Saturated Vapor Pressure Research Articles

Enhanced Light Absorption and Elevated Viscosity of Atmospheric Brown Carbon through Evaporation of Volatile Components.

Samples of brown carbon (BrC) material were collected from smoke emissions originating from wood pyrolysis experiments, serving as a proxy for BrC representative of biomass burning emissions. The acquired samples, referred to as "pyrolysis oil (PO1)," underwent subsequent processing by thermal evaporation of their volatile compounds, resulting in a set of three additional samples with volume reduction factors of 1.33, 2, and 3, denoted as PO1.33, PO2, and PO3. The chemical compositions of these POx samples and their BrC chromophore features were analyzed using a high-performance liquid chromatography instrument coupled with a photodiode array detector and a high-resolution mass spectrometer. The investigation revealed a noteworthy twofold enhancement of BrC light absorption observed for the progression of PO1 to PO3 samples, assessed across the spectral range of 300-500 nm. Concurrently, a decrease in the absorption Ångstrom exponent (AAE) from 11 to 7 was observed, indicating a weaker spectral dependence. The relative enhancement of BrC absorption at longer wavelengths was more significant, as exemplified by the increased mass absorption coefficient (MAC) measured at 405 nm from 0.1 to 0.5 m2/g. Molecular characterization further supports this darkening trend, manifesting as a depletion of small oxygenated, less absorbing monoaromatic compounds and the retention of relatively large, less polar, more absorbing constituents. Noteworthy alterations of the PO1 to PO3 mixtures included a reduction in the saturation vapor pressure of their components and an increase in viscosity. These changes were quantified by the mean values shifting from approximately 1.8 × 103 μg/m3 to 2.3 μg/m3 and from ∼103 Pa·s to ∼106 Pa·s, respectively. These results provide quantitative insights into the extent of BrC aerosol darkening during atmospheric aging through nonreactive evaporation. This new understanding will inform the refinement of atmospheric and chemical transport models.

The search for sparse data in molecular datasets: Application of active learning to identify extremely low volatile organic compounds

The formation of aerosol particles in the atmosphere is driven by the gas to particle conversion of extremely low volatile organic compounds (ELVOC), organic compounds with a particularly low saturation vapor pressure (pSat). Identifying ELVOCs and their chemical structures is both experimentally and theoretically challenging: Measuring the very low pSat of ELVOCs is extremely difficult, and computing pSat for these often large molecules is computationally costly. Moreover, ELVOCs are underrepresented in available datasets of atmospheric organic species, which reduces the value of statistical models built on such data. We propose an active learning (AL) approach to efficiently identify ELVOCs in a data pool of atmospheric organic species with initially unknown pSat. We assess the performance of our AL approach by comparing it to traditional machine learning regression methods, as well as ELVOC classification based on molecular properties. AL proves to be a highly efficient method for ELVOC identification with limitations on the type of ELVOC it can identify. We also show that traditional machine learning or molecular property-based methods can be adequate tools depending on the available data and desired degree of efficiency.

Experimental research and estimation model of gasoline evaporative emissions from vehicles in China

Evaporative emission is an important source of vehicle pollutant emission and volatile organic compounds (VOCs), causing serious environmental pollution. Carbon canisters are used to store fuel vapor in evaporative emission control (EVAP) system, but canisters are prone to saturation, leading to the direct release of fuel vapor into the atmosphere. Therefore, accurate estimation of fuel vapor generation is crucial for EVAP system. Gasoline evaporation rate is mainly influenced by vapor-liquid interface area, gasoline saturated vapor pressure, filling level and temperature. The quantitative relation between different parameters and gasoline evaporation rate has rarely been reported, and a gasoline evaporative emission estimation model suitable for China needs to be proposed urgently. In this study, gasoline evaporative emission tests have been carried out in VT-SHED, and the effects of vapor-liquid interface area, filling level and temperature on gasoline evaporative emissions have been analyzed under the premise of consistent gasoline temperature and ambient temperature. Some valuable conclusions are obtained. The results show that different from expectation, gasoline evaporative emissions are not positively correlated with the vapor-liquid interface area. There is an approximately exponential relationship between the headspace volume and gasoline evaporative emissions. The widely used Reddy equation and Hata equation underestimate the gasoline vapor generation in China. Based on China VI test program and gasoline, accurate estimation of mass transfer coefficient has been conducted, and a new semi-empirical estimation model for vapor generation has been proposed. The model can accurately estimate the fuel evaporation of vehicles in China, providing guidance for the matching and optimization of EVAP system.

Vaporization Phase Transition in Cryogenic Liquid Oxygen Sealing Film on Spiral Groove Faces.

The property of vaporization phase transition in liquid oxygen face seals is a key factor affecting the stability of mechanical face seals in many fields, especially under cryogenic conditions. Here, a numerical model based on the saturated vapor pressure is established to investigate the vaporization phase transition property of liquid oxygen sealing film. The novelty of this model is to take the influence of heat transfer and face distortions into consideration at the same time. The pressure and temperature distributions as well as face distortions are calculated, and then the property of vaporization phase transition and sealing performance are analyzed. It is found that spiral grooves may lead to the complex film temperature distributions and irregular vaporization distributions. With the increase in seal temperature and decrease in seal pressure, the vaporization area extends from the low-pressure side to the grooves area, and the vaporization rate increases rapidly. The more important thing is that the vaporization often brings a drastic fluctuation and non-monotonic change in opening force. Specifically, with the increase inin seal temperature from 55 K to 140 K, the opening force fluctuates violently, and the fluctuation range is more than 50%, showing an obvious instability. Finally, this study provides a design range of pressure and temperature values for liquid oxygen face seals. In these ranges, this kind of face seals can have a stable operation, which is beneficial to the practice engineering related to the complex properties of sealing fluid.

Experimental and theoretical investigation on the mechanism of cationic surfactants-assisted phosphogypsum crystal transformation

The massive discharge and stockpiling of phosphogypsum became an increasingly severe issue on environment. The transformation of phosphogypsum into fibrous alpha-type hemihydrate gypsum (α-HH) with high L/D(ratio of length-to-diameter) is one of the effective routes to achieve the high-valued utilization. In this work, six types of cationic surfactants, including CTAB, STAC, CHEC, CGG, CPAM and PDDA were selected to investigate their different effects on shape of α-HH crystals through hydrothermal method under the condition of 160 °C(0.6 MPa saturated vapour pressure) for 3 h. The results showed that the introduction of all selected surfactants can increase the length-to-diameter (L/D) ratio of α-HH crystals. As the concentration of surfactants increases, the L/D ratio first increases and then decreases, and the highest L/D ratio of 171.3 was obtained by using CTAB at 0.6 %. The mechanism of regulated growth of α-HH crystals into fibrous structure following c-axis in the presence of six cationic surfactants was also demonstrated. Moreover, the adsorption mechanism of cationic surfactants on the α-HH surface was investigated by molecular dynamics simulation and theoretical analysis. It is found that the order of binding energy (Eb) between the addition and α-HH crystal faces is Eb(11¯0) > Eb(110) > Eb(200) > Eb(002). This work provides insightful guidance from both experimental and theoretical perspectives for controlling the crystal form of α-HH and preparing high-strength gypsum.

Clean and efficient recovery of silver from silver-tin alloys by vacuum evaporation-multistage condensation

The recycling of waste lead-free solder and the tin refining process generates large quantities of silver-tin alloys, which have a very high potential for recovery but for which there is no clean and efficient means of recovery. This study examined the saturation vapour pressure, separation coefficients, prediction of the T-x(y) phase diagram of the silver-tin alloys, and condensation rate to explore the feasibility of using vacuum evaporation-multistage condensation as a method for separating silver-tin alloys. The results suggest that in the process of vacuum evaporation, both silver and tin will evaporate, and the evaporability of silver is slightly greater than that of tin. In the process of multistage condensation, tin condenses before silver. Furthermore, the vacuum evaporation-multistage condensation method was experimentally validated. The results suggest that the TF consists of crude silver, with a silver content of 98.17 wt% and a silver distribution rate of 43.60%. The MP consists of a silver-tin alloy with 7.87 wt% silver content and exhibits a silver distribution rate of 53.06%. The RE is crude tin containing 0.27 wt% of silver content and a silver distribution rate of 5.14%. The separation rate of Ag is 96.64%. This study provides a clean and efficient method that is instructive for the recovery of Ag-Sn alloys.

Association rule mining of air quality through an improved Apriori algorithm: A case study in 244 Chinese cities

AbstractPredicting air pollution is complex due to intertwined factors among local climate, built environment, and development stages. This study leverages K‐means clustering and an improved Apriori algorithm to investigate the combined effects of local meteorological, morphological, and socioeconomic factors on air quality in 244 prefectural‐level Chinese cities. Results reveal that the secondary industry in GDP and saturation vapor pressure strongly relate to air quality. Severe air pollution occurs when urban development is coupled with reduced green areas and high temperatures, confirming that a single factor cannot predict air quality well. For example, we find that combining low population, low regional GDP, high maximum temperatures, and longer roads worsens air quality in small urban built‐up areas. Additionally, temperature and altitude differences associate with highway passenger volume, regional GDP, and population differently. Given our rules mining methods have broader applications in diversified urban environments, this study provides new insights for improving air quality and local Sustainable Development Goals.

Co-solvent strategy for highly efficient perovskite solar cells by spray coating

The ultrasonic spray coating has been shown to be an effective technique for scaling up production. The nucleation and crystallization process of the perovskite film prepared by the ultrasonic spraying approach is more complicated than that by the spin coating, but they are essential to gaining efficient perovskite solar cells (PSCs). At the same time, the green solvent is the primary problem that must be solved in the process of PSCs commercialization. In this paper, the low boiling point and green solvent isopropyl alcohol (IPA) is introduced into the perovskite precursor solution to prepare FAPbI3 perovskite by ultrasonic spraying. The addition of IPA enhanced the saturated vapor pressure of the precursor solution, which can create the local chemical microenvironment on the film surface and subsequently retard the nucleation rate from 8.31 s to 8.54 s at nucleation stage. The local chemical improves the initial homogeneity of the sol–gel phase and then leads to improved structural and optoelectronic properties within the FAPbI3 film via sufficient crystallization from the sol–gel phase to α-FAPbI3. Ultimately, IPA-based PSCs exhibit the champion device efficiency of 22.43 %. The good long-term stability of PSCs (maintain more than 90 % of the initial efficiency after 1000 h, and keep 80 % after 400 h) in ambient conditions.

Topography formation driven by sublimation of pure species on icy airless worlds

Sublimation can drive morphologic changes on the surfaces of icy, airless worlds; the magnitude of these changes depends sensitively on their surface shape, subsurface geology, and volatility of the ice species present. To predict the steady-state and stability of the surface, we examine the molecular transport conditions and their constraints for several pure species sublimating from irregular surfaces in a free-molecular regime subject to variations in thermal conditions at or near the surface. We find that the temperature difference, ΔT∗ between the high and low points on the surface required for morphological instability changes of a given surface geometry increases as the volatility of the ice species increases. From Figure 4, for k=1 and Ts=150K, ΔT∗ is about 3K for H2O and 5K for CO2. Furthermore, we developed an analytical relationship between the saturation vapor pressure of a pure species, its surface geometry and temperature profile, and the required molecular transport conditions.

Novel method for recovering valuable metals from Sn ash: Vacuum carbothermal reduction-directional condensation

Sn ash recycling is an industry with positive development prospects, as it provides better-protected resources, promotes sustainable development, and lays a solid foundation for future development. In this study, an innovative vacuum carbothermal reduction-directional condensation process was developed. The thermodynamic analysis results indicated that the initial reaction pressure and temperature for the carbothermal reduction of the system was 1–10 Pa and 998–1063 K, respectively. The saturation vapor pressure, separation coefficient, and condensation temperature of Sn, Pb, and Zn in the reduced products differed significantly, and their separation could be achieved by controlling the volatilization and condensation temperatures. A single-factor experiment investigated the effects of carbon ratio, temperature, and time on the reduction efficiency, direct yield, and recovery rate. The optimal experimental conditions were the ratio of MeO to C of 4:1, temperature of 1373 K, and time of 120 min. Sn, Pb, and Zn products were obtained at different positions. This process shortens the traditional process, reduces the reduction cost of Sn, and enables the implementation of the process, making it environmentally friendly.

The Impact of Gravity Waves on the Evolution of Tropical Anvil Cirrus Microphysical Properties

AbstractAnvil cirrus generated by deep convection covers large fractions of the tropics and has important impacts on the Earth's radiation budget and climate. In situ measurements made with high‐altitude aircraft indicate a rapid transition in ice crystal size distributions and habits as anvil cirrus ages. We use numerical simulations to investigate the impact of high‐frequency gravity waves on the evolution of anvil cirrus microphysical properties. The impacts of both monochromatic gravity waves and ubiquitous stochastic mesoscale temperature fluctuations are simulated. In both cases, the interplay between wave‐driven temperature fluctuations, deposition growth/sublimation, and sedimentation causes accelerated removal of both small ice crystals (diameters less than about 10 μm) and large crystals (diameters larger than ≈30 μm). These changes are consistent with the observed evolution of anvil cirrus microphysical properties. The Kelvin effect (higher saturation vapor pressure over curved surfaces) is a critical factor in the anvil evolution, driving mass transfer from small to large ice crystals. The wave‐driven decrease in ice concentration is much faster for typical anvil cirrus detrained at ≃11.5–12.5 km than for less frequent anvils at 15.5–17.5 km because of the strong temperature dependence of deposition growth and sublimation rates. The simulations also show that waves, along with the Kelvin effect, drive growth of mid‐sized (5–20 μm) ice crystals, which is consistent with the observed transition to bullet rosette habits in aging anvil cirrus. We conclude that high‐frequency gravity waves, which are generally not resolved in large‐scale models, likely have important impacts on anvil cirrus microphysical properties and lifetimes.

Purification of metallurgical-grade crude tellurium based on viscous distillation and gas-phase separation

A method for preparing high-purity tellurium based on viscous distillation and gas-phase separation was developed. By adjusting the condenser structure and condensing temperature to achieve viscous distillation, the dominant condensation zone for tellurium was controlled; hence, poorly volatile substances remained in the crucible, while selenium was separated from tellurium in the gas phase to achieve the purification of metallurgical-grade crude tellurium. Specifically, the saturated vapor pressure, mean free path of tellurium, impurity distribution, and morphologies of the condensate at different locations were investigated in detail. The results for a 500 g upscaled experiment showed that the direct yield of Te was 83.40%, the purity of Te reached higher than 99.9996 wt.% and the selenium content in the dominant condensation zone was reduced to 2.76×10−4 wt.% under the optimal experimental conditions of 5 Pa, 773 K and 90 min.

The effect of temperature on the pressure energy distribution in the process of near-wall single bubble collapse

At the interface between rotating components and the working medium in fluid machinery, cavitation in the liquid is induced. The temperature of the working medium has a significant influence on the cavitation. However, the effect of temperature on the pressure and pressure energy in the collapse of bubbles cannot be explained accurately. This study established cavitation models containing insoluble gases at different temperatures and iron walls. The Transferable Intermolecular Potential 4 Points-Fluctuating Bonds water model and the Reax force field were selected to study the influence of temperature on pressure energy and pressure in the process of bubble collapse. Employing the model, we examined variations in release pressure and the pressure energy associated with bubble collapse within the system at diverse temperatures. This investigation was conducted by establishing 24 monitoring points. The findings revealed that the near-wall single-bubble collapse process could be delineated into four distinct stages: the precollapse stage, the inertia stage, the rebound stage, and the collapse stage. These four stages manifest on both the pressure curve in the simulation and the curve depicting changes in the cavity area during the experimental phase. The influence of temperature on bubble collapse primarily stemmed from its impact on saturation vapor pressure and viscosity. This influence was observed during the precollapse process, where saturation vapor pressure played a dominant role, and in the collapse stage, where viscosity was predominant.

Geographic Variation and Environmental Predictors of Nontuberculous Mycobacteria in Laboratory Surveillance, Virginia, USA, 2021-20231.

Because epidemiologic and environmental risk factors for nontuberculous mycobacteria (NTM) have been reported only infrequently, little information exists about those factors. The state of Virginia, USA, requires certain ecologic features to be included in reports to the Virginia Department of Health, presenting a unique opportunity to study those variables. We analyzed laboratory reports of Mycobacterium avium complex (MAC) and M. abscessus infections in Virginia during 2021-2023. MAC/M. abscessus was isolated from 6.19/100,000 persons, and 2.37/100,000 persons had MAC/M. abscessus lung disease. M. abscessus accounted for 17.4% and MAC for 82.6% of cases. Saturated vapor pressure was associated with MAC/M. abscessus prevalence (prevalence ratio 1.414, 95% CI 1.011-1.980; p = 0.043). Self-supplied water use was a protective factor (incidence rate ratio 0.304, 95% CI 0.098-0.950; p = 0.041). Our findings suggest that a better understanding of geographic clustering and environmental water exposures could help develop future targeted prevention and control efforts.

An Unexpected Decline in Spring Atmospheric Humidity in the Interior Southwestern United States and Implications for Forest Fires

Abstract On seasonal time scales, vapor pressure deficit (VPD) is a known predictor of burned area in the southwestern United States (“the Southwest”). VPD increases with atmospheric warming due to the exponential relationship between temperature and saturation vapor pressure. Another control on VPD is specific humidity, such that increases in specific humidity can counteract temperature-driven increases in VPD. Unexpectedly, despite the increased capacity of a warmer atmosphere to hold water vapor, near-surface specific humidity decreased from 1970 to 2019 in much of the Southwest, particularly in spring, summer, and fall. Here, we identify declining near-surface humidity from 1970 to 2019 in the southwestern United States with both reanalysis and in situ station data. Focusing on the interior Southwest in the months preceding the summer forest fire season, we explain the decline in terms of changes in atmospheric circulation and moisture fluxes between the surface and the atmosphere. We find that an early spring decline in precipitation in the interior region induced a decline in soil moisture and evapotranspiration, drying the lower troposphere in summer. This prior season precipitation decline is in turn related to a trend toward a Northern Hemisphere stationary wave pattern. Finally, using fixed humidity scenarios and the observed exponential relationship between VPD and burned forest area, we estimate that with no increase in temperature at all, the humidity decline alone would still lead to nearly one-quarter of the observed VPD-induced increase in burned area over 1984–2019. Significance Statement Burned forest area has increased significantly in the southwestern United States in recent decades, driven in part by an increase in atmospheric aridity [vapor pressure deficit (VPD)]. Increases in VPD can be caused by a combination of increasing temperature and decreasing specific humidity. As the atmosphere warms with climate change, its capacity to hold moisture increases. Despite this, there is a decrease in near-surface air humidity in the interior southwestern United States over 1970–2019, which during the summer is likely caused by a decline in early spring precipitation leading to limited soil moisture and evaporation in spring and summer. We estimate that this declining humidity alone, without an increase in temperature, would cause about one-quarter of the VPD-induced increase in burned forest area in this region over 1984–2019.

Complete Prevention of Bubbles in a PDMS-Based Digital PCR Chip with a Multifunction Cavity.

In a chamber-based digital PCR (dPCR) chip fabricated with polydimethylsiloxane (PDMS), bubble generation in the chambers at high temperatures is a critical issue. Here, we found that the main reason for bubble formation in PDMS chips is the too-high saturated vapor pressure of water at an elevated temperature. The bubbles should be completely prevented by reducing the initial pressure of the system to under 13.6 kPa to eliminate the effects of increased-pressure water vapor. Then, a cavity was designed and fabricated above the PCR reaction layer, and Parylene C was used as a shell covering the chip. The cavity was used for the negative generator in sample loading, PDMS degassing, PCR solution degassing in the digitization process and water storage in the thermal reaction process. The analysis was confirmed and finally achieved a desirable bubble-free, fast-digitization, valve-free and no-tubing connection dPCR.

Energy-efficient biphasic solvents for industrial CO2 capture: Absorption mechanism and stability characteristics

The traditional CO2 capture process represented by monoethanolamine has excessive energy consumption, serious oxidative degradation and metal corrosion, which limits its potential for large-scale industrial applications. This study produced a highly effective biphasic 3-amino-1-propanol (MPA)–polyethylene glycol dimethyl ether (NHD)–H2O absorbent with easy modulation of phase separation and low levels of oxidative degradation and metal corrosion. The principal absorbent was MPA, and NHD served as the phase separation solvent. NHD's solvent effect decreased the energy barrier preventing MPA from forming zwitterions (MPA+COO−) and carbamate, thus promoting chemical absorption. The large polarity difference between the reaction products and NHD triggered phase separation, producing a low-polarity CO2-lean phase and a high-polarity CO2-rich phase; 97.41% of the absorbed CO2 accumulated in 43.7% of the CO2-rich phase solution. The sensible heat and latent heat of the MPA–NHD–H2O absorbent were relatively low because of the low saturation vapor pressure, high vaporization enthalpy, and excellent phase separation performance of NHD. The regeneration energy was as low as 2.66 GJ/t CO2, which was 30% less than that for monoethanolamine. Additionally, the oxidative degradation rate for the proposed absorbent was only 10.7% of that for monoethanolamine. This study provides a theoretical reference for application of the MPA–NHD–H2O biphasic absorbent.

Innovative approach for predicting daily reference evapotranspiration using improved shallow and deep learning models in a coastal region: A comparative study

Accurate and reliable estimation of Reference Evapotranspiration (ETo) is crucial for water resources management, hydrological processes, and agricultural production. The FAO-56 Penman-Monteith (FAO-56PM) approach is recommended as the standard model for ETo estimation; nevertheless, the absence of comprehensive meteorological variables at many global locations frequently restricts its implementation. This study compares shallow learning (SL) and deep learning (DL) models for estimating daily ETo against the FAO-56PM approach based on various statistic metrics and graphic tool over a coastal Red Sea region, Sudan. A novel approach of the SL model, the Catboost Regressor (CBR) and three DL models: 1D-Convolutional Neural Networks (1D-CNN), Long Short-Term Memory (LSTM), and Gated Recurrent Unit (GRU) were adopted and coupled with a semi-supervised pseudo-labeling (PL) technique. Six scenarios were developed regarding different input combinations of meteorological variables such as air temperature (Tmin, Tmax, and Tmean), wind speed (U2), relative humidity (RH), sunshine hours duration (SSH), net radiation (Rn), and saturation vapor pressure deficit (es-ea). The results showed that the PL technique reduced the systematic error of SL and DL models during training for all the scenarios. The input combination of Tmin, Tmax, Tmean, and RH reflected higher performance than other combinations for all employed models. The CBR-PL model demonstrated good generalization abilities to predict daily ETo and was the overall superior model in the testing phase according to prediction accuracy, stability analysis, and less computation cost compared to DL models. Thus, the relatively simple CBR-PL model is highly recommended as a promising tool for predicting daily ETo in coastal regions worldwide which have limited climate data.

Separation of arsenic from tin anode slime by vacuum distillation

Tin anode slime (TAS) is a high-value waste produced by electrolytic refining of crude tin. In order to reduce the discharge of harmful waste and realize rational recycling, a process of removing arsenic from TAS by vacuum distillation was proposed, and theoretical and experimental studies were carried out. The saturated vapor pressure of each element in TAS and the activation energy of arsenic evaporation during vacuum distillation was calculated. The evaporation temperature and holding time of vacuum distillation for arsenic removal were investigated. The effects of evaporation temperature and holding time on arsenic removal were discussed. The results showed that the residual arsenic content is 0.32–0.19%, and the removal rate of arsenic is 84.87–91.90% at 1153 K and the range of holding time is 30–120min. When the temperature is 1353 K and the holding time from 30 to 120 min, the residual arsenic content is 0.029–0.025% and the removal rate is 99.43–99.59%. The activation energy for the evaporation of arsenic from TAS in vacuum distillation is EAs = 52.76 kJ/mol. The removal of arsenic improves the recycling value of TAS, and provides ideas for treating harmful substances from industrial wastes and recovering valuable metals.

A Study for Estimating the Overall Heat Transfer Coefficient in a Pilot-Scale Indirect Rotary Dryer

An experimental study and dimensional analysis of the effective heat transfer coefficient in a continuous-indirect rotatube dryer using forest biomass as the granular material isare developed in the present work. The study employed a factorial design 33 to investigate the effects of feed flow frequency (20–35–50 (Hz)), drum rotational velocity (6–8–10 (rpm)), and saturated vapor pressure (4–5–6 (bar)) on the heat transfer coefficient. During steady state conditions, the moisture content profiles and inlet and outlet temperatures were measured within the experimental region, and parameters, such as the effective heat transfer coefficient, solid retention change, and moisture content ratio were studied. The results showed that heat transfer was optimized with high solid feeding rates, low pressure, and low rotation, with solid feeding being the predominant factor. The moisture content profiles revealed a change in the hydrodynamic behavior, with the center point of the experimental region being the least optimal. The dimensional analysis yielded a Nu number as a function of Pe, Fr, and the feeding dimensionless number. A new dimensionless energy efficiency number improved the coefficient correlation from 85.88 (%) to 94.46 (%), indicating the developed model potential to predict dimensionless variables and scale continuous-indirect rotatube dryers.