated Model of LMFBR Rotating Shield Plug Annulus, (I)

Experimental study was made to investigate the controlling factors on the vapor deposition rate on reactor operational shield plug annulus, which is exposed to the vapor entrained cover gas during reactor operation. Two simulated test assemblies having annuli were made for this purpose and were installed into a small test vessel. In the experiment, the average deposition rates on the annular walls of the test assemblies were measured for various pool temperatures, and their dependents upon such parameters as pool temperature, Ts (or the saturated vapor pressure Ps at pool surface), cover gas pressure Pg , and temperature drop ΔTa across cover gas, were studied. The results revealed that the dominant controlling factor was the vapor pressure Ps at pool surface. Dependent of the average deposition rate φbard. upon the above parameters was simply expressed by: φbard=BσpsDsΔTG , where, σs is the saturated vapor concentration at pool surface, Ds , the vapor diffusion coefficient, and B the proportional constant. To these experimental results, the previously published evaporation rate data and the theoretical evaporation rate equation based on Epstein & Rosner's theory were reviewed. Then correlation between the deposition and the evaporation rates was discussed.