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At least 73 records · Page 4

Marangoni instability induced convection in an evaporating liquid droplet

The processes occurring when a liquid drop undergoes evaporation are described. When a liquid drop undergoes evaporation, its surface temperature decreases. If the droplet is free floating in a microgravity environment, the heat transfer process inside the droplet is initially condition controlled. As the process continues, a radial temperature gradient builds up at the free surface until the critical Marangoni number is exceeded. Then the onset of instability induces thermocapillary convective flows, which in turn speed up the evaporation. The convective flows will subside when the interior of the droplet reaches a certain equilibrium temperature, and the process will return to the diffusion controlled mode. Both preliminary modeling and recent laboratory data have confirmed that Marangoni instability induced convection can and does occur in the droplet evaporation process. Mathematical models representing Marangoni instability in an evaporating liquid drop are presented. An ideal space experiment to study and characterize the onset of Marangoni instability in an evaporating liquid droplet and to establish the effect of Marangoni instability induced convection on the droplet evaporation rate is outlined and the need for conducting such experiments in space is highlighted. However, before an opportunity to conduct experiments in space arises, ground based experiments have to be conducted to study feasibility issues and proof of concept. A ground based experiment of this type is outlined.

Chai, An-Ti↗

A New Approach to Measure Contact Angle and Evaporation Rate with Flow Visualization in a Sessile Drop

The contact angle and the spreading process of sessile droplet are very crucial in many technological processes, such as painting and coating, material processing, film-cooling applications, lubrication, and boiling. Additionally, as it is well known that the surface free energy of polymers cannot be directly, measured for their elastic and viscous restraints. The measurements of liquid contact angle on the polymer surfaces become extremely important to evaluate the surface free energy of polymers through indirect methods linked with the contact angle data. Due to the occurrence of liquid evaporation is inevitable, the effects of evaporation on the contact angle and the spreading become very important for more complete understanding of these processes. It is of interest to note that evaporation can induce Marangoni-Benard convection in sessile drops. However, the impacts of the inside convection on the wetting and spreading processes are not clear. The experimental methods used by previous investigators cannot simultaneously measure the spreading process and visualize the convection inside. Based on the laser shadowgraphic system used by the present author, a very simple optical procedure has been developed to measure the contact angle, the spreading speed, the evaporation rate, and to visualize inside convection of a sessile drop simultaneously. Two CCD cameras were used to synchronously record the real-time diameter of the sessile drop, which is essential for determination of both spreading speed and evaporation rate, and the shadowgraphic image magnified by the sessile drop acting as a thin plano-convex lens. From the shadowgraph, the inside convection of the drop can be observed if any and the image outer diameter, which linked to the drop profile, can be measured. Simple equations have been derived to calculate the drop profile, including the instantaneous contact angle, height, and volume of the sessile drop, as well as the evaporation rate. The influence of the inside convection on the wetting and spreading processes can be figured out through comparison of the drop profiles with and without inside convection when the sessile drop is placed at different evaporation conditions.

Zhang, Nengli↗

Investigation of Transient Gas Phase Column Density Due to Droplet Evaporation

A NASA robotic refueling mission experiment on board the International Space Station (ISS) was designed to repeatedly transfer simulated cryogenic propellant between two dewars. After each metered transfer, the cryogen was to be vented overboard via sublimation or evaporation. ISS payload providers must conduct analyses to demonstrate that any planned gaseous venting generate no more than a certain level of material that may interfere with optical measurements from other payloads that may be located nearby. This requirement is expressed in terms of a maximum column number density (CND). For the experiment under consideration, fluid droplets likely would accompany any such vapor. Earlier related studies led to development of analytical expressions for column density along general paths for a number of practical cases under steady conditions, including droplet evaporation. These expressions are not appropriate for rapid evaporation of small droplets however, since the droplets cannot sustain mass flow rates consistent with steady conditions. In this work, analytical expressions are developed for estimating column density near a rapidly evaporating droplet along general paths. The influence for instantaneous evaporation is created first as a limiting case, where it is found the peak value occurs at the time it takes a wave of vapor to reach the closest point along the optical path traveling at its most probable thermal speed. Next, the case for finite-period evaporation is evaluated for constant conditions. Compared to the instantaneous case, peak column density occurs shortly after droplet extinction, but at a lower intensity. A new mathematical function is discovered that solves the integrals associated with this case. Finally, ways to account for droplet motion and changes in evaporation rate with size and temperature are discussed in this framework.

Woronowicz, M. S.↗

On falling film evaporator – A review of mechanisms and critical assessment of correlation on a horizontal tube bundle with updated development

Optimization of the energy efficiency and reduction of the greenhouse gas emission for the heat pump system is imperative to meet the net-zero goals at 2050. Chillers with falling film evaporator design not only possess better system performance but also contain less refrigerant inventory. Hence, accurate prediction of the evaporator performance is pivotal especially when charged with low-GWP refrigerant. Here, the study reviews the correlations for falling film evaporator with a horizontal tube bundle configuration. The major efforts of this study include four tasks: (a) literature review of the experimental studies and available empirical correlations; (b) comprehensive discussion of the falling film evaporation heat transfer mechanism; (c) development of a new rationally based correlation based on available literature; and (d) comparison of different correlations based on the existing data. The collected data includes 4114 data points from 8 sources, 6 refrigerants (R-600a, R-290, R-245fa, R-134a, R-1234ze(E), R-123), 5 types of the tubes (Plain, Turbo-GII-HP, GEWA-B, Low-fin, High-Flux), liquid Weber number from 2.2 × 10 –6 to 0.7, imposed vapor Weber number from 0 to 37.2, heat flux from 2.5 to 151.5 kW/m 2 , and film Reynolds number from 1 to 3159.8. The new correlation gives a MAD of 28.3%, and an R 2 of 0.86. Yet, the developed correlation considers various heat transfer mechanisms, including the transition point from falling film evaporation to the nucleate boiling, local evaporation, dry-out, mist flow, imposed flow, and enhanced tube effects.

42 ENGINEERING↗

Elucidating the Mechanism of Helium Evaporation from Liquid Water

Here, we investigate the evaporation of trace amounts of helium solvated in liquid water using molecular dynamics simulations and theory. Consistent with experimental observations, we find a super-Maxwellian distribution of kinetic energies of evaporated helium. This excess of kinetic energy over typical thermal expectations is explained by an effective continuum theory of evaporation based on a Fokker–Planck equation, parametrized molecularly by a potential of mean force and position-dependent friction. Using this description, we find that helium evaporation is strongly influenced by the friction near the interface, which is anomalously small near the Gibbs dividing surface due to the ability of the liquid–vapor interface to deform around the gas particle. Our reduced description provides a mechanistic interpretation of trace gas evaporation as the motion of an underdamped particle in a potential subject to a viscous environment that varies rapidly across the air–water interface. From it we predict the temperature dependence of the excess kinetic energy of evaporation, which is yet to be measured.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Insights Into the Aerodynamic Versus Radiometric Surface Temperature Debate in Thermal-Based Evaporation Modeling

Global evaporation monitoring from Earth observation thermal infrared satellite missions is historically challenged due to the unavailability of any direct measurements of aerodynamic temperature. State-of-the-art one-source evaporation models use remotely sensed radiometric surface temperature as a substitute for the aerodynamic temperature and apply empirical corrections to accommodate for their inequality. This introduces substantial uncertainty in operational drought mapping over complex landscapes. By employing a non-parametric model, we show that evaporation can be directly retrieved from thermal satellite data without the need of any empirical correction. Independent evaluation of evaporation in a broad spectrum of biome and aridity yielded statistically significant results when compared with eddy covariance observations. While our simplified model provides a new perspective to advance spatio-temporal evaporation mapping from any thermal remote sensing mission, the direct retrieval of aerodynamic temperature also generates the highly required insight on the critical role of biophysical interactions in global evaporation research.

54 ENVIRONMENTAL SCIENCES↗

Microphysics Dominates Sub‐Cloud Rain Evaporation in Trade Cumuli Over Barbados

This study investigates the microphysical and thermodynamic influences on North Atlantic trade-cumulus rain evaporation in the sub-cloud layer over Barbados from January to November 2020. Using radar observations and a 1-D model, the results reveal that microphysical properties, namely geometric mean diameter (D g ) and raindrop concentration, primarily control evaporation processes under conditions of limited thermodynamic variability. Thermodynamic factors like cloud base height and relative humidity exert a smaller influence due to their narrow observed ranges. Small D g leads to rapid increases in rain evaporation fraction (REF), as small drops evaporate completely, while larger D g yields slower, more gradual REF changes. Frequent weak-rain cases reduce the mean evaporation flux, whereas infrequent intense-rain events substantially enhance it. These findings highlight the pivotal role of microphysical variability in shaping sub-cloud evaporation in this trade cumulus regime, while thermodynamic effects may be more important in other environments.

54 ENVIRONMENTAL SCIENCES↗

Laser heating and evaporation of a single droplet

The laser technology is being abundantly studied for controlled energy deposition for a range of applications in aerodynamic flow control, material processing, ignition, and combustion. The absorption of laser radiation by liquid droplets affects further propagation of laser in the atmosphere and causes bleaching of suspended droplets while the ignition and combustion characteristics in combustors are influenced by the evaporation rate of the sprayed fuel. In this work, we present a multi-dimensional mathematical model built on OpenFOAM for laser heating and evaporation of a single droplet in the diffusion dominated regime taking into account absorption of the laser radiation, evaporation process and vapor flow dynamics. The developed solver is validated against available experimental and numerical data for the ethanol and water droplet heating and evaporation. For continuous heating the peak temperature is established by the balance of cooling, evaporation and heating and results in high temperature for larger droplets. It has been shown that for heating by a single laser pulse the maximum temperature of droplets depends only on the peak intensity of the laser radiation. Furthermore, for the peak irradiance close to the transition to the boiling regime, temporal dynamics of the droplet temperature is independent of the droplet size. With proper normalization of time, the dynamics of the droplet shrinkage and cooling is shown to be independent of droplet sizes and peak laser intensities. The influence of cooling and evaporation processes on droplet heating was found to be controlled by the pulse repetition rate for repeated pulse operation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Deuteron Evaporation from N = Z Compound Nuclei

Deuteron evaporation was observed from the N = Z compound nuclei 52 Fe ⋆ , 56 Ni ⋆ , and 64 Ge ⋆ in an experiment conducted at Argonne National Laboratory, USA. The experiment included a novel combination of two highly pixelated double-sided Si-strip detectors inside the Microball chargedparticle detection array, allowing for unequivocal discrimination of evaporated deuterons from protons and α particles. In conjunction with the Gammasphere array, Neutron Shell, and additional ancillary detectors, decay paths into various residual nuclei were investigated. The study provides insights into the competition of deuteron vs. proton-neutron evaporation as a function of available excitation energy and populated angular momentum. Results are interpreted using a statistical evaporation formalism for multiple subsequent particle emissions. The decisive factor in the comparison appears to be the available excitation energy in the residual system, with single nucleon evaporation preferred over deuteron evaporation for higher excitation energies.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

A dual membrane-adsorption evaporator for solar-powered lithium extraction from complex brines

A reliable supply of lithium is required to meet the increased demand for batteries over the coming decades. In this work, we demonstrated the potential to effectively extract lithium from brines by coupling solar-powered evaporation, adsorption, and membrane technologies together. We first synthesized a three-dimensional adsorptive evaporator by coating a lithium manganese oxide material onto a cotton stick using an easily scalable, one-step method. An osmotic membrane was then installed at the root of the evaporator to enhance the lithium to magnesium selectivity, prevent scaling caused by divalent cations, and thus further increase the water evaporation flux. The operation of the dual membrane-adsorption evaporator is entirely driven by osmosis and capillary force, demanding no extra energy input. The integration of the osmotic membrane was found to increase the lithium to magnesium selectivity over 10-fold to higher than 40. The dual process also produced high lithium to calcium selectivity and proved to sustain long-term stability by self-managing its internal osmotic pressure. Last, a test was done in three simulated brine solutions with varied brine chemistry and the evaporation rate stayed high and consistent throughout the long-term test. This illustrates that this technology can be used in varied brine solutions throughout the world providing efficient lithium capture and separation from competing divalent cations.

Eskafi, Aydin F. [University of California, Berkel↗

Minimizing Cr-Evaporation from Balance Of Plant Components By Utilizing Cost-Effective Alumina-Forming Austenitic Steels

A solid oxide fuel cell (SOFC) is a clean and efficient energy conversion device. The development of intermediate-temperature SOFCs has made it preferable to use metallic interconnects (MICs) to greatly reduce the cost and significantly increase the efficiency compared to ceramic interconnect materials. However, gaseous chromium species will evaporate from the chromium-containing layer formed on the surface of commonly used MICs and balance of plant (BoP) components. Volatile chromium species have been shown to form solid deposits which poison the cathodes of SOFCs, causing drastic cell performance degradation and thereby limiting commercialization. In order to alleviate the Cr poisoning and achieve long-term high performance of SOFC stacks, various Al 2 O 3 -forming austenitic (AFA) stainless steels applied at different temperatures are evaluated in this project. Based on our Phase I results (500 h operation), it is shown that on the AFAs, an alumina-based protective layer forms under high temperature that is invulnerable to water vapor effects and suppresses the diffusion of chromium and manganese which can prevent the generation of spinels on the alloy surface. Therefore, 310S, OC4 and OC5 at 800 °C and 625, OC11 and OC11LZ at 900 °C are selected to be tested in the Phase II long-term operation. From the results, we find that besides the lower Cr evaporation rates and better oxidation resistance of AFAs than benchmark alloys after short-term (500 h) operation, AFAs also possess the sturdy and compact alumina layer after a long-term operation (5000 h). A protective oxide layer is of great importance for the long-term high-temperature operation of structural materials. The high-temperature oxidation behavior of AFAs and commercial 310S and 625 alloys in Air + 10% H 2 O at 800 °C and 900 °C is systematically investigated. Severe breakaway oxidation and minor spallation are observed for the 310S and 625 after the long-term operation, while the AFAs show high oxidation resistance. It is found that the formation of a continuous alumina layer could greatly prevent the volatilization of chromium vapors. In addition, the corresponding evolving models are discussed. Chromium evaporation from BoP components in high-temperature environment could severely deteriorate the electrochemical performance of SOFC. Several methods were applied to evaluate the Cr evaporation rates of BoP after 500 h exposure at 800 °C to 900 °C in air with 10% H 2 O. An optimal method was designed to exclude the effect of silicon (Si) deposits from quartz tube and sodium (Na) deposits from the sodium carbonate on the oxidation process and the chemical interaction between Cr gaseous species and alumina tube which could provide further quantitative correlation of the evaporated Cr species quantities and degradation rates of SOFC. Based on the great performance of AFAs after long-term operation, AFAs are assembled with Anode-supported cells (ASC) to investigate the the Cr deposition of anode-supported cell under a constant current density of 0.5 A cm -2 at 800 °C with AFA alloys compared with commercial alloys. In addition, the anodic and cathodic processes are deconvoluted by distribution of relaxation times (DRT) method which are comprehensively discussed. It is found out that the voltage exhibited a slight decrease of 5.09 % and 1.54 % in the presence of OC11 and OC11LZA alloy, respectively. However, a considerable decrease of 22.14 % and 12.06 % was determined in the presence of 310S and 625 alloy, respectively. AFAs possessing the low-cost, low Cr evaporation rates and the high oxidation resistance will make it of great potential to replace the existing BoP components.

01 COAL, LIGNITE, AND PEAT↗

Characterization Results for the March 2022 Tank Farm 3H Evaporator Overhead Sample

On an annual basis, Savannah River Mission Completion (SRMC) provides 2H and 3H evaporator overhead samples to Savannah River National Lab (SRNL) to be analyzed per Section 5.2 of the Effluent Treatment Project (ETP) Waste Compliance Plan (WCP) and the Waste Acceptance Criteria (WAC). This report presents characterization results for the March 2022 3H evaporator overhead sample. The sample was clear and colorless with no visible solids. The results provide measurements for cesium-137 ( 137 Cs), strontium-90 ( 90 Sr), and iodine-129 ( 129 I) with the radionuclide concentration limits specified by the WAC. These analyses were performed on a single sample replicate. A summary of the analytical results for the 3H evaporator overhead sample includes the following. The measured cesium-137 activity in the 3H evaporator overhead sample is 4.59E+02 dpm/mL which is above the ETP WAC limit of 3.28E+02 dpm/mL. The strontium-90 activity in the 3H evaporator overhead sample is <2.95E+01 dpm/mL. This is below the ETP WAC limit of 1.76E+02 dpm/mL. The iodine-129 activity in the 3H evaporator overhead sample is <1.92E-02 dpm/mL. This is below the ETP WAC limit of 1.00E+00 dpm/mL.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Characterization Results for the September 2023 Tank Farm 3H Evaporator Overhead Sample

On an annual basis, Savannah River Mission Completion (SRMC) provides 2H and 3H evaporator overhead samples to Savannah River National Lab (SRNL) to be analyzed per Section 5.2 of the Effluent Treatment Project (ETP) Waste Compliance Plan (WCP) and the Waste Acceptance Criteria (WAC). This report presents the average characterization results for the September 2023 3H evaporator overhead sample. The sample was clear and colorless with no visible solids. The results provide measurements for cesium-137 ( 137 Cs), strontium-90 ( 90 Sr), and iodine-129 ( 129 I) with the radionuclide concentration limits specified by the WAC. These analyses were performed in duplicate, and all three measured radionuclide concentrations were within ETP WAC limits. A summary of the analytical results for this 3H evaporator overhead sample includes the following: The measured cesium-137 activity in the 3H evaporator overhead sample averaged 5.70E+01 dpm/mL, which is below the ETP WAC limit of 1.30E+03 dpm/mL. As seen through historical results, Cs-137 continues to present a decreasing activity since 2020. The strontium-90 activity in the 3H evaporator overhead sample averaged <2.16E00 dpm/mL, which is below the ETP WAC limit of 1.76E+02 dpm/mL. The iodine-129 activity in the 3H evaporator overhead sample averaged <9.08E-02 dpm/mL, which is below the ETP WAC limit of 1.00E+00 dpm/mL

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Characterization Results for the October 2024 Tank Farm 3H Evaporator Overhead Sample

On an annual basis, Savannah River Mission Completion (SRMC) provides 2H and 3H evaporator overhead samples to Savannah River National Lab (SRNL) to be analyzed per Section 5.2 of the Effluent Treatment Project (ETP) Waste Compliance Plan (WCP) and the Waste Acceptance Criteria (WAC). This report presents characterization results for the October 2024 3H evaporator overhead sample. The sample was clear and colorless with no visible solids. The results provide measurements for cesium-137 (137Cs), strontium-90 (90Sr), and iodine-129 (129I) with the radionuclide concentration limits specified by the WAC. These analyses were performed in duplicate, and a summary of the analytical results for this 3H evaporator overhead sample includes the following: The measured cesium-137 activity in the 3H evaporator overhead sample averaged 6.72E+01 dpm/mL, (3.90E+00 %RSD), which is below the ETP WAC limit of 1.30E+03 dpm/mL. The strontium-90 activity in the 3H evaporator overhead sample averaged <2.72E+00 dpm/mL, which is below the ETP WAC limit of 1.76E+02 dpm/mL. The iodine-129 activity in the 3H evaporator overhead sample averaged <1.63E-01 dpm/mL, which is below the ETP WAC limit of 1.00E+00 dpm/mL.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Characterization Results for the August 2025 Tank Farm 2H Evaporator Overhead Sample

On an annual basis, Savannah River Mission Completion (SRMC) provides 2H and 3H evaporator overhead samples to Savannah River National Lab (SRNL) to be analyzed per Section 5.2 of the Effluent Treatment Project (ETP) Waste Compliance Plan (WCP) and the Waste Acceptance Criteria (WAC). This report presents the average characterization results for the August 2025 2H evaporator overhead sample. The sample was clear and colorless with no visible solids. The results provide measurements for cesium-137 ( 137 Cs), strontium-90 ( 90 Sr), and iodine-129 ( 129 I) with the radionuclide concentration limits specified by the WAC. These analyses were performed in duplicate, and all three measured radionuclide concentrations were within ETP WAC limits. A summary of the analytical results for this 2H evaporator overhead sample includes the following: The measured cesium-137 activity in the 2H evaporator overhead sample averaged 3.02E+02 dpm/mL, which is below the ETP WAC limit of 1.30E+03 dpm/mL. The strontium-90 activity in the 2H evaporator overhead sample averaged 3.33E+00 dpm/mL, which is below the ETP WAC limit of 1.76E+02 dpm/mL. The iodine-129 activity in the 2H evaporator overhead sample averaged 1.20E-01 dpm/mL, which is below the ETP WAC limit of 1.00E+00 dpm/mL. Although the measurements for Cs-137 and Sr-90 are lower compared to previous years, the results remain within a similar range to past measurements and are well below the WAC limits. Iodine-129 indicates detectable results compared to previous years, which can be attributed to recent salt batch processing trending close to the WAC limit for saltstone production. However, these results are still below the ETP WAC limit.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Evaporation rate and vapor pressure of selected polymeric lubricating oils.

A recently developed ultrahigh-vacuum quartz spring mass sorption microbalance has been utilized to measure the evaporation rates of several low-volatility polymeric lubricating oils at various temperatures. The evaporation rates are used to calculate the vapor pressures by the Langmuir equation. A method is presented to accurately estimate extended temperature range evaporation rate and vapor pressure data for polymeric oils, incorporating appropriate corrections for the increases in molecular weight and the change in volatility of the progressively evaporating polymer fractions. The logarithms of the calculated data appear to follow linear relationships within the test temperature ranges, when plotted versus 1000/T. These functions and the observed effusion characteristics of the fluids on progressive volatilization are useful in estimating evaporation rate and vapor pressure changes on evaporative depletion.

Gardos, M. N.↗

Maximum Evaporation Rates of Water Droplets Approaching Obstacles in the Atmosphere Under Icing Conditions

When a closed body or a duct envelope moves through the atmosphere, air pressure and temperature rises occur ahead of the body or, under ram conditions, within the duct. If cloud water droplets are encountered, droplet evaporation will result because of the air-temperature rise and the relative velocity between the droplet and stagnating air. It is shown that the solution of the steady-state psychrometric equation provides evaporation rates which are the maximum possible when droplets are entrained in air moving along stagnation lines under such conditions. Calculations are made for a wide variety of water droplet diameters, ambient conditions, and flight Mach numbers. Droplet diameter, body size, and Mach number effects are found to predominate, whereas wide variation in ambient conditions are of relatively small significance in the determination of evaporation rates. The results are essentially exact for the case of movement of droplets having diameters smaller than about 30 microns along relatively long ducts (length at least several feet) or toward large obstacles (wings), since disequilibrium effects are then of little significance. Mass losses in the case of movement within ducts will often be significant fractions (one-fifth to one-half) of original droplet masses, while very small droplets within ducts will often disappear even though the entraining air is not fully stagnated. Wing-approach evaporation losses will usually be of the order of several percent of original droplet masses. Two numerical examples are given of the determination of local evaporation rates and total mass losses in cases involving cloud droplets approaching circular cylinders along stagnation lines. The cylinders chosen were of 3.95-inch (10.0+ cm) diameter and 39.5-inch 100+ cm) diameter. The smaller is representative of icing-rate measurement cylinders, while with the larger will be associated an air-flow field similar to that ahead of an airfoil having a leading-edge radius comparable with that of the cylinder. It is found that the losses are less than 5 percent. It is concluded that such losses are, in general, very small (less than 1 percent) in the case of smaller obstacles (of icing-rate measurement- cylinder size); the motional dynamics are such, however, that exceptions will occur by reason of failure of very small droplets (moving along stagnation lines) to impinge upon obstacle surfaces. In such cases, the droplets will evaporate completely.

Lowell, H. H.↗

A theory of nondilute spray evaporation based upon multiple drop interactions

Drop interactions, changes in drop temperature, and the evolution of the ambient conditions due to heating and evaporation were taken into account in a theory of drop evaporation. A sphere of influence is defined for each drop, with all droplets having equal separation distances. Global conservation and state equations for a droplet spray are formulated, together with equations for single drop evaporation in finite surroundings. A criterion is defined for complete evaporation and the dynamics of spray evaporation are discussed. The theory is noted to be applicable for both dilute and nondilute spray evaporation effects.

Bellan, J.↗