Phase Mass Transfer Research Articles

Effect of surfactant on dynamics and gas-liquid mass transfer for single carbon dioxide bubbles

In carbonation reaction, the impact of surfactants on the movement and mass transfer behavior of carbon dioxide bubbles were crucial for the production of high-quality silicon dioxide products. The study employed the Matlab image processing system to investigate the shapes, motion velocities, and rise path of single carbon dioxide bubbles within varying concentrations of cetyltrimethyl ammonium bromide (CTAB) solutions. This exploration aimed to elucidate the effect of CTAB on the movement and mass transfer coefficient (MTRC) of single carbon dioxide bubbles. Alterations in the CTAB solution concentration and bubble sizes significantly influenced the mass transfer and movement characteristics of single carbon dioxide bubbles. The conclusion was drawn through the computation of the MTRC of single carbon dioxide bubbles in deionized water and CTAB solutions: the addition of CTAB significantly reduced the mass transfer efficiency of carbon dioxide in deionized water, with the MTRC of CTAB solutions decreasing as the solution concentration increased. Utilizing the stagnant cap model, it can be concluded that CTAB's reduction of the MTRC of carbon dioxide was attributed to the high viscosity of the medium, low bubble velocity, stable flow conditions, and intensified adsorption degree of CTAB molecules at the gas-liquid interface. According to the significant periodic trajectories of single carbon dioxide bubbles in the stable range, the correlation between the trajectories of compressible bubbles in surfactant solution and mass transfer in liquid phase was established, and the previous method based on rigid sphere model was modified. The paper proposed the mechanism of CTAB's influence on single carbon dioxide bubbles, offering crucial theoretical insights into the industrial application of surfactants in the carbonation process for producing silicon dioxide.

Effect of growth conditions and reactor configuration on the growth uniformity of large-scale graphene by chemical vapor deposition

Chemical vapor deposition (CVD) is an affordable method for the preparation of large-scale and high-quality graphene. With the increase in CVD reactor size, gas mass transfer, flow state, and gas phase dynamics become more complicated. In this study, computational fluid dynamics is used to investigate factors affecting the uniformity of large-scale graphene growth under different growth conditions and reactor configurations. The dimensionless number defined in this paper and the Grashof number are utilized to distinguish the species transfer patterns and the flow states, respectively. A gas-surface dynamics model is established to simulate the graphene growth. Results reveal that the graphene growth rate uniformity is the highest at very low pressure and flow rate due to the flow symmetry and diffusion-dominated species transfer. At an increased pressure of 20 Torr, the uniformity of the graphene growth rate becomes higher axially and lower circumferentially with an increasing inlet mass flow rate. When the flow rate is fixed at 1500 SCCM and pressure is reduced from 20 to 2 Torr, graphene growth uniformity first increases and then decreases due to the influence of gas phase dynamics. Graphene growth rates are analyzed across ordinary reactor configurations and four configurations with inner tubes at 20 Torr pressure and 1500 SCCM flow rate. Comprehensive evaluation suggests that the ordinary reactor configuration performs best under these conditions. This research offers insights into the macroscopic growth mechanism of large-scale graphene and provides guidance for designing growth conditions in large-area graphene production.

A Channel to Form Fast-spinning Black Hole–Neutron Star Binary Mergers as Multimessenger Sources. II. Accretion-induced Spin-up

In this work, we investigate an alternative channel for the formation of fast-spinning black hole–neutron star (BHNS) binaries, in which super-Eddington accretion is expected to occur in accreting BHs during the stable mass transfer phase within BH-stripped helium (BH–He-rich) star binary systems. We evolve intensive MESA grids of close-orbit BH–He-rich star systems to systematically explore the projected aligned spins of BHs in BHNS binaries, as well as the impact of different accretion limits on the tidal disruption probability and electromagnetic (EM) signature of BHNS mergers. Most of the BHs in BHNS mergers cannot be effectively spun up through accretion if the accretion rate is limited to ≲10ṀEdd , where ṀEdd is the standard Eddington accretion limit. In order to reach high spins (e.g., χ BH ≳ 0.5), the BHs are required to be born less massive (e.g., ≲3.0 M ⊙) in binary systems with initial periods of ≲0.2–0.3 days and accrete material at ∼100ṀEdd . However, even under this high accretion limit, ≳6 M ⊙ BHs are typically challenging to significantly spin up and generate detectable associated EM signals. Our population simulations suggest that different accretion limits have a slight impact on the ratio of tidal disruption events. However, as the accretion limit increases, the EM counterparts from the cosmological BHNS population can become bright overall.

Highly sensitive plasmonic paper substrate fabricated via amphiphilic polymer self-assembly in microdroplet for detection of emerging pharmaceutical pollutants

We report an innovative and facile approach to fabricating an ultrasensitive plasmonic paper substrate for surface-enhanced Raman spectroscopy (SERS). The approach exploits the self-assembling capability of poly(styrene-b-2-vinyl pyridine) block copolymers to form a thin film at the air-liquid interface within the single microdroplet scale for the first time and the subsequent in situ growth of silver nanoparticles (AgNPs). The concentration of the block copolymer was found to play an essential role in stabilizing the droplets during the mass transfer phase and formation of silver nanoparticles, thus influencing the SERS signals. SEM analysis of the morphology of the plasmonic paper substrates revealed the formation of spherical AgNPs evenly distributed across the surface of the formed copolymer film with a size distribution of 47.5 nm. The resultant enhancement factor was calculated to be 1.2 × 107, and the detection limit of rhodamine 6G was as low as 48.9 pM. The nanohybridized plasmonic paper was successfully applied to detect two emerging pollutants—sildenafil and flibanserin—with LODs as low as 1.48 nM and 3.45 nM, respectively. Thus, this study offers new prospects for designing an affordable and readily available, yet highly sensitive, paper-based SERS substrate with the potential for development as a lab-on-a-chip device.

Impurities removal from acidic solution of nickel cobalt complex hydroxide using pulsed disc and doughnut column

In this work, a 30 mm diameter pulsed disc and doughnut solvent extraction column was used for impurities removal from nickel cobalt complex hydroxide acid solution by solvent extraction. The effects of dispersed phase velocity, continuous phase velocity and pulse intensity on drop diameter, dispersed phase holdup and mass transfer were investigated. The results show that the drop size decreases gradually, and the dispersed phase holdup decreased initially and then increased with the increase of pulse intensity. The dispersed phase holdup increases with the increase of dispersed phase velocity but is independent of the continuous phase velocity. The experimental data of this study are predicted by correlations with regressed parameters. The average absolute relative error of drop size and dispersed phase holdup were 10.07 % and 18.28 %. With the increase of pulse intensity, the extraction efficiency of impurities decreased firstly and then increased. The number of mass transfer units and the height of mass transfer unit were calculated. The trend of number of mass transfer units of impurities are similar to extraction efficiency. Mass transfer results indicate that pulsed disc and doughnut column can be applied to the nickel cobalt complex hydroxide acid solution-P204/kerosene system.

Review of Heat Transfer Characteristics of Natural Gas Hydrate

As a typical unconventional energy reservoir, natural gas hydrate is believed to be the most promising alternative for conventional resources in future energy patterns. The exploitation process of natural gas hydrate comprises a hydrate phase state, heat and mass transfer, and multi-phase seepage. Therefore, the study of heat transfer characteristics of gas hydrate is of great significance for an efficient exploitation of gas hydrate. In this paper, the research methods and research progress of gas hydrate heat transfer are reviewed from four aspects: measurement methods of heat transfer characteristics, influencing factors of heat transfer in a hydrate system and hydrate-containing porous media systems, predictive models for effective thermal conductivity, and heat transfer mechanisms of hydrate. Advanced measurement techniques and theoretical methods that can be adopted for the heat transfer characteristics of gas hydrate in the future are discussed.

Mass transfer performance of pulsed disk and doughnut column (PDDC) in the extraction of active ingredients in peppermint extract obtained by hot percolation

AbstractThe active ingredients in peppermint are widely used in the pharmaceutical, food, cosmetic, and other industries. The traditional methods for producing peppermint extract through hydrodistillation (HD) and percolation are long process with low efficiency. The aim of this study is the improvement of the extraction performance and the efficiency of the extract obtained from hot percolation via pulsed disk and doughnut columns (PDDC), which is one of the most important pieces of liquid–liquid extraction (LLE) equipment. Peppermint extract was used as the continuous phase in the PDDC. n‐Hexane was considered as the dispersed phase in this column. In this study, the effects of three operating parameters were investigated, including the pulse intensity, continuous phase height, and dispersed phase flow rate, on the extraction efficiency of active ingredients in peppermint. The response surface method (RSM) was used to investigate the effect of these parameters on the extraction efficiency. The efficiency of this column in the extracting of active ingredients from peppermint was measured by UV–vis spectrophotometry, via the absorption rate of the main active ingredients of peppermint (menthol) in the samples, and the efficiency was 75% on average. The experimental and theorical of dispersed phase mass transfer coefficient were evaluated and compared. The results showed that the PDDC improved the extraction and mass transfer. By increasing the flow rate of the dispersed phase and the height of the continuous phase, the extraction efficiency and the mass transfer coefficient were increased.

Dephosphorization Kinetics of Hot Metal at Low Slag Basicity and Low Temperature under the Different Fe2O3 Addition Amounts

In this article, the influence of the Fe2O3 addition amount on the dephosphorization kinetics of hot metal at the low slag basicity (CaO/SiO2) of about 1.6 and low temperature of 1623 K is investigated with laboratorial experiments and the kinetic model. Si and P contents in the hot metal during the whole dephosphorization process, and the endpoint FeO content in the slag, show good agreements between the calculated results with the kinetic model and experimental results. The peak value of dephosphorization rate linearly increases from 8.35 × 10−5 to 4.52 × 10−4 mass% s−1 when the weight ratio of Fe2O3 is increased from 5 to 10/100 g hot metal. With the increase in Fe2O3 addition amount, the mass transfer coefficient in the hot metal phase (km) and that in the slag phase (ks) and dephosphorization rate constant (k) all increase. The value of km is found to be 4.34 times that of ks. During the dephosphorization process, the rate‐controlling step converts from the mass transfer in slag phase to the mass transfer in hot metal phase in less than 10 min. With the increase in Fe2O3 addition amount, the value of interfacial oxygen activity of increases from 0.0102 to 0.0201.

Simulation analysis of microwave sintering of recycled building bricks based on three-phase porous medium model

The visualization and quantification characteristics of numerical simulation can overcome many obstacles caused by experimental conditions and contribute to the development of the microwave sintering mechanism of recycled building bricks (RBB). However, existing research has paid little attention to the numerical simulation of the microwave sintering of RBB. This study considers the phase transition and mass transfer of three-phase porous media, and establishes a fully coupled model of electromagnetic, heat transfer, and three-phase porous media to study the thermal behavior of RBB under microwave irradiation. The results indicate that the electric field inside the cavity exists in a non-uniform form with high and low energy regions. The addition of RBB will see a redistribution of the electric field in the cavity. The non-uniform distribution of electric field and the selective heating of microwaves result in the appearance of hot and cold regions inside RBB during sintering. Phase transition and mass transfer are beneficial for improving the uniformity of temperature field. The geometric size and position of RBB will affect the uniformity of the temperature field of RBB, and adding SiC board can be effective to improve the uniformity.

Importance of stable mass transfer and stellar winds for the formation of gravitational wave sources

ABSTRACT The large number of gravitational wave (GW) detections have revealed the properties of the merging black hole binary population, but how such systems are formed is still heavily debated. Understanding the imprint of stellar physics on the observable GW population will shed light on how we can use the GW data, along with other observations, to constrain the poorly understood evolution of massive binaries. We perform a parameter study on the classical isolated binary formation channel with the population synthesis code seba to investigate how sensitive the properties of the coalescing binary black hole population are on the uncertainties related to first phase of mass transfer and stellar winds. We vary five assumptions: (1) and (2) the mass transfer efficiency and the angular momentum loss during the first mass transfer phase, (3) the mass transfer stability criteria for giant donors with radiative envelopes, (4) the effective temperature at which an evolved star develops a deep convective envelope, and (5) the mass-loss rates of stellar winds. We find that current uncertainties related to first phase of mass transfer have a huge impact on the relative importance of different dominant channels, while the observable demographics of GW sources are not significantly affected. Our varied parameters have a complex, interrelated effect on the population properties of GW sources. Therefore, inference of massive binary physics from GW data alone remains extremely challenging, given the large uncertainties in our current models.

Development and validation of a numerical model for frost growth based on nucleation theory

Cold surface frosting is a complex process involving multi-component phase change heat and mass transfer and variable void structure. It is very challenging to deeply understand the frosting law and mechanism and accurately simulate the frosting process. Existing numerical models of frost growth have many shortcomings, such as a narrow application range, few verification parameters and low reliability. For these reasons, this paper developed a numerical model of frost layer growth based on nucleation theory, modified the phase transition model, and proposed a formula for constraining the picking limit of the frost layer. Additionally, it introduced a formula for calculating the average temperature of the two phases in the frost layer. The simulation results for frost layer thickness, density, temperature, and distribution were extensively verified using experimental data obtained by different scholars under various conditions and compared with simulation results in related literatures. The results show that the simulation results of all parameters under different conditions are in good agreement with the experimental data, with a maximum deviation of less than 15 %. Notably, the simulation results for frost thickness and distribution are more accurate than those found in existing literatures. The model developed in this paper offers a higher number of validation parameters, a wider validation range, and greater accuracy and reliability. This model can provide a solid theoretical foundation for studying frost characteristics under complex conditions and for the optimal design of frost-prone heat exchangers.

Overpotential Behavior of Electrolysis and Fuel Cell Modes of Molten Carbonate Cells

Molten carbonate is an high operating temperature electrolyte for the fuel cell (MCFC) and electrolysis cells (MCEC). In particular, the liquid molten carbonates allow the reversible operation between fuel cell and electrolysis cells. The electrode kinetics and mass transfer characteristics of MCFC have been rather extensively investigated compared with those of MCEC. In this work, the mass transfer behaviors between MCFC and MCEC have been focused by experimental way with 100 cm2 class bench cells.The electrodes and matrix in the cell were supplied by KIST in Korea. The cells were operated at 923K under atmospheric pressure. The hydrogen electrode was supplied by a mixture of H2:CO2=1:1, 2:1, 1:2 ratios at 20% or 40% H2O. The oxygen electrode was fed by Air:CO2=0.7:0.3 atm. The steady state polarization (SSP) from 0 to 150 mA cm-2, inert gas step addition (ISA), and reactant gas addition (RA) methods were employed. The ISA adds inert gas to the hydrogen or oxygen electrodes, then the addition varies reactants flow rate and partial pressures. Consequently, the variations are reflected to the cell voltage at open circuit and polarization states. The voltage shift by the flow and partial pressure change represents overpotential behaviors at the electrodes [1]. The RA method uses a reactant gas instead of inert gas in the ISA. Therefore, the RA provides the overpotential information of the added reactant species [2].From the experimental investigations, the total voltage loss at the FC is larger than that of EC mode. In addition, the hydrogen electrode has significant gas phase mass transfer resistance due to the H2, CO2, and H2O species at the FC and EC modes. A similar overpotential was observed at the hydrogen electrode. On the other hand, the oxygen electrode has much less overpotential at the EC mode than the FC mode. Since the oxygen reduction at the FC mode contains O2 dissolution and mass transfer through the carbonate electrolytes, liquid phase mass transfer resistance is dominant. However, the oxidation of carbonate ions to oxygen does not contain liquid phase mass transfer process at the EC mode. Therefore, much less overpotential was observed at the oxygen electrode at the EC mode than the FC mode. This can be a reason of smaller total voltage loss at the MCEC than the MCFC.[1] Samuel Koomson, Choong-Gon Lee, J. Electroanalytical Chemistry, 925, 116896 (2022).[2] C.-G. Lee, H.-C. Lim, J. Electrochem. Soc., 152, A219-A228 (2005).

Research on minimizing the MFC internal resistance via a shared electrode MFC-MEC coupling system

Although microbial fuel cells (MFCs) are a very clean electricity-producing bioelectrochemical technology, their large internal resistance limits their power generation capacity. To reduce the MFC internal resistance, according to the principle of favorable electric field, a microbial electrolysis cells (MECs) was coupled with MFC to form two kinds of MFC-MEC coupling systems: a shared anode MFC-MEC system (SA-MFC) and a shared cathode MFC-MEC system (SC-MFC). Compared with those of the uncoupled MFC, the total internal resistances (Rtol) of the SA-MFC and the SC-MFC were 2119.04 Ω and 2416.44 Ω, respectively, lower than that of the uncoupled MFC (3392.05 Ω). The average working voltages of the SA-MFC and the SC-MFC reached 121.40 mV and 100.43 mV, respectively, which were 41.71% and 17.23% higher than that of the uncoupled MFC (85.67 mV), and the maximum power output reached 121.03 mW and 94.09 mW, respectively, which were 1.93 times and 1.50 times that of the uncoupled MFC (62.58 mW), indicating that the SA-MFC had optimal power production performance. The reasons for these differences were that the external electric field provided by the MEC created an additional driving force for the electrode reaction, extracellular electron transfer and liquid phase mass transfer, resulting in weakened electrode polarization. This research provides a new way to reduce the internal resistance of MFCs and increase their power output.

Simulation and Experimental Study of Solid-Liquid Extraction of Coal Tar Residue Based on Different Extractants.

Coal tar residue (CTR) is recognized as a hazardous industrial waste with a high carbon content and coal tar consisting mainly of toxic polycyclic aromatic hydrocarbons (PAHs). The coal tar in CTR can be deeply processed into high-value-added fuels and chemicals. Effective separation of coal tar and residue in CTR is a high-value-added utilization method for it. In this paper, ethyl acetate, ethanol, and n-hexane were chosen as extractants to study the extraction process of coal tar from CTR, considering the mass transfer in the liquid phase outside the CTR particles and the diffusion inside the CTR particles, and a mathematical model of the solid-liquid extraction process of CTR was established based on Fick's second law. First, the mass-transfer coefficients (kf) and effective diffusion coefficients (De) of ethyl acetate, ethanol, and n-hexane in solid-liquid extraction at 35 °C were determined to be 1.54 × 10-5 and 4.99 × 10-10 m2·s-1, 1.14 × 10-5 and 3.57 × 10-10 m2·s-1, and 1.01 × 10-5 and 3.48 × 10-10 m2·s-1, respectively. Furthermore, the simulated values obtained by the model also maintained a high degree of agreement with the experimental results, which indicates the high accuracy prediction of the model. Finally, the model was used to investigate the effects of the solvent-solid ratio, temperature, and stirring speed on the extraction rates with the three extractants. According to the analysis with gas chromatography-mass spectrometry (GC-MS), among the three solvents, n-hexane extracted the highest content of aliphatic hydrocarbons (ALHs), ethyl acetate extracted the highest content of oxygenated compounds (OCs), and ethanol extracted the highest content of aromatic hydrocarbons (ARHs). The model and experimental data can be used to provide accurate predictions for industrial utilization of CTR.

A New Model of Bubble Migration Velocity in Deep Water Wellbore Considering Hydrate Phase Transition

Mass transfer and phase transition have an important effect on the velocity of bubble migration in deepwater wellbores, and accurate prediction of bubble migration velocity is crucial for calculating the safe shut-in period of deepwater oil and gas wells. Therefore, the effect of bubble dissolution mass transfer and hydrate phase transition on bubble migration behavior in the deepwater environment have attracted extensive attention from researchers in the fields of energy, marine chemistry, and marine engineering safety. In this work, a new model of bubble migration velocity in deepwater is developed, which considers the effect of hydrate phase transition and gas-water bidirectional cross-shell mass transfer during bubble migration. Based on the observation data of bubble migration in deepwater, the reliability of the model in predicting bubble migration velocity is verified. Then, the model is used to calculate and analyze the bubble migration velocity and bubble migration cycle under different initial bubble size, different annular fluid viscosity, and density. The results show that the initial size of bubble and the viscosity of annulus fluid are the main factors affecting the migration velocity of the bubble, but the density of annulus fluid has little effect on the migration velocity of the hydrated bubble and clean bubble. In addition, the migration velocity of the clean bubble gradually increases during the migration process from the bottom to the wellhead, while the migration velocity of the hydrated bubble is divided into a gradually decreasing stage and a slowly increasing stage. The gas consumption and the thickening of hydrate shell in the gradually decreasing stage play a dominant role, and the increase of bubble volume caused by the decrease of pressure in the slowly increasing stage is the most important factor. The formation of the hydrated bubble can significantly reduce the migration velocity of the bubble and effectively prolong the safe shut-in period. This study provides a reference for quantitative description and characterization of complex bubble migration behavior with phase change and mass transfer in deepwater environment.

The role of asymmetric metal flow on weld formation and solidification characteristics during pulsed laser butt welding with assembly tolerance

In comparison to other laser-assisted welding techniques, the pulsed laser welding process (PLBW) provides cost-effectiveness and ease of operation while effectively connecting butt-assembled thin plates with manufacturing tolerances (both air gap and edge misalignment). A combination of numerical simulations and experimental studies was conducted to analyze the forming mechanism and solidification behavior of the weld. In this paper, a transient three-dimensional heat-flow-metallurgical model has been established for a PLBW process of mild steel plates with a thickness of 1.8 mm. The predicted weld pool profiles were consistent with the experimental findings. The finding suggested the molten metal, driven by surface tension and recoil pressure, successively generated liquid bridges on the rear and front sides of the pool. The two sheets were joined as the molten metal gradually solidified. The energy absorptivity was highly correlated with the weld pool and keyhole dynamics, and the laser energy absorbed by the metal was mainly transferred in the form of thermal convection. The kinematic features of the melt were observed by the liquid phase mass transfer rate and surface fluctuations. According to the Fourier analysis results, the molten pool oscillated at the characteristic frequency of the laser pulse frequency. The spatial and temporal distributions of solidification parameters aided in analyzing the solidification features within the pool. The asymmetric flow had a greater influence on the temperature gradient. These findings addressed the roles of PLBW on fluid flow, heat behaviors, and solidification parameters of welds with assembly tolerances, as well as the reasons for improved weld formation.

The Effect of Irradiation on the Spin of Millisecond Pulsars

A millisecond pulsar (MSP) is an old neutron star (NS) that has accreted material from its companion star, causing it to spin up, which is known as the recycling scenario. During the mass transfer phase, the system manifests itself as an X-ray binary. PSR J1402+13 is an MSP with a spin period of 5.89 ms and a spin period derivative of . These properties make it a notable object within the pulsar population, as MSPs typically exhibit low spin period derivatives. In this paper, we aim to explain how an MSP can possess a high spin period derivative by binary evolution. By utilizing the stellar evolution code MESA, we examine the effects of irradiation on the companion star and the propeller effect on the NS during binary evolution. We demonstrate that irradiation can modify the spin period and mass of an MSP, resulting in a higher spin period derivative. These results suggest that the irradiation effect may serve as a key factor in explaining MSPs with high spin period derivatives.

The main evolutionary pathways of massive hierarchical triple stars

Context. So far, stellar population studies have mainly focused on the evolution of single and binary stars. Recent observations show that triple and higher order multiple star systems are ubiquitous in the local population, especially among massive stars. Introducing three-body dynamical effects can influence the evolution of an individual stellar system and can therefore affect the predicted rates of astrophysical sources that are a product of stellar evolution. Therefore, predictions of triple star evolution are necessary for a more complete understanding of the evolutionary behaviour of stellar populations and their end products. Aims. We aim to constrain the main evolutionary pathways of massive hierarchical triple star systems and to quantify the effect of the third star on the evolution of the system. Methods. We model the massive triple star population by performing simulations of triple star evolution with the TRES code, which combines stellar evolution with secular evolution of triple systems, and explore how robust the predictions of these simulations are under variations of uncertain initial conditions. We focus on coeval, hierarchical stellar triples in pre-mass-transfer phases. Results. Interactions are common among massive triple stars. The majority of systems (65%–77%) experience a phase of mass transfer in the inner binary, often with a main sequence donor star. This differs significantly from isolated binary evolution, where mass transfer is less frequent (52.3% instead of 67% for our fiducial model) and the donors are typically post-main sequence stars. Initial constraints for dynamical stability as well as eccentricity oscillations driven by the third body facilitate the occurrence of interactions, such as mass transfer. The requirement of dynamical stability at formation places quite stringent constraints on allowed orbital properties, reducing uncertainties in triple evolution that resort from these initial conditions. Ignoring three-body dynamics during evolution of non-interacting triples leads to triple compact-object systems with stronger eccentricity oscillations and thereby likely over-predicts the merger rate of compact objects in such systems.

Kinetics of Fixed Bed Sorption Processes

Adsorption and ion exchange are examples of fixed-bed sorption processes that show transient behavior. This means that differential equations are needed to design them. As a result, numerical methods are commonly utilized to solve these equations. The solution frequently used in analytical methods is called the Thomas solution. Thomas gave a complete solution that adds a nonlinear equilibrium relationship that depends on second-order reaction kinetics. A computational approach was devised to solve the Thomas model. The Thomas model's validity was established by conducting three distinct sets of experiments. The first entails the adsorption of acetic acid from the air through the utilization of activated carbon. Following this, zeolite-5A adsorbs trichloroethylene (TCE) from the air. Finally, activated carbon is employed for the purpose of adsorbing o-cresol from aqueous solutions. A study was done to estimate phase equilibria and interphase mass transfer rates. To find the kinetic mass-transfer coefficient (K) for gases, the phase coefficients for mass transfer in the fluid phase ( ) and the pore phase ( ) were added together. The estimation of (K) for liquid was performed using the mass transfer coefficient for the solid phase and togather. The results suggest that the adsorption of acetic acid from air on activated carbon gives a good agreement with the Thomas model. The other sets of data demonstrate a disparity due to the underlying assumptions inherent in the Thomas model.

A Study of Ten Early-type Contact Binary Stars in the Small Magellanic Cloud

To study early-type binary systems in different evolutionary stages or environments, the Small Magellanic Cloud (SMC) is an ideal laboratory due to its low metallicity compared to that of the Milky Way. We conduct a study on the period changes of the close binary systems with B-type spectral classifications in the SMC using OGLE collections. Ten B-type binaries that show no significant periodic variations based on the current observational data were analyzed. Through O − C analysis, four of the ten early-type binaries show a long-term period decrease, one shows a long-term period increase, and the other five systems are ambiguous due to the limitations of the observational data. Among the period-decreasing systems, two may be mainly caused by mass transfer, while the rest may be caused by angular momentum loss. The Wilson-Devinney code (W-D method) is used to analyze their I-band photometric light curves. According to the W-D results, five early-type binaries are in the deep contact state, three are in the shallow contact state, while two are in the medium contact state, and the temperature ratios of these early-type binaries are all close to unity. The five deep contact binaries are highly unstable systems and therefore serve as important objects for the study of binary mergers. Finally, a discussion on the evolution of early-type binary stars is conducted by combining the analyses of the light curves and the periodic changes of ten early-type binaries, that implies that the majority of early-type binaries in the SMC may form contact binaries from a phase of rapid mass transfer.