Mass Transfer Coefficient Research Articles

ABSTRACT This study investigates the removal of low-concentration iodine vapor from air using aqueous sodium hydroxide ( NaOH ) in a laboratory-scale packed column, employing both experimental and modelling approaches. Experiments were conducted to determine the overall volumetric mass transfer coefficient ( K G a eff ) and assess the influence of gas flow rate, liquid flow rate, NaOH concentration, and packing type. Results showed that K G a eff and the effective interfacial area were strongly dependent on the gas-phase Reynolds number ( R e G ), while liquid-phase parameters had minimal impact under most conditions. However, at high gas Reynolds numbers and low NaOH concentrations, the liquid flow rate progressively affected K G a eff , indicating a transition in the controlling mass transfer regime. A correlation for K G a eff was developed and integrated into a one-dimensional finite difference solver to simulate the absorption process. The predicted outlet iodine concentrations agreed with experimental results, with deviations within 10%. Phase resistance analysis revealed a shift from gas-phase-controlled to mixed gas-liquid controlled mass transfer at R e G ≥ 25 and [ OH ] ≤ 0.25 M. Additionally, porosity was found to inversely affect K G a eff , underscoring the importance of selecting packing materials that minimize gas-phase resistance. These findings highlight the critical role of gas-phase hydrodynamics and hydroxide concentration in optimizing iodine removal. The insights gained are valuable for the design and operation of caustic scrubbers intended to control radioactive iodine emissions in nuclear and radiochemical facilities.

A new method for estimating the globally averaged mass transfer coefficient in liquid-particle agitated vessels

Computation of volumetric mass transfer coefficient ka in a twin-blade counter-rotating reactor for polymer devolatilization

Understanding mineralogical transformations and elemental mobility during limestone weathering is critical for deciphering carbon cycling and critical zone evolution in karst terrains. This study investigates an in situ limestone weathering profile (12.6 m depth) in Shimen, Hunan Province, using integrated mineralogical (XRD, EPMA-EDS), elemental (XRF, ICP-MS), and Sr isotopic (MC-ICP-MS) analyses. Results reveal a two-stage pedogenic model: (1) Rapid dissolution of primary calcite (>95 wt% in bedrock to 1.1–48.5 wt% in soil) creates an abrupt bedrock–soil interface via volumetric collapse (>90%), accumulating acid-insoluble residues (quartz-dominated); (2) Subsequent weathering drives illitization of K-feldspar, trace element enrichment (e.g., Ni, Tl, Th τ up to 180) via illite adsorption, and radiogenic 87Sr/86Sr evolution (0.7076 in bedrock to 0.7292 in soil). Depth-dependent increases in chemical index of alteration (CIA: 6.79–79.96) and mass transfer coefficients confirm progressive weathering intensity. The profile acts as a net carbon source (58.5% depletion in soil inorganic carbon), highlighting significant CO2 release during pedogenesis. These findings provide mechanistic insights into subtropical critical zone evolution and element cycling in carbonate-dominated systems.

A greenhouse solar dryer was used to study the drying behavior of mesquite pods, and a radiation model for participating media was numerically solved to predict the air temperature in the dryer. The model was solved for a stationary state by considering the environmental conditions. The transfer coefficients were calculated for natural and forced convection. In the case of forced convection, an average airflow of 0.5668 m/s (SD = 0.1121) was provided over the trays. The weight of the pods, their temperature, air temperature, ambient temperature, relative humidity, and solar irradiation were recorded. The average heat transfer coefficients for natural and forced convection were 2.9294 W/m2 °C and 6.3772 W/m2 °C, respectively. The average mass transfer coefficients for natural and forced convection were 0.002987 kg/m2 s and 0.00601 kg/m2 s, respectively. The greenhouse dryer showed a high dependence on the weather conditions, showing important disturbances to air temperature. For the experiment with forced convection, a reabsorption of moisture was observed during the night; nevertheless, the final moisture content of the pods was below 0.05 g moisture/g dry matter, which was convenient for the subsequent grinding process. The radiation model correctly describes the average air temperature in the greenhouse volume. A reduction in thermal fluctuations will be important to improve the process.

ABSTRACT The present study aims to quantify the diffusion-controlled process of electropolishing inclined planes under free convection using a dimensionless mass transfer equation, enabling the production engineer to predict the limiting current required to polish the workpiece. To this end, the effects of H3PO4 concentration (physical properties of the solution) and angle of inclination of a flat copper plate (θ) on the limiting current were studied at 22 ± 1 °C. The limiting current was found to increase with decreasing inclination angle to the horizontal axis, and increasing H3PO4 concentration was found to reduce the limiting current. For a given set of conditions, an undivided cell produced a higher limiting current than a divided cell, ranging from 15% to 43%. This is attributed to the stirring effect of cathodic H2 evolution in the case of a single-compartment cell. The rate of polishing in a divided cell was expressed in terms of the mass transfer coefficient by the dimensionless equation: Sh = 1.122 ( Sc Grcos ⁡ θ ) 0.3 Although the average limiting current is higher in the case of a single-compartment cell compared to that obtained from a divided cell, the limiting current distribution is more uniform in the case of a divided cell, owing to the absence of stirring effect of cathodic H2 which is effective in the upper anode area while natural convection alone dominates the lower area.

An extensive investigation of multiphase flow and mass transfer in aerated stirred reactors will provide methods for improving reactor performance. In this study, a computational fluid dynamics (CFD) model that characterizes gas–liquid two-phase flow in a reactor equipped with a dual-impeller and a gas sparger was developed. The numerical simulations were performed to predict the gas and liquid flow fields, gas holdup, and volumetric mass transfer coefficient (kLa). Experiments were conducted to determine bubble size distribution, bubble diameter, gas holdup and kLa with respect to impeller speed, gas flow rate and temperature. The CFD model was validated against the measured kLa and gas holdup, and then five mass transfer models were examined to propose an appropriate one that would best predict the kLa. Moreover, the effects of agitation and aeration on the overall gas holdup, the kLa, and the power consumption were evaluated. The results demonstrate that reactors with a rounded-bottom work better than those with a flat-bottom in terms of hydrodynamic performance and mass transfer efficiency, that the optimal number of holes in a gas sparger is determined by the mixing scenarios of a reactor, and that the mass transfer coefficient increases with the increase in impeller speed and operating temperature.

Comparative study of CO₂ nanobubbles and macrobubbles: Effects on water chemistry, microalgal growth, and carbon utilization.

Roles of diffusive boundary layer and initial contamination in back diffusion from heterogeneous low permeability sediments: A source-history-inversion-independent model and field application.

Microfluidic process enhancement in liquid-liquid extraction: efficient extraction and recovery of valuable metals.

A novel framework for forward osmosis in zero- and low-flow conditions: Applicability and fundamental differences from reverse osmosis.

Airlift bioreactors have been classified as a promising technology for microalgae cultivation. Several improvements have contributed to increasing the mixing efficiency and production. However, some challenges are still facing this biological process. One challenge is the efficient dissolution and delivery of carbon dioxide to microalgae cells, which remains a limiting factor in the biological processes. On the other hand, sparging the gas in large quantities may lead to gas loss if microorganisms do not completely consume it. In this study, microalgae were cultivated in two stages and compared: the first stage of injecting 5 ml of carbon solution into a conical flask and the second stage of sparging 5 liters/hour in an airlift bioreactor with increasing sparging time this is done by sparging carbon dioxide gas at the same flow rate from day to day, but increasing the sparging time by 30 seconds, starting with sparging the gas for one minute until reaching 7 minutes. The results showed that the airlift bioreactor gives a higher growth rate of microalgae than that produced in a conical flask. The maximum biomass concentration reached 5 g/L in the airlift bioreactor culture with a maximum specific growth rate of 0.324 day−1, while it reached 1.0799 g/L in the conical flask culture with a specific growth rate of 0.187 day−1. This result shows the importance of the airlift bioreactor in microalgae cultivation. Also, the internal composition of the biomass was found that the airlift bioreactor was the best, as the amount of lipids, carbohydrates and protein was (2.06, 1.43, and 18.03 g per 30 g of dry biomass), respectively, while the internal composition of the control cultivation was (0.005386, 0.00428, 0.05754 and g/L), respectively. The volumetric mass transfer coefficient showed that when the sparging time increases, the oxygen gas transfer coefficient increases until it reaches 1.0397 s−1. The pH value was also maintained around 7, which is the appropriate value for increasing the growth rate.

Implications for modeling anion exchange treatment of perfluoroalkyl substances in drinking water and related natural organic impacts: a pilot study.

Abstract The performance of an axial spiral stirrer in mixing two aqueous and organic phases in a tank at different test conditions has been studied, and its effect on copper ion extraction was determined. The influence of speed, O/A, pH, and tank baffle parameters were investigated. Experiments were also done without a baffle, requiring a smaller tank diameter to study the effect of radial tip clearance without baffles. Mass transfer has been assessed by measuring the overall mass transfer coefficient and Sherwood number. Examination of the samples collected from nine locations on the stirring tank wall with the larger baffled tube diameter showed that apart from the speed of the stirrer, the extraction of Cu ions was influenced by the presence of baffle, liquid O/A ratio, and pH in that order. Cu ion extraction at optimal conditions (600 rpm, O/A = 1.2, pH = 2.5, and with baffle) at the end of the stirring time (180 s) was already at 99.5%. Moreover, the stirred flow axial concentration was uniform. The results of tests with a smaller diameter tank (i.e., without baffle) showed that the radial distance between this stirrer and the tank wall without the baffle after 360 s had only a 6.5% negative impact on Cu ion extraction effectiveness with the same optimal test conditions (600 rpm, O/A = 1.2, pH = 2.5), and an axially non‐uniform fluid concentration was observed. Also, the large value of Sherwood numbers acquired from all the experiments (in the 300 s) gave insight into the improved performance of this stirrer design compared to pure diffusion.

The functional properties of nanocrystals can be finely tuned through controlled morphology and size. However, this can be challenging for metastable nanostructures that require harsh synthesis conditions, such as high temperatures. Here, we present a method for preparing large ε-Fe2O3 nanorods that are not affected by magnetic relaxation. This study presents a novel growth mechanism in which high-aspect-ratio rods evolve from spherical ε-Fe2O3 particles in a silica matrix containing Y3+. With the presence of Y3+, the glassy matrix undergoes a metastable binodal decomposition yielding the formation of nanodroplets of a Y-rich silicate of composition ∼Y2Si2O7. This Y silicate selectively coats the ε-Fe2O3 planes perpendicular to the rod axis along the [100] direction but is not observed in the rod apexes. Structural optimizations and energy calculations of different crystal faces of ε-Fe2O3 in contact with Y2Si2O7 obtained using machine-learning force fields provide an atomistic interpretation of these observations: the affinity of Y with the oxygen atoms exposed at ε-Fe2O3 surfaces explains the preferential capping of ε-Fe2O3 surfaces that present a large density of oxygen atoms and its absence in surfaces such as (100), where this density is significantly lower. The presence or absence of the silicate capping layer results in different surface energies and/or mass transfer coefficients across the interface, originating two independent Ostwald ripening processes, which drive the high aspect ratio growth. By using La3+ instead of Y3+, ε-Fe2O3 rods with even larger aspect ratios are obtained. Notably, this synthetic approach counteracts the progressive diminution of the average nanoparticle size observed in ε-(Fe1-xCrx)2O3 upon Cr3+ addition, enabling to elucidate the effect of this substitution on the intrinsic magnetic anisotropy and the anisotropy fields that determine the high-frequency ferromagnetic resonances of this phase.

The article examines mathematical modeling as an effective tool for theoretical research of heat and mass transfer processes in autoclavetreatment of concrete products. The aim of the study is to construct a mathematical model that describes the regularities of heat and moistureexchange and cement hydration under steaming conditions, considering the structural features of the autoclave and the thermophysicalproperties of concrete products. To achieve this goal, methods of mathematical physics are applied, particularly differential heat conductionequations with appropriate initial and boundary conditions.The study formulates key assumptions to simplify the process analysis: one-dimensional heat propagation, negligible influence ofcondensate film and reinforcement, and constant volume of concrete products. The thermal nature of the processes occurring during steamingis analyzed, and heat flux dependencies for the upper and lower surfaces of the product are established. The effect of heat release due to theexothermic cement hydration reaction is taken into account, as it significantly impacts concrete structure formation and strength development.Special attention is given to the mathematical modeling of cement hydration, describing the transition of water between active and passivestates in a closed system. Substance transfer mechanisms (diffusion and convection) are considered in relation to the kinetics of chemicalinteractions at various hydration stages. As a result, it is found that heat transfer and mass transfer coefficients are critical for efficientautoclave operation, and the proposed model enables optimization of steaming parameters at the design stage.The findings can be applied to develop a comprehensive mathematical model of the material and energy balance in the autoclave,facilitating the implementation of automated control systems for the technological process, aimed at improving energy efficiency and thequality of the final product.

Abstract The phenomena of bubble formation from the venturi pipe microbubble generator were investigated. The air hole sizes were varied at 1, 0.5, and 0.3 mm while the volumetric flow rates were set at 4, 5, 6, 7, and 8 LPM. Insertion of a guitar string with a diameter of 0.2 mm into the 0.5 mm air hole size was also performed to examine its effect. The simulation of the bubble shrinkage process in water (sizes of 25, 50, 75, and 100 μm) was held with and without saturated nitrogen at 0.25, 0.5, 0.75, 0.875, and 1 atm. The experiment shows that average bubble sizes for air hole sizes of 1, 0.5, and 0.3 mm are 1.37, 1.40, and 1.09 mm, respectively. The flow rate alteration significantly affects the bubble sizes for air hole sizes of 0.5 and 0.3 mm but is not meaningful for 1 mm. In addition, the guitar string insertion also produces spherical bubbles with a size of 1.33 mm for deep depth location. Moreover, simulation results prove that smaller bubble sizes lead to prolonged shrinkage time and a greater mass transfer coefficient in the liquid phase with and without saturated nitrogen.

The utilization of CO2 is crucial to convert waste into valuable products, such as fuels. Microchannel reactor technology has gained attention for CO2 utilization due to their higher interfacial area compared to traditional reactors. Understanding flow regimes is critical for optimizing mass transfer efficiency. Hence, this project aims to create a new flow pattern map for CO2 and water and investigate how gas bubble and liquid slug properties are affected by the change in superficial velocity. Thus, the interfacial area for each flow pattern can be observed which affects the mass transfer performance. The dimensions of flow pattern were measured, so the interfacial area could be calculated accordingly. The amount of CO2 absorbed into water was determined using the titration method. Then the liquid side mass transfer coefficient for slug flow was determined from the models proposed by van Baten and Krishna (2004). In the end, the rate of mass transfer was determined for slug flow. The results show that slug flow is formed at high gas-to-liquid ratio. Longer slug flow has higher interfacial area and more CO2 is absorbed through diffusion. A larger interfacial area contributes to higher mass transfer rate, so this proves that the microchannel is good for CO2 utilization process.

To enable a sustainable fuel cycle, any deuterium-tritium fusion reactor must breed its tritium fuel onsite. Lead-lithium (PbLi), a eutectic metal, is a leading liquid breeder material for tritium generation. One challenge with PbLi blanket technology is the extraction of tritium from the molten eutectic. Three technologies are the focus of worldwide research: the vacuum permeator, the vacuum sieve tray, and the gas-liquid contactor (GLC). The present work offers a methodology for designing, sizing, optimizing, and costing a trickle-bed GLC for tritium extraction from PbLi. The traditional packed bed mass transfer coefficient and film theory models are applied to experimental data from the MELODIE experiments. Analysis revealed that traditional packed bed mass transfer models do not match the MELODIE loop experimental data regardless of the PbLi tritium solubility value used (Rieter versus Aiello). However, the film theory liquid mass transfer coefficient, Delt-Olujic wettability model, and Reiter tritium solubility values fit the MELODIE data best and were utilized for both the design and the economic analysis. A techno-economic analysis of the GLC was conducted to evaluate three design sizes, all of which achieved a minimum extraction efficiency of 90%. A 325-fold increase in the sweeping gas flow rate is required to achieve the same target extraction efficiency at the same packing height when using the tritium solubility values of Aiello, compared to those of Reiter.

Synechococcus HS-9 is being recognized as one of the potential strains for biodiesel production due to its high levels of fatty acid methyl ester (FAME), which are around 70–78%. The first stage in producing microalgae biodiesel involves the biomass production process through a photobioreactor cultivation process. In addition to microalgae strains, the optimization of the photobioreactor’s performance is essential for producing high biomass. In this case, biotic factors (microalgae inoculum) and abiotic factors (nutrients, temperature, light, pH, carbon dioxide (CO2), fluid flow, hydrodynamic processes, and mass transfer processes) are being regulated and optimized in the photobioreactor, which is influencing the growth rate of microalgae. The main objective of this study is examining the effect of hydrodynamics and mass transfer processes using the Rectangular Airlift Photobioreactor with Baffles (RAPBR-Bs) to increase the growth of Synechococcus HS-9 during the cultivation process. The study is consisting of two main parts: collecting bubble photography and video, and the cultivation process of Synechococcus HS-9. During the cultivation of Synechococcus HS-9, hydrodynamics, mass transfer, optical density (OD), and biomass weight data are being measured. The research results indicate that hydrodynamic parameters, including bubble properties such as bubble velocity (0.0064 m/s), bubble diameter (720 μm), non-dimensional numbers (Re 4.51; Eo 0.0126; Mo 8.87 × 10−12; We 6.85 × 10−5), superficial gas velocity (0.0008 m/s), bubble rise velocity (0.117 m/s), gas holdup (0.0072), and the mass transfer process (kLa O₂ (oxygen) 0.114 s−1; kLa CO₂ 0.099 s−1) in RAPBR-Bs are influencing and contributing to the growth of Synechococcus HS-9 during cultivation. The study found that Synechococcus HS-9 cultivated in RAPBR-Bs exhibited significant growth because the mixing and aeration processes are optimal. An optimal aeration process enhances the mass transfer coefficient, which in turn improves the overall mass transfer capacity of the RAPBR-Bs. The results are showing that the hydrodynamic and mass transfer properties of these RAPBR-Bs are being more efficient than those that are reported for other PBRs. Optimal conditions for Synechococcus HS-9 cultivation are occurring at day 13, as it is reaching the late exponential phase. The weight of the cultivated Synechococcus HS-9 biomass is 3.226 g.Supplementary InformationThe online version contains supplementary material available at 10.1038/s41598-025-13711-y.