Droplet Evaporation Rate Research Articles

Evaporation of a sessile droplet on a slope

We theoretically examine the drying of a stationary liquid droplet on an inclined surface. Both analytical and numerical approaches are considered, while assuming that the evaporation results from the purely diffusive transport of liquid vapor and that the contact line is a pinned circle. For the purposes of the analytical calculations, we suppose that the effect of gravity relative to the surface tension is weak, i.e. the Bond number (Bo) is small. Then, we express the shape of the drop and the vapor concentration field as perturbation expansions in terms of Bo. When the Bond number is zero, the droplet is unperturbed by the effect of gravity and takes the form of a spherical cap, for which the vapor concentration field is already known. Here, the Young-Laplace equation is solved analytically to calculate the first-order correction to the shape of the drop. Knowing the first-order perturbation to the drop geometry and the zeroth-order distribution of vapor concentration, we obtain the leading-order contribution of gravity to the rate of droplet evaporation by utilizing Green’s second identity. The analytical results are supplemented by numerical calculations, where the droplet shape is first determined by minimizing the Helmholtz free energy and then the evaporation rate is computed by solving Laplace’s equation for the vapor concentration field via a finite-volume method. Perhaps counter-intuitively, we find that even when the droplet deforms noticeably under the influence of gravity, the rate of evaporation remains almost unchanged, as if no gravitational effect is present. Furthermore, comparison between analytical and numerical calculations reveals that considering only the leading-order corrections to the shape of the droplet and vapor concentration distribution provides estimates that are valid well beyond their intended limit of very small Bo.

Rates of High-Temperature Evaporation of Promising Fire-Extinguishing Liquid Droplets

Differences in the rates of heating and evaporation of droplets with the component composition are important parameters of heat transfer processes and phase transformations. This paper presents the values of high-temperature (up to 600 °C) evaporation rates of droplets of promising fire-extinguishing compositions (water, bentonite suspension, bischofite solution, EA-5 solution, and foaming agent emulsion) at convective (in the air stream), conductive (on a heated surface), and radiation (in a muffle furnace) heating. A high-speed video recording system and tracking software algorithms are used. At identical initial sizes of droplets of fire-extinguishing suspensions, known as emulsions and solutions, the times of their complete evaporation are shown to differ 3.7 times when heating on the substrate, 1.25 times in the air flow, and 1.9 times in the muffle furnace. A general approximation expression is formulated, and the empirical constants are calculated to predict the evaporation rate of the droplets of extinguishing agents in a wide range of temperatures (up to 600 °C) and heat fluxes (up to 100 kW/m2), which are characteristic of forest fires. With the use of the experimental data obtained, it is possible to predict the completeness of evaporation of promising extinguishing liquids at different schemes of heat supply.

Contact angle dynamics for evaporating droplet on contrast nano-structured surface

In this work, a series of experiments was carried out to study the evaporation rate of sessile and suspended droplets. The basic geometric characteristics of an evaporating drop from a biphilic surface are investigated. Evaporation dynamics data have been obtained, showing that evaporation from an inverted substrate is faster than evaporation of a sessile drop.

Measurement of transient evaporation of an ethanol droplet stream with phase rainbow refractometry and high-speed microscopic shadowgraphy

Quantifying the evaporation rate of droplets is of great importance in many applications and this is especially true if the evaporation occurs in a rapidly changing environment, such that models describing evaporation under steady state conditions are no longer valid. To achieve such information from experiments, the phase rainbow refractometry (PRR) technique has recently be shown to be capable of simultaneously measuring temperature, size, and size variation at the nanometer scale, quantities essential for quantifying transient evaporation rates. The present study examines the use of the PRR technique to characterize the evaporation of monodispersed droplets in a droplet stream injected into ambient air. This is combined with high-speed microscopic shadowgraphy, yielding as measured quantities droplet diameter, diameter change, temperature evolution, velocity and computed transient evaporation rate of the droplet stream. The accuracy and resolution of the measurements are evaluated by comparison with theoretical values and values measured with alternative means. Furthermore, the results are used to investigate how the evaporation rate is modified by interaction among droplets in the droplet stream and how these rates differ from evaporation rates predicted for isolated droplets, using the well proven Abramzon and Sirignano model. Finally, the evaporation rate, including the influence of droplet interaction, is shown to be in line with correlations suggested by Virepinte; refinement to this correlation is proposed.

Evaporation of ethanol-water sessile droplet of different compositions at an elevated substrate temperature

We experimentally investigate the evaporation dynamics of sessile droplets with different compositions of ethanol-water binary mixture at different substrate temperatures. At room temperature, a binary droplet undergoes two distinct evaporation stages unlike only the pinned stage evaporation for pure droplets. In the binary droplets, the more volatile ethanol evaporates faster leading to a nonlinear trend in the evaporation process. At elevated substrate temperature, we observed an early spreading stage, an intermediate pinned stage and a late receding stage of evaporation. Increasing the substrate temperature decreases the lifetime of binary droplets rapidly. At high substrate temperature, we found that the lifetime of the droplet exhibits a non-monotonic trend with the increase in ethanol concentration in the binary mixture, which can be attributed to the non-ideal behaviour of water-ethanol binary mixtures. Interestingly, the evaporation dynamics for different compositions at high substrate temperature exhibits a self-similar trend showing a constant normalised volumetric evaporation rate for the entire evaporation process. This indicates that the evaporation dynamics of a binary droplet of a given composition at high substrate temperature is equivalent to that of another pure fluid with a higher volatility at room temperature. The evaporation rates of pure and binary droplets at different substrate temperatures are compared against a theoretical model developed for pure and binary mixture droplets. The model predictions are found to be quite satisfactory for the steady evaporation phase of the droplet lifetimes.

Evaporation Rate of Colloidal Droplets of Jet Fuel and Carbon-Based Nanoparticles: Effect of Thermal Conductivity

Adding nanoparticles to liquid fuel is known to promote its combustion characteristics through improving several thermo-physical properties. This study investigates the effects of adding carbon nanoparticles on thermal conductivity and evaporation rate of liquid jet fuel. Multi-walled carbon nanotubes, activated carbon nanoparticles, and graphene nanoplatelets were added to jet fuel at different concentrations to prepare colloidal suspensions. Thermal conductivity is determined by passing known amounts of heat through a very thin layer of fuel and measuring temperature difference across its thickness. A fiber-supported droplet technique is also used to evaluate evaporation rate due to force convection of a hot inert gas. It is observed that both thermal conductivity and evaporation rate increase as a result of nanoparticle addition. Since there is no radiation heat transfer mechanism, the increase in evaporation rate is concluded to be only due to enhanced thermal conductivity.

The study of evaporation characteristics of the desulfurization wastewater (electrolyte solution) droplet

In this study, the evaporation behavior of a desulfurization wastewater (electrolyte solution) droplet with different solute concentration at different ambient gas temperature, was investigated by hanging on a glass fiber in a hot constant chamber. A high speed camera was used to record the evaporation process of the droplet. The radius change of the droplet in different conditions were given. A fine thermocouple was inserted in the distilled water droplet to record the temperature history during evaporation. A mathematical model was built with consideration of the effects on the concentration of the water activity and the density change. The results showed that concentration in the surface region was higher than that in the uniform concentration model. The uniform concentration was an assumption of less precision for this droplet evaporation calculation. Additionally, for the wastewater solution whose density changed greatly with concentration, the results showed the density change gave the dominated factor affecting the change of the droplet evaporation rate. Finally, the evaporation and crystallization process gave the effect on the surface region of the droplet keeping the solute concentration relatively high. This lead to the lower evaporation rate when adding non-evaporating dissolved solutes at the beginning period of evaporation.

Effect of air turbulence and fuel composition on bi-component droplet evaporation

Understanding the influence of fuel composition and air turbulence on evaporation of bi-component fuel droplet is the aim of the current investigation. Experiments were carried out with a single fuel droplet (a mixture of n-heptane and ethanol) suspended using the cross-wire technique within a box of turbulence facility that is capable of generating near zero-mean homogeneous and isotropic turbulence at its center. The fuel composition (i.e. the volume fraction of ethanol) as well as turbulent intensity within the chamber were varied over a wide range. The images of the evaporating droplet were recorded using back-light illumination. The initial droplet size was about 30–40 times smaller than the integral length scale of air turbulence, while it was about 10 times larger than the Kolmogorov length scale. For each fuel composition, five different turbulent conditions were considered. While the effect of turbulence was found to enhance droplet evaporation rate for all cases, the extent of its influence depends on fuel vapor mass diffusivity in air, and, in addition, on the initial fuel composition of the binary mixtures. The evaporation constant for the first stage of evaporation is sensitive to both air turbulence level and composition, while that for the second stage of evaporation shows a specific trend with fuel composition for all cases of turbulent intensity. Finally, an experimental correlation for normalized evaporation constant is presented.

Experimental study on the evaporation and micro-explosion characteristics of nanofuel droplet at dilute concentrations

The evaporation and micro-explosion characteristics of nanofuel droplets were investigated using high-speed backlight imaging technique at 873 K and 1 bar. Cerium oxide (CeO2) nanoparticles were utilized as nano-additives at dilute concentration of 0.05% and 0.25% by weight added to diesel. The results showed that micro-explosion mechanism of DCe-0.05 and DCe-0.25 consisted of 8 distinct processes: first class bubble formation (caused by volatile components), porous spherical shell formation, second class bubble formation (caused by nanoparticles), agglomeration of bubbles, micro-explosion, steady evaporation, concentration of nanoparticles near the droplet surface, and compact spherical shell formation. However, only processes 1, 4, 5 and 6 occurred for diesel droplets. The evaporation rate of diesel droplets were significantly affected by nano-CeO2 concentrations. An increase in the evaporation rate with nanoparticle concentrations, but a decrease in the evaporation rate at steady evaporation stage. This is because the formation of a compact spherical shell on the droplet surface suppressed liquid fuel diffusion. The micro-explosion delay of DCe-0.05 and DCe-0.25 decreased by 24.1% and 47.1% compared with diesel. Two new parameters were proposed for quantitative analysis expansion and micro-explosion characteristics, namely, expansion and micro-explosion intensity. The micro-explosion intensity of DCe-0.05 and DCe-0.25 increased by 37.5% and 49.5%, respectively.

Numerical investigation of evaporation and radiation absorption of a non-spherical water droplet under asymmetrically radiative heating

A numerical model for evaporation along with internal radiation absorption of a non-spherical droplet is presented. In this model, the VOF method is utilized to trace the interface and the radiative transfer is taken into account by using the Monte Carlo method combined with a contour based interface reconstruction algorithm. Meanwhile, the dynamic mesh technique is applied to increase the computational efficiency. The validated model is used to investigate the radiation absorption inside prolate and oblate water droplets under infrared laser irradiation, and a parametric study for the effects of droplet’s shape and size is presented. The results reveal that the shape of droplet dominates the spectral absorptance when the droplet’s optical thickness is small, but for optically thick droplets, the radiation absorption turns to be dominated by the spectral reflectivity of the irradiated surface. For a deformable droplet under asymmetrically radiative heating, the incident radiation can significantly enhance the heat transfer and evaporation processes. In addition, the assumption of uniform radiation absorption is found to be valid to optical thin droplets, whereas this assumption will underestimate the average interface temperature and evaporation rate of droplets with large optical thickness.

Simultaneous removal of nitrogen oxides and sulfur dioxide using ultrasonically atomized hydrogen peroxide.

A new method was developed for denitrification and desulfurization using hydrogen peroxide with the aid of an ultrasonic nebulizer to obtain high removal efficiency of NOx and SO2. Comparing with the atomizing nozzles having the aperture size of 0.01~0.02mm, the droplets generated using the ultrasonic nebulizer show the smallest d50 value of 7.2μm, with 72% possessing the size less than 10μm. Based on the numerical simulation of the vaporization rate of droplets, it is indicated that the droplets with the size of 7.2μm can be vaporized totally at very short residence time (0.11s) under 130°C. Effects of influence factors including the reaction temperature, the initial H2O2 concentration, pH value, and the flue gas flow rate were studied on the removal efficiencies of NO and SO2. Using the in-series double-oxidation subsystems with H2O2 concentration of 6wt%, pH5.0, and the reaction temperature of 130°C, the removal efficiencies of SO2 and NO are respectively 100% and 89.3% at the short residence time of 1.8s, and the removal efficiency of NO can be increased to 100% as the residence time is longer than 3.7s. It is confirmed that the ultrasonically atomized H2O2 can indeed enhance the removal efficiencies of NO and SO2 at the optimal temperature, owing to the fast vaporization rate of fine droplets as well as the formation of more active radicals to be captured by NO and SO2 simultaneously. The results here provide a promising route to remove effectively the emissions of NO and SO2 simultaneously. Graphical abstract.

Multi-Solvent Microdroplet Evaporation: Modeling and Measurement of Spray-Drying Kinetics with Inhalable Pharmaceutics.

Evaporation and particle formation from multi-solvent microdroplets containing solid excipients pertaining to spray-drying of therapeutic agents intended for lung delivery were studied. Various water and ethanol co-solvent systems containing a variety of actives and excipients (beclomethasone, budesonide, leucine, and trehalose) were considered. Numerical methods were used to predict the droplet evaporation rates and internal solute transfers, and their results verified and compared with results from two separate experimental setups. In particular, an electrodynamic balance was used to measure the evaporation rates of multicomponent droplets and a monodisperse droplet chain setup collected dried microparticles for further analytical investigations and ultramicroscopy. The numerical results are used to explain the different particle morphologies dried from solutions at different co-solvent compositions. The obtained numerical data clearly show that the two parameters controlling the general morphology of a dried particle, namely the Péclet number and the degree of saturation, can change with time in a multi-solvent droplet. This fact complicates product development for such systems. However, this additional complexity vanishes at what we define as the iso-compositional point, which occurs when the solvent ratios and other composition-dependent properties of the droplet remain constant during evaporation, similar to the azeotrope of such systems during distillation. Numerical and experimental analysis of multi-solvent systems indicate that spray-drying near the iso-compositional ratio simplifies the design and process development of such systems.

Modeling of Sessile Droplet Evaporation on Engineered Surfaces

The evaporation of sessile drop has a wide range of application that includes printing, washing, cooling, and coating. Due to the complex nature of drop evaporation process, this phenomenon is reliant on several parameters such as ambiance and physiochemical properties of liquid and surface. In the present study, a mathematical model of water droplet evaporation on an engineered aluminum surface is developed. Experimental study is carried out for the validation of code. The data obtained from the simulation is validated against the data obtained from an experimental study as well as the data available in the literature and good agreement was found among them. Post-validation, the effect of surface wettability and environment conditions on a droplet evaporation rate is estimated. It is inferred from the outcomes that the temperature at the apex of the drop varies linearly with the increasing relative humidity. Droplet volume has a significant impact on the evaporation rate and comparatively higher evaporative flux for a smaller volume of the drop with large contact angles. This unveils the possibility of achieving the required evaporation rate by controlling surface wettability and relative humidity conditions near the drop.

Warming-up and evaporation characteristics of homogeneous and heterogeneous water droplets

The study reports the experimental results of warming-up and evaporation of homogeneous and heterogeneous water droplets at high temperatures, 100–600 °C. The heterogeneous water droplet is formed by covering a solid opaque graphite particle by a thin water layer. Differences between the warming-up mechanisms of the homogeneous and heterogeneous water droplets with an initial liquid volume from 10 μl to 20 μl at the convective heating are shown. The contactless method Planar Laser-Induced Fluorescence allows the analysis of the temperature distributions inside the homogeneous droplets and inside a liquid phase of the heterogeneous droplets, laying emphasis on the novelty of the research. A maximum temperature in the central part of the liquid phase of the heterogeneous droplets is approx. 90 °C; a maximum temperature in the homogeneous droplets is approx. 50 °C. The heterogeneous droplet heats up by 20 ± 3% longer than the homogeneous one. Moreover, a warming-up rate of the liquid phase of the heterogeneous droplet is less than that of the homogeneous water droplet by 85%. However, the size decreasing rate of the heterogeneous droplets is sometimes higher than that of the homogeneous droplets by 80%. The mean and instant evaporation rate of homogeneous and heterogeneous water droplets are compared. The study discusses an influence of convection in the liquid phase of the heterogeneous droplets on evaporation characteristics. The time of the complete water evaporation decreases by 40% due to a solid inclusion presence. A dimensionless criterion of the convective heat transfer enhancement in a water droplet containing the solid opaque inclusion is used to generalize the experimental data. The findings obtained are critically important to improve the existing high-temperature technologies and methods of water purification and to develop innovative ones.

Theoretical study on combustion of non-spherical particles in nano-aluminized propellant in air**Foundation Item: Science & Department of Heibei Province (No. 16211013D), Handan Science & Technology Development Bureau (No. 1511103015).

To investigate the deflagration phenomenon of an aluminized solid propellant during the combustion process, an improved theoretical combustion model has been developed. The model uses non-spherical particles for predicting the instantaneous mass evaporation rates of droplets as well as the burning time. The burning behavior of individual prolate and oblate spheroidal droplets, including the surface-area ratio, Nusselt numbers, temperature, and size change rate, was theoretically analyzed to elucidate the effect of non-spherical grains on the burning stability. Models for the Al evaporation rates and burnout time of both prolate and oblate spheroids in the diffusion-kinetics controlled regimes were established. According to the results, the particle morphology, size, and Reynolds numbers significantly affect the burning characteristics of nano-aluminized propellants. The proposed model is useful for steady-state combustion-performance assessment of aluminized solid propellants.

Droplet evaporation characteristics of aviation kerosene surrogate fuel and butanol blends under forced convection

A droplet evaporation model for blends of aviation kerosene surrogate fuel (n-decane and toluene) and butanol (a promising bio-jet fuel) was presented and validated by conducting droplet suspension experiments. The model incorporates the non-ideal effects of blended fuels using the component activity coefficient, which turns out to greatly deviate from unity for test fuels and thus significantly influence their evaporation rate. The effects of recirculation inside the suspended droplet on the heat and mass diffusion were also considered. The experimental data were largely consistent with simulated results under different ambient temperatures and different convention velocities. With increasing butanol content, the droplet evaporation rate increased and the micro-bubble phenomenon was more likely to occur. The convection velocity exhibited a significant influence on the evaporation process as Reynolds number and Sherwood number rose under forced convection conditions. The discrepancy between experimental data and simulated results at the convection velocity of 0.05 m/s was small and comparable with that at the convection velocity of 0.1 m/s and 0.5 m/s, which implies the model could reflect the convection effect reasonably. Temporal evolutions of component concentrations at the liquid surface demonstrated that butanol and toluene were likely to evaporate at a faster rate than n-decane.

Multi-component droplet evaporation model incorporating the effects of non-ideality and thermal radiation

Currently, sophisticated fuel formulation and high temperature combustion in gas turbine and internal combustion engines make it important to investigate the effects of mixture non-ideality and radiation absorption on fuel droplet evaporation. In this study, an improved evaporation model by considering activity coefficients (AC) and external thermal radiation was established to simulate the evaporation process of multi-component non-ideal fuel droplets, and droplet suspension experiment was performed to validate the proposed model. It was found that the accuracy of simulated results was enhanced by considering activity coefficients and radiation absorption, and both effects were dependent on ambient temperature. The effect of activity coefficient was significant at low temperature (503 K), under which the droplet evaporation rate in the initial period was obviously faster than that at later stage. Consequently, the droplet lifetime decreased by about 8% at low temperature when activity coefficient was taken into consideration. At high temperature (703 K), however, the effect of activity coefficient or non-ideality on the droplet evaporation rate turned out to be insignificant. The radiation had a strong influence on evaporation at high temperature with the droplet lifetime decreasing 48% when ambient temperature increased from 503 K to 703 K. There seemed to be a critical diameter, under which the effect of radiation became negligible. It is also demonstrated that the component concentration gradients existed inside the non-ideal droplets in the initial period because of relatively low mass diffusion rate. As time elapsed, the gradients gradually disappeared due to the fact the components with large activity coefficient nearly completely evaporated.

Characteristics of Spray Atomization for Liquid Droplets Formed Using a Rotary Bell Atomizer

In automotive engineering, paint evaporation is considered one of the major sources of volatile organic compound emission. The rotary bell atomizer (RBA) is a special atomizer used for improved automotive painting. A model to predict the droplet size was developed by combining two already-reported models. Further, the calculated values of evaporation rate constant, K, and the RBA nozzle parameter, K1, for water and clearcoat at room temperature (24 °C) are presented here. K1 was dependent on the flow rate and bell speed, but its variance for clearcoat was less than the measurement uncertainty. The Sauter mean diameter of the particle leaving the RBA at different flow rates and bell speeds can be predicted using K1. The values of K were 1.3 × 10−5 to 2.0 × 10−5 cm2/s for clearcoat and 8.6 × 10−6 to 1.53 × 10 −5 cm2/s for water. A generic model which can anticipate the evaporation rate of droplets with time length was also introduced.

Thermo-fluid simulation of the gas turbine performance based on the first law of thermodynamics

The thermal efficiency of the gas turbine depends on the compression work which is in direct relationship with the working fluid temperature. Amongst various solutions presented to augment gas turbines and combined cycle power plants output, wet compression is known as the most cost-effective method. This paper provides a method of simulating wet compression, based on the first law of thermodynamics. Water droplet evaporation rate, compression work, and the concept of wet compression efficiency are described. Results of first law and second law analyses are compared, and the effect of wet compression on gas turbine performance is indicated. Moreover, the results of the wet compression procedure are compared with both the values obtained for the dry compression process and the results of wet compression analysis using the second law. Finally, it is seen that the first law analysis provides equally consistent results with the experimental data for the cases considered in the paper.

Modeling pressure loads during a premixed hydrogen combustion in the presence of water spray

This paper proposes a method for pressure evolution modeling during combustion process in presence of water spray. A simplified model based on empirical correlations is developed, which allows the estimation of the main factors influencing the pressure evolution, such as the combustion rate, the convective heat loss and the droplet evaporation rate. The results are then used as a guideline to adjust the parameters of a three-dimensional hydrodynamic code based on CREBCOM combustion model developed and validated for large-scale hydrogen combustion. This methodology provides an approach to estimate the important parameters for the determination of the pressure loads. Simulation results for hydrogen-air combustion in presence of water spray using the present model compare favorably to the experimental data of Carlson et al. [1].