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The key to rationally and rapidly designing high‐performance materials is the monitoring and comprehension of dynamic processes within individual particles in real‐time, particularly to gain insight into the anisotropy of nanoparticles. The intrinsic property of nanoparticles typically varies from one crystal facet to the next under realistic working conditions. Here, we introduce the operando collision electrochemistry to resolve the single silver nanoprisms (Ag NPs) anisotropy in photoelectrochemistry. We directly identify the effect of anisotropy on the plasmonic‐assisted electrochemistry at the single NP/electrolyte interface. The statistical collision frequency shows that heterogeneous diffusion coefficients among crystal facets facilitate Ag NPs to undergo direction‐dependent mass transfer toward the gold ultramicroelectrode. Subsequently, the current amplitudes of transient events indicate that the anisotropy enables variations in dynamic interfacial electron transfer behaviors during photothermal processes. The results presented here demonstrate that the measurement precision of collision electrochemistry can be extended to the sub‐nanoparticle level, highlighting the potential for high‐throughput material screening with comprehensive kinetics information at the nanoscale. [ABSTRACT FROM AUTHOR]

In this study, the influence mechanisms of the nanopore width on mass transfer characteristics for methane nanofluidic are explored by non-equilibrium multiscale molecular dynamics simulation systematically. The numerical results indicate that the diffusion coefficient increases with the increase in the nanopore width via the quasi-parabolic paths. In the middle of nanopore, the local diffusion coefficients increase with the increase in the wall–fluid interaction strength factor; however, the change of local diffusion coefficient is reversed in the fluid domain near the nanopore wall. Moreover, the results show that the residual decreases with the increase in the degree polynomial of 1 h . According to these fitting functions, it can be found that the diffusion coefficient approaches 80% of that of bulk system when the nanopore width increases to 14 times the diameter of methane molecule. Furthermore, the velocity autocorrelation functions and the diffusion coefficients (x, y, and z direction) demonstrate that the methane nanofluid shows anisotropy characteristics. In addition, the mean interaction force potential and slip velocity also indicate that the wall–fluid interaction strength factor and the nanopore width significantly affect the mass transfer characteristics of nanofluidic. The numerical results would be helpful to comprehend the mass transfer characteristics of nanofluidics. It should be considered in the optimal design of nano-devices. [ABSTRACT FROM AUTHOR]

The study of diffusion in biological materials is crucial for fields like food science, engineering, and pharmaceuticals. Research that combines numerical and analytical methods is needed to better understand diffusive phenomena across various dimensions and under variable boundary conditions within food matrices. This study aims to bridge this gap by examining the diffusion of substances through biological materials analytically and numerically, calculating diffusivity and conducting surface analysis. The research proposes a process for sweetening Bing-type cherries (Prunus avium) using sucrose/xylitol solutions and a staining technique utilising erythrosine and red gardenia at varying concentrations (119, 238 and 357 ppm) and temperatures (40, 50 and 60 °C). Given the fruit's epidermis resistance, the effective diffusivities of skin were inferior to those in flesh. Temperature and concentration synergise in enhancing diffusion coefficients and dye penetration within the food matrix (357 ppm and 60 °C). Red gardenia displayed significant temperature-dependent variation (p = 0.001), whereas erythrosine dye remained stable by temperature changes (p > 0.05). Gardenia's effective diffusivities in cherry flesh and skin, at 357 ppm and 60 °C, 3.89E−08 and 6.61E−09 m2/s, respectively, significantly differed from those obtained at lower temperatures and concentrations. The results highlight the temperature-concentration impacts on mass transfer calculations for food colouring processes and preservation methodologies. [ABSTRACT FROM AUTHOR]

Tender coconut water has been very popular as a natural beverage rich in various electrolytes, amino acids, and vitamins, and hence a large amount of tender coconut kernel is left without efficient utilization. To explore the possibility of making infused tender coconut kernel, we investigated the effects of two osmosis methods, including solid-state osmotic dehydration and liquid-state osmotic dehydration, as well as two osmosis agents such as sorbitol and sucrose, on the mass transfer of coconut kernel under solid-state osmotic dehydration conditions. The results showed that under the conditions of solid-state osmosis using sucrose and liquid-state osmosis using sucrose solution, the water diffusion coefficients were 9.0396 h−1/2 and 2.9940 h−1/2, respectively, with corresponding water mass transfer coefficients of 0.3373 and 0.2452, and the equilibrium water loss rates of 49.04% and 17.31%, respectively, indicating that the mass transfer efficiency of solid-state osmotic dehydration of tender coconut kernel was significantly higher than that of liquid-state osmotic dehydration. Under solid osmosis conditions, the water loss rates using sucrose and sorbitol were 38.64% and 41.95%, respectively, with dry basis yield increments of 61.38% and 71.09%, respectively, demonstrating superior dehydration efficiency of sorbitol over sucrose under solid-state osmosis. This study can provide a reference for the theoretical study of the mass transfer of tender coconut kernel through osmotic dehydration, and also provide technical support for the development and utilization of tender coconut kernel. [ABSTRACT FROM AUTHOR]

The objective of this study was to develop a dried apple snack enriched with probiotics, evaluate its viability using Refractance Window (RWTM) drying, and compare it with conventional hot air drying (CD) and freeze-drying (FD). Apple slices were impregnated with Lacticaseibacillus rhamnosus and dried at 45 °C using RWTM and CD and FD. Total polyphenol content (TPC), color (∆E*), texture, and viable cell count were measured, and samples were stored for 28 days at 4 °C. Vacuum impregnation allowed for a probiotic inoculation of 8.53 log CFU/gdb. Retention values of 6.30, 6.67, and 7.20 log CFU/gdb were observed for CD, RWTM, and FD, respectively; the population in CD, RWTM remained while FD showed a decrease of one order of magnitude during storage. Comparing RWTM with FD, ∆E* was not significantly different (p < 0.05) and RWTM presented lower hardness values and higher crispness than FD, but the RWTM-dried apple slices had the highest TPC retention (41.3%). Microstructural analysis showed that RWTM produced a smoother surface, facilitating uniform moisture diffusion and lower mass transfer resistance. The effective moisture diffusion coefficient was higher in RWTM than in CD, resulting in shorter drying times. As a consequence, RWTM produced dried apple snacks enriched with probiotics, with color and TPC retention comparable to FD. [ABSTRACT FROM AUTHOR]

The effective diffusion of a solute in a rectangular two-dimensional channel is experimentally studied. We experimentally examine the effective diffusion of Rhodamine B dissolved in water oscillating in a rectangular Hele–Shaw cell. The concentration of Rhodamine B in water is measured by the intensity of its fluorescence emission. In particular, we consider two problems: (i) effective diffusion of solute in water oscillating in a two-dimensional rectangular channel (Hele–Shaw cell) and (ii) effective diffusion of solute in pores between monosized hard spheres randomly packed in a rectangular Hele–Shaw cell. It is revealed that the rate of solute mass transfer exceeds the molecular diffusion rate in both cases. It has been demonstrated that when water oscillates between parallel walls, diffusion is accelerated by Taylor dispersion with the effective diffusion coefficient D eff exceeding the molecular diffusion coefficient D m by 1–2 orders of magnitude. The effective diffusion coefficient D eff depends only on the relative amplitude but not on the frequency of the fluid oscillations in the studied range of frequencies and amplitudes. When the fluid oscillates in the pores of the porous medium, solute transport is faster than in the case of Taylor dispersion. Here, the effective diffusion coefficient depends on both the frequency and amplitude of oscillations. The analysis shows that the experimental data obtained at various frequencies and amplitudes of oscillations are consistent with the relation D eff / D m ∼ P e 2 (Pe is the Peclet number). We suggest that the enhanced solute mass transfer is associated with the time-averaged fluid flows that arise due to spatial heterogeneity of the amplitude of water oscillations in the pores between randomly packed hard spheres. [ABSTRACT FROM AUTHOR]

Metal-halide perovskite thin monocrystals featuring efficient carrier collection and transport capabilities are well suited for radiation detectors, yet their growth in a generic, well-controlled manner remains challenging. Here, we reveal that mass transfer is one major limiting factor during solution growth of perovskite thin monocrystals. A general approach is developed to overcome synthetic limitation by using a high solute flux system, in which mass diffusion coefficient is improved from 1.7×10–10 to 5.4×10–10 m2 s–1 by suppressing monomer aggregation. The generality of this approach is validated by the synthesis of 29 types of perovskite thin monocrystals at 40–90 °C with the growth velocity up to 27.2 μm min–1. The as-grown perovskite monocrystals deliver a high X-ray sensitivity of 1.74×105 µC Gy−1 cm−2 without applied bias. The findings regarding limited mass transfer and high-flux crystallization are crucial towards advancing the preparation and application of perovskite thin monocrystals. Liu et al. report a universal solution growth method for perovskite thin monocrystals by improving the mass transfer in the high solute flux system. The approach is applied to 29 types of perovskites with growth velocity up to 27.2 µm min-1 and enables efficient self-driven X-ray detectors. [ABSTRACT FROM AUTHOR]

Nanofluid is a particle suspension composed of liquid and nanoparticles, and has great potential to enhance mass transfer. Most previous studies have only considered the effect of the Brownian motion of nanoparticles on mass transfer. In this study, the two-dimensional Lattice Boltzmann method (LBM) combined with the cell automation (CA) probabilistic model is proposed to investigate the mass transfer of CO 2 in nanofluids. The model predictions were in good agreement with experimental data, validating the developed mass transfer model. The simulation results indicated that the Brownian motion and grazing effect enhanced the mass transfer in nanofluids, and should be considered simultaneously. Comparing with the pure water, adding 0.1 wt% SiO 2 nanoparticles increased the absorption rate up to 58.3 %, and the effective diffusion coefficients reached 5.41 × 10−9 m2s−1. In addition, changing the physical parameters directly affected the Brownian motion and grazing effect, and changed the effective diffusion coefficient of CO 2 in the nanofluid. The effective diffusion coefficient decreased with an increase in particle size and increased with an increase in fluid temperature. [Display omitted] • The LBM combined with the CA was proposed to investigate the mass transfer of CO 2 in nanofluids. • In our developed model, the nanoparticles can move independently in the solution and absorb CO 2. • The effect of nanoparticles's Brownian motion and grazing effect on mass transfer were both considered. • The effects of different physical parameters on mass transfer in nanofluids were analyzed. [ABSTRACT FROM AUTHOR]

Gas adsorption–migration in coal is of crucial importance for coalbed methane (CBM) recovery; however, the effect of coal deformation on it is not yet very clear, especially at the molecular level. In this study, the effects of uniaxial tension–compression strains on the CH4/CO2/N2 adsorption–migration characteristics in bituminous coal matrix were investigated by integrating the grand canonical Monte Carlo and molecular dynamics methods. The results show that the dual-mode equation fits the isothermal adsorption results, and the adsorption concentration and Langmuir volume are positively correlated with strain. Tension strain has a small effect on a thermodynamic factor but a large effect on Henry constant. In addition, the swelling resistance of coal matrix is positively correlated with tension strain which has a greater impact on the shear resistance of coal matrix containing CO2. The average mass density of the gas is linearly positively correlated with strain that has a large impact on N2 stability. More significantly, the self-diffusion coefficient (Ds) of CH4 is larger than that of CO2/N2, and the relationship between Fick diffusion coefficient and strain is roughly similar to that between Ds and strain. Also, the mass transfer of CO2 permeation is more significant compared to N2, especially for tension strain. These research results provide a basis for the optimization design of CBM recovery in deformed coal reservoirs. [ABSTRACT FROM AUTHOR]

We study the temporal evolution of solute dispersion in three‐dimensional porous rocks of different heterogeneity and pore structure. To this end, we perform direct numerical simulations of pore‐scale flow and transport in a sand pack, which exhibits mild heterogeneity, and a Berea sandstone, which is characterized by strong heterogeneity as measured by the variance of the logarithm of the flow velocity. The impact of medium structure and pore‐scale mass transfer mechanisms is probed by effective and ensemble dispersion coefficients. The former is a measure for the typical width of a plume, while the latter for the deformation, that is, the spread of a mixing front. Both dispersion coefficients evolve from the molecular diffusion coefficients toward a common finite asymptotic value. Their behavior is governed by the interplay between diffusion, pore‐scale velocity fluctuations and medium structure, which determine the characteristic mass transfer time scales. We find distinctly different dispersion behaviors in the two media, which can be traced back to how particles sample pore‐scale velocity variability and how this depends on the medium structure. These are key elements for the upscaling of transport, mixing and reaction from the pore to the continuum scale. Key Points: Pore‐scale simulations of temporal evolution of solute dispersion in three‐dimensional porous rocksThe impact of medium structure and diffusion on solute transport is studied in terms of effective and ensemble dispersion coefficientsThe evolution of dispersion coefficients indicates how particles sample pore‐scale velocities and how this depends on the medium structure [ABSTRACT FROM AUTHOR]

Due to the inherent deposition environment and extraction challenges in a coal seam, quantification of its gas transport behavior serves as the prerequisite to predict and evaluate accurately dynamic coalbed methane (CBM) recovery. In this work, a dual-porosity/single-permeability (DPSP) model is proposed for evaluating the gaseous methane flow performance by considering both the free gas density gradient and pressure gradient. More specifically, methane extraction dynamics was monitored via on-site boreholes with different spacings, and the two key gas flow parameters (i.e., diffusion coefficient and permeability coefficient) were determined and validated by minimizing the deviations between the field measurements and the simulated production profiles. Sensitivity analysis was conducted to examine the effect of both gas flow rate in a borehole and gas mass transfer flux from coal matrix to fractures on the production performance. The gas flow rate was found to be very sensitive to the permeability coefficient at the early extraction stage and then dominated mainly by the diffusion coefficient during the later extraction stage. The gas mass transfer flux from the matrix subsystem to the fracture subsystem exhibited distinct peak features due to the hysteresis of gas desorption in coal matrix. To extract methane in a coal seam, gas pressure in the matrix subsystem decreases much less than that in the fracture subsystem. Compared with the traditional single-porosity/single-permeability model, the newly proposed DPSP model allowed us to correct the overestimated CBM production and identify the underlying gas flow mechanisms. By introducing a critical extraction radius (CER) during a CBM extraction process, a theoretical equation associated with the CER, original methane content in a coal seam and methane extraction time was eventually formulated so that the CER and borehole spacing in some coal seam areas with different methane contents can be determined in a convenient and accurate manner. [ABSTRACT FROM AUTHOR]

Highlights: What are the main findings? The diffusion coefficient of the Chinese cabbage leaf is insignificantly different regardless of its position due to similarities in leaf thickness. Soluble solid uptake by the Chinese cabbage midrib is not influenced by shrinkage for a brining period between 0 and 48 h. More rapid soluble solid uptake occurs in the Chinese cabbage leaf blade than in the midrib. Numerical models provide insight into the influence of shrinkage during Chinese cabbage osmotic dehydration. What is the implication of the main finding? Optimal Brining Conditions: Different sections of Chinese cabbage (CC) respond uniquely to brining time, suggesting the need to optimize brining conditions based on the equilibrium concentrations observed at positions 1 to 4. Early Soluble Solid Uptake: Rapid soluble solid uptake in CC leaf blade and midrib during the initial 0–18 h underscores the importance of monitoring and controlling the early stages of brining to influence efficient soluble solid uptake. Shrinkage Effect Considerations: Shrinkage significantly affects CC midrib in the first 18 h and becomes visible between 48 and 120 h, emphasizing the time-dependent impact of shrinkage. For short-term brining (up to 48 h), shrinkage may be negligible, but for longer durations, especially midrib at position 1, considering shrinkage is crucial for accurate modeling. Computational Simplification: Experimental and simulated results agreement suggests that, for short-term brining processes, excluding the shrinkage effect from diffusion models may be justifiable. This implies a potential reduction in computational complexity without compromising accuracy. The mass transfer and shrinkage characteristics of Chinese cabbage (CC) during osmotic dehydration (OD) were investigated. The leaves were grouped into four sections and analyzed based on their morphological characteristics (i.e., maturity, width, and thickness). The sections were immersed in 2.0 mol/m3 NaCl for 120 h at 25 ± 2 °C. The diffusion coefficient (D) of the leaf blade was not significantly different with respect to the sections that were formed, but it was significantly different in the midrib in the increasing order of P1, P4, P3, and P2, with values of 1.12, 1.61, 1.84, and 2.06 (× 10−6), respectively, after a 1 h soaking period due to the different characteristics in morphology and structure, such as porosity (0.31, 0.41, 0.42, and 0.38 for positions 1, 2, 3, and 4, respectively) and fiber contents. Numerical simulation (NS) for CC was conducted with and without the consideration of shrinkage during OD. The shrinkage effect on the NaCl uptake analyzed using NS indicated no significant difference between 0 to 48 h for both models. However, changes in the NaCl concentration were observed from 48 h onwards, with a lesser concentration in the model with shrinkage for all sections. The difference in NaCl concentration for the models with and without shrinkage was within the standard error range (±0.2 mol/m3) observed during experimental analysis. This implies that the shrinkage effect can be overlooked during the modeling of CC to reduce computational power. [ABSTRACT FROM AUTHOR]

Detailed knowledge of the flow characteristics, bubble movement, and mass transfer is a prerequisite for the proper design of multiphase bioreactors. Often, mechanistic spatiotemporal models and computational fluid dynamics, which intrinsically require computationally demanding analysis of local interfacial forces, are applied. Typically, such approaches use volumetric mass-transfer coefficient (kLa) models, which have demonstrated their predictive power in water systems. However, are the related results transferrable to multiphase fermentations with different physicochemical properties? This is crucial for the proper design of biotechnological processes. Accordingly, this study investigated a given set of mass transfer data to characterize the fermentation conditions. To prevent time-consuming simulations, computational efforts were reduced using a force balance stationary 0-dimension model. Therefore, a competing set of drag models covering different mechanistic assumptions could be evaluated. The simplified approach of disregarding fluid movement provided reliable results and outlined the need to identify the liquid diffusion coefficients in fermentation media. To predict the rising bubble velocities uB, the models considering the Morton number (Mo) showed superiority. The mass transfer coefficient kL was best described using the well-known Higbie approach. Taken together, the gas hold-up, specific surface area, and integral mass transfer could be accurately predicted. [ABSTRACT FROM AUTHOR]

A new methodology using microwave extraction, gas-diffusion microextraction (GDME) and high-performance liquid chromatography-mass spectrometer (HPLC-MS) was developed for the analysis of the quantitative detection of gaseous and solid benzotriazole (BTA) and the mass transfer behavior of BTA in volatile corrosion inhibitor (VCI) packaging. The best extraction conditions of BTA in the VCI films were obtained, and the vapor pressure of BTA in the VCI packaging was detected and characterized by a mathematical model using the new methodology. The migration content of BTA in the VCI films and the BTA content on the surface of the films were detected, and the diffusion coefficients at three temperatures were calculated. The vapor pressure and diffusion coefficients of BTA increased with increasing temperature, and the volatilization of BTA promoted the migration of BTA from the VCI films. Moreover, a molecular dynamics (MD) simulation was performed to determine the migration of the BTA molecules within the VCI films at three temperatures; the overall trend of the experimental values was the same and the simulated values were generally within two orders of magnitude of the corresponding experimental values, with the difference likely due to the ignoring of the crystallinity of LDPE. [ABSTRACT FROM AUTHOR]

In this study, the leaching of sucrose from sugar beet was investigated in a batch process using distilled water solvent. Extraction kinetics was explored at low and high solutions/solid mass ratios. The experimental data were examined by a mathematical model based on Fick's second law and the Azuara model as a semi-empirical model to determine diffusion coefficients, equilibrium concentrations, and dissociation coefficient K (the ratio of the concentration at the sample to concentration in solution). Diffusion coefficients were calculated by nonlinear regression of the experimental findings. The diffusion coefficients of sucrose (ranging from 2.4831 × 10−10 to 3.2023 × 10−10 m2/s) were higher in the high solution/solid mass ratios compared to the low ratios (ranging from 0.5231 × 10−10 to 0.8728 × 10−10 m2/s) due to higher mass transfer driving force. Also, the proposed empirical Azuara model could properly describe equilibrium concentrations by predicting results (squared mean square error less than 0.0082) close to experimental data at different operating conditions. [ABSTRACT FROM AUTHOR]

A single-phase incompressible bicomponent transient oil mixing model was established based on the mechanism of flow, heat, and mass transfer of refined oils to obtain the flow field and concentration distribution of the component at the mixed segment during the batch transportation process. A new model for the axial diffusion coefficient was proposed, which included the turbulent diffusion coefficient and the coefficients derived from the differences in fluid physical properties. The new diffusion coefficient calculation formula presented in this paper could make the error very small when the calculated concentration distribution value of the mixing section is compared with the experimental value. Based on the many factors that affect the flow features during the oil replacement process in the mixed-oil section, the main dimensionless parameters (Reynolds, Peclet, Prandtl, Richardson, Schmidt) are selected by using the dimensional analysis method. The mixed segment had a high Pr and Pe. With an increasing concentration of lighter oil, the Pr decreased while the Pe and Re increased. The Ri was always less than 1, which implied that the buoyancy is not important, and the gravity effect can be ignored during the generation process of oil mixing according to the definition of Ri that buoyancy is dominant when it is greater than 1. The change of Sc versus the concentration of gasoline was small, and Sc was always close to 100, which indicated that the momentum diffusion was greater than the mass diffusion in the process of oil mixing. Sensitivity analysis was carried out based on the tailing amount and tailing length of the mixed section. It was concluded that the influence of pipe diameter, flow rate, temperature, and diffusion coefficient on the tailing amount and tailing length had the same trend. A single-phase incompressible two-component transient oil-mixing model is established to obtain the flow field and component concentration distribution in the mixing section during batch transportation in this paper. The flow characteristics and tailing phenomena of the mixed-oil section are determined by studying the dimensionless numbers (Reynolds, Peclet, Prandtl, Richardson, Schmidt) in the oil change process of the mixed-oil section. The experimental results could predict the distribution of oil mixture concentration under specific working conditions. The influences of the difference of oil physical properties, turbulence effect as well as the adsorption effect of the pipe wall on the distribution of oil mixture concentration have also been discussed. The research results show that this technology provides the location and concentration distribution of the mixed oil segment when it is applied to practical cases, which gives technical support for detecting and cutting the mixed oil segment during the process of batch transportation and also guides the accurate cutting of the mixing segment. [ABSTRACT FROM AUTHOR]

Transient uptake curves for propane gas in a bed of HZSM-5 using a volumetric frequency response setup (batch system) were obtained. Thereby, a perturbation, such as a change in volume, was applied to the solid/gas system, and the resulting change in pressure was detected. Two cases of mass transfer limitations (bed diffusion control and micropore diffusion control) were compared, and it was concluded that, in the presented case, micropore diffusion is the rate-determining process. The obtained micropore diffusion coefficient for propane in HZSM-5 was, on average, about 1.2 × 10−10 m2 g−1, which is in good agreement with other frequency response studies shown by literature data. The homemade setup and the modeling presented in this work serve as the basis for ongoing numerical simulations. [ABSTRACT FROM AUTHOR]

The diffusivity in the upper Cu-Chabazite layer of a dual layer ammonia oxidation catalyst with a lower Pt layer was investigated. In a first step, the pore structure of the upper Cu-Chabazite catalyst layer was determined by Focused Ion Beam-Scanning Electron Microscopy (FIB-SEM) slice&view tomography. From the FIB-SEM data the 3D pore structure of the catalyst was reconstructed and diffusion simulations were performed on the reconstructed pore geometry, resulting in an estimated effective diffusivity of Deff/Dgas = 0.31. To validate the FIB-SEM derived estimates of the diffusivity, measurements of CO oxidation on the dual layer catalyst were performed, where the CO was oxidized in the lower Pt-layer while the upper SCR layer served as an inactive diffusion barrier. In this way, the effective diffusivity can be determined from the measured CO conversion. An effective diffusion coefficient of Deff/Dgas = 0.11 was obtained from the CO oxidation measurements, three times lower than the value obtained from the FIB-SEM data, but in line with previous literature data for the effective diffusivity in monolith washcoat layers. Additional NH3 oxidation experiments were performed on the dual layer catalyst. The results were well reproduced by a reactor model applying the effective diffusion coefficient obtained by the CO oxidation experiments. The origin of this apparent inconsistency is currently not understood and requires further investigation. [ABSTRACT FROM AUTHOR]

Dissolution of drug from its solid form to a dissolved form is an important consideration in the design and optimization of drug delivery devices, particularly owing to the abundance of emerging compounds that are extremely poorly soluble. When the solid dosage form is encapsulated, for example by the porous walls of an implant, the impact of the encapsulant drug transport properties is a further confounding issue. In such a case, dissolution and diffusion work in tandem to control the release of drug. However, the interplay between these two competing processes in the context of drug delivery is not as well understood as it is for other mass transfer problems, particularly for practical controlled-release considerations such as an encapsulant layer around the drug delivery device. To address this gap, this work presents a mathematical model that describes controlled release from a drug-loaded device surrounded by a passive porous layer. A solution for the drug concentration distribution is derived using the method of eigenfunction expansion. The model is able to track the dissolution front propagation, and predict the drug release curve during the dissolution process. The utility of the model is demonstrated through comparison against experimental data representing drug release from a cylindrical drug-loaded orthopedic fixation pin, where the model is shown to capture the data very well. Analysis presented here reveals how the various geometrical and physicochemical parameters influence drug dissolution and, ultimately, the drug release profile. It is found that the non-dimensional initial concentration plays a key role in determining whether the problem is diffusion-limited or dissolution-limited, whereas the nature of the problem is largely independent of other parameters including diffusion coefficient and encapsulant thickness. We expect the model will prove to be a useful tool for those designing encapsulated drug delivery devices, in terms of optimizing the design of the device to achieve a desired drug release profile. [Display omitted] [ABSTRACT FROM AUTHOR]

The drying process is one of the oldest methods used to obtain food products that could be stored for a long time. However, drying is an energy-intensive process. Additionally, convective drying, due to the high temperature used during the process, results in loss in bioactive substances as well as nutritional value. Thus, in this research, apple slices were dried in a combined hot air–infrared air dryer with four different drying strategies and drying kinetics, internal and external mass transfer (Crank and Dincer models), and then the energy parameters were investigated. The first, second, third, and fourth strategies, respectively, include one-stage drying with a hot air (HA) or infrared energy source (IR), one stage but with two sources of hot air and infrared (HA–IR), and then there are two stages of first hot air and then infrared drying (HA+IR) and vice versa (IR+HA). According to the results, the highest effective moisture diffusion coefficient of the two Crank and Dincer models was equal to 1.49 × 10−9 and 1.55 × 10−8 m2/s, obtained in the HA70–IR750, and the lowest effective moisture diffusion coefficient was equal to 1.8 × 10−10 and 2.54 × 10−9 m2/s, obtained in IR250+HA40. The maximum (10.25%) and minimum (3.61%) energy efficiency were in the IR750 and HA55–IR250 methods, respectively. Moreover, the highest drying efficiency (12.71%) and the lowest drying efficiency (4.19%) were obtained in HA70+IR500 and HA40–IR250, respectively. The value of specific energy consumption was 15.42–51.03 (kWh/kg), the diffusion activation energy was 18.43–35.43 (kJ/mol), and the value of the specific moisture extraction rate (SMER) was in the range of 0.019–0.054 (kWh/kg). Compared to the other strategies, the second strategy (HA–IR) was better in terms of drying time and mass transfer, and the third strategy (HA+IR) was more efficient in terms of energy efficiency and drying efficiency. The infrared drying in the first strategy was better than that in the other methods in the other strategies in terms of retention of bioactive compounds. [ABSTRACT FROM AUTHOR]

The influence of internal circulation on the heat and mass transfer within dispersed fluid drops in translation was studied numerically using the computational fluid dynamics simulation tool ANSYS FLUENT. The three phases identified for heat/mass transfer are: the initial and final diffusion‐dominated phases and a middle convection‐dominated phase. Non‐isothermal mass transfer simulations using temperature‐dependent diffusion coefficients were carried out to investigate the influence of heating and cooling of the drop on the solute transfer. Mass transfer is slower compared to heat transfer and the final diffusion‐dominated mass transfer occurs at the final temperature attained by the drop. Mass transfer is faster for drop heating than for drop cooling, as the final diffusion phase is rate controlling and significant solute transfer occurs at the final higher temperature. [ABSTRACT FROM AUTHOR]

Structured packings in distillation columns present an opportunity for process optimization. Therefore, current design processes for columns with structured packings are evaluated with respect to their industrial applicability, and a power law equation is proposed for transferring HETP values of a reference system to a test system. A design process that includes CFD simulations is presented, and the CFD simulation setup is introduced. The validity of the simulation setup is examined with regard to the following mixtures: nitrogen/oxygen, chlorobenzene/ethylbenzene, and cyclohexane/n-heptane. Diffusion coefficients are varied in the simulation, and their influence on the HETP value is evaluated. The simulated HETP values are then compared with established mass transfer models and demonstrate a high level of agreement. [Display omitted] • Equilibrium stage and transfer unit concepts for packed column design are compared. • A novel HETP scaling equation for improved packed column design is proposed. • GCST model is successfully used for two-phase CFD simulation in structured packing. • Distillation reference mixtures are found to be suitable for the simulation setup. • Separation efficiencies from simulation are comparable to mass transfer models. [ABSTRACT FROM AUTHOR]

Polyhydroxy alcohol-mediated curing has great potential for producing low-salt cured meat products. This study investigated the mass transfer kinetics and the one-way diffusion simulation of sodium chloride (NaCl) during the curing process. Furthermore, Fick's second law determined the NaCl diffusion coefficient (De) of xylitol-mediated cured pork tenderloin. The results demonstrated that adding xylitol could reduce the De of NaCl. The De of NaCl, calculated using the one-way model, was 1.29 × 10−9 m2·s−1, 1.22 × 10−9 m2·s−1, 1.2 × 10−9 m2·s−1, and 1.15 × 10−9 m2·s−1 when the amount of xylitol added was 0%, 4%, 8%, and 12% (w/w), respectively. This result agrees with the predicted values from the power function time-varying model. Moreover, a three-dimensional simulating model of mass transfers constructed using COMSOL Multiphysics was developed to evaluate the NaCl diffusion in pork tenderloin during the curing process. This model has high accuracy and can be used to describe the diffusion of NaCl in curing. Overall, this study provided a foundation for NaCl diffusion and distribution during the curing process. [ABSTRACT FROM AUTHOR]

CaCO 3 /CaO is a promising thermochemical energy storage material to achieve the continuous and stable operation of renewable energy, due to its unique merits such as high energy storage density and long storage time. However, it makes stringent demands on mass transfer to obtain a high energy discharging performance. This study investigated the synergetic effect of complex pore structures and different operating conditions on the micro-flow diffusion mass transfer performance inside CaO materials. We found that the effective gas diffusion coefficient increased with increasing porosity, and decreased with an increase in fractal dimension. In addition, under different operating conditions, the difference in the effective gas diffusion coefficient inside CaO materials with high porosity and low fractal dimensions was much larger than that inside CaO materials with low porosity and high fractal dimensions. This indicated that the synergetic effect should be considered for mass transfer performance inside CaO materials with high porosity and low fractal dimensions. To better understand this synergetic effect, a prediction model was proposed based on machine learning, where its average error was around 12%, and the root means square error was around 0.04138, which was better than that of the traditional Maxwell model. This proposed model may provide theoretical guidance for the design of Ca-based materials with high performance, and it could also be used in reactor design or system thermodynamic investigations. [ABSTRACT FROM AUTHOR]

Mass transport in textiles is crucial. Knowledge of effective mass transport properties of textiles can be used to improve processes and applications where textiles are used. Mass transfer in knitted and woven fabrics strongly depends on the yarn used. In particular, the permeability and effective diffusion coefficient of yarns are of interest. Correlations are often used to estimate the mass transfer properties of yarns. These correlations commonly assume an ordered distribution, but here we demonstrate that an ordered distribution leads to an overestimation of mass transfer properties. We therefore address the impact of random ordering on the effective diffusivity and permeability of yarns and show that it is important to account for the random arrangement of fibers in order to predict mass transfer. To do this, Representative Volume Elements are randomly generated to represent the structure of yarns made from continuous filaments of synthetic materials. Furthermore, parallel, randomly arranged fibers with a circular cross-section are assumed. By solving the so-called cell problems on the Representative Volume Elements, transport coefficients can be calculated for given porosities. These transport coefficients, which are based on a digital reconstruction of the yarn and asymptotic homogenization, are then used to derive an improved correlation for the effective diffusivity and permeability as a function of porosity and fiber diameter. At porosities below 0.7, the predicted transport is significantly lower under the assumption of random ordering. The approach is not limited to circular fibers and may be extended to arbitrary fiber geometries. [ABSTRACT FROM AUTHOR]

This work presents comprehensive mathematical modelling employed to describe the ozone (O 3) mass transfer in the hollow fibre membrane contactor (HFMC) system. Using the model, impacts of operating parameters and membrane specification such as gas phase and liquid flow rates, porosity-to-tortuosity and membrane length on the dissolved ozone at the reactor outlet as well as ozone concentration distribution were simulated. Also, experimental data were used to validate the created simulation model and it was observed that there is reasonable agreement between experimental results and modelling output in terms of dissolved ozone at the reactor outlet at various water flow rate and initial ozone concentration. Based on the simulation outputs, the gas flow rate as well as porosity (ε)-to-tortuosity (τ) do not have impact on the dissolved ozone at reactor outlet while there was slight increase in the ozone outlet concentration with the enhancement of membrane length. Furthermore, the main resistance for ozone mass transfer was liquid phase and it was indicated that the gas phase and membrane subdomain resistance is lower for ozone mass transfer due to higher ozone diffusion coefficient in the gas phase. [ABSTRACT FROM AUTHOR]

When separating enantiomers on chiral crystals of achiral substances, it was found that a relatively high enantioselectivity is accompanied by a low efficiency of columns. Therefore, work was carried out to evaluate the influence of the coefficients of the van Deemter equation on the broadening of the peaks of camphor enantiomers on a chiral stationary phase based on enantimorphic α-NiSO4⋅6H2O crystals (retgersite). From an experimental van Deemter curve, the contributions of vortex and longitudinal diffusion, as well as the resistance to mass transfer, were calculated in the value of an introduced magnitude equivalent to the theoretical plate (h). It is shown that the right branch of the curve for enantiomers of camphor differs. It is established that this difference is caused by different values of resistance to mass transfer in the stationary phase Cs caused by the difference in diffusion coefficients in the pore space. [ABSTRACT FROM AUTHOR]

The diffusion coefficient of gases in a wide range of chemical processes is of great importance. Semi-empirical models for diffusion coefficient prediction are useful due to their relatively lower cost compared to laboratory methods. In this study, to facilitate the equations and accelerate the calculations, appropriate models have been presented using existing parameters such as molecular weight and critical properties to determine the binary diffusion coefficient of gases. The calculations have been performed using a particle swarm optimization (PSO) algorithm. This model has been used to obtain the diffusion coefficient of 84 gas dual systems at P=101.325 kPa and variable temperature (373.15-673.15 K). Also, during the validation phase, the suggested model attained the most accurate prediction with R² = 0.9989. This model is capable to predict the diffusion coefficient of gases with a mean relative error percentage of 2.57% and mean square error percentage of 0.15% compared to actual data. These results are significantly better than those obtained from other models. [ABSTRACT FROM AUTHOR]

As is known, the theory of diffusion in liquids has not yet been sufficiently developed, which makes it difficult to accurately calculate the coefficients of this process. Obtaining reliable mass transfer characteristics necessary for the design of extraction apparatuses is impossible without a preliminary evaluation of diffusion processes. Therefore, the study of mass transfer characteristics and the determination of diffusion coefficients play an important role in the determination of the mass transfer rate and in the design of extractors. In this regard, the determination of diffusion coefficients, which plays an important role in determining the mass transfer rate, is very relevant. With an accurate explanation of the mass transfer mechanism, diffusion coefficients can be calculated. The kinematic theory has proven to be extremely useful for calculating diffusion coefficients and other characteristics. The purpose of this study is to select methods for determining the diffusion coefficients in extractors with a mechanical agitator in wastewater treatment for water reuse. Wastewater samples containing butyl glycol acetylacetone and phenylisopropanol are used when studying the liquid extraction process. Isopropyl ether is used as an extractant. The study proposes numerous formulas for determining the diffusion coefficients, substantiates the choice of an equation for their determination, and calculates the coefficients of turbulent and effective diffusion, the degree of entrainment of particles by a pulsating medium, and the average velocity depending on the dynamic flow velocity and the volume fraction of the dispersed phase. It is established that the average circulation velocity is related to the drop velocity. Considering that it is necessary to have the concentration gradient along the flow from the inlet to the outlet of the apparatus, which must continuously change for the implementation of mass transfer processes, the intensive mixing also causes longitudinal mixing that reduces the longitudinal concentration gradient and worsens separation. The characteristics of the mass transfer process necessary for the design of extraction apparatuses for water reuse are studied. [ABSTRACT FROM AUTHOR]

Understanding the diffusion process of hydrophobic molecules through natural phospholipid (half-)membranes is of great importance, as it occurs within organisms and therefore, offers potential applications in encapsulation in natural carriers. One illustrative case involves oleosomes, lipid droplets found in eukaryotic cells, which possess a phospholipid-protein monolayer facilitating the incorporation of lipophilic compounds into their inner core. Our approach entailed the development of a mathematical model to elucidate the diffusion of a lipophilic molecule, specifically curcumin, into oleosomes. In this model, oleosomes were represented as multilayer spheres with position-dependent diffusion and partition coefficients. We derived the model parameters through experimental techniques and stablished empirical equations. The model showed that 80% of curcumin reached the oil core while 20% stayed within the membrane (phospholipid heads and tails). Beyond its application to oleosomes and curcumin, the model presented herein holds broad application for describing the encapsulation of various lipophilic molecules into carriers featuring phospholipid (half-)membranes. [Display omitted] • A dynamic 1D model is used to study the mass transfer of curcumin in oleosomes. • The model is experimentally validated at equilibrium. • 80% of curcumin penetrated the oleosome core, while 20% at the interface. • The oil core contained the highest encapsulated mass. [ABSTRACT FROM AUTHOR]

The microstructural stability and coarsening kinetics of γ′ precipitates in a nickel-based single crystal superalloy (Ni-SX) were thoroughly investigated under various thermal exposure treatments. The evolutions of characteristic parameters including γ′ size, morphology, area fraction, and γ channel width were documented. Coarsening rate constants and particle size distributions (PSDs) were calculated and recorded based on measured precipitate sizes at temperatures ranging from 800 ℃ to 1100 ℃ and durations ranging from 100 h to 1010 h. The experimentally derived rate constants were compared with the calculated theoretical values from two mainstream models: matrix-controlled diffusion (LSW model) and interface-controlled diffusion (TIDC model). Notably, transitional coarsening kinetics of γ′ precipitates from the LSW model to the TIDC model was observed at high temperatures over time. Through a comprehensive consideration of key coarsening kinetics parameters such as elemental diffusivity, trans-interface diffusion coefficient, coarsening rate constant, γ/γ′ interfacial area, and solute mass transfer, the transformation of the coarsening kinetics from matrix-controlled diffusion to interface-controlled diffusion was quantitatively discussed. The emergence of the TIDC model as the dominant mechanism was attributed to relatively smaller solute mass transfer through the interface. Moreover, the degradation of γ/γ′ interfacial energy and interfacial area, coupled with the increase in solute diffusion coefficient in the matrix, facilitated the trans-interface diffusion to act as a limiting factor throughout the coarsening process. [Display omitted] • The microstructural stability and coarsening kinetics of γ′ are thoroughly investigated and documented. • The particle size distributions of γ′ evolve from a single LSW model to a joint control cooperating with the TIDC model. • Relatively smaller solute mass transfer through the interface is the reason for the TIDC model emerging its head. [ABSTRACT FROM AUTHOR]

Thin-film composite reverse osmosis (RO) membranes have dominated desalination technology for decades, with the solution diffusion model (SDM) serving as the gold standard for interpreting mass transfer phenomena since its inception. However, debates still persist regarding the effect of charge on separation performance, owing to the SDM's inability to explore membrane charge. In this study, polyethyleneimine (PEI) was utilized to modify the surface of a commercial seawater desalination membrane (SW30, Dupont Company), imparting regulatable charge properties based on the solution pH. The separation performance of the modified RO membrane was experimentally validated under varying NaCl feed salinities. Specifically, the Donnan-steric pore model with dielectric exclusion (DSPM-DE), known as a charge-responsive model, was employed and juxtaposed with SDM to authenticate the experimental findings. The results indicated that the dielectric effect primarily governed ion distribution (Na+ and Cl−) within the membrane, followed by the steric effect, and ultimately, the Donnan effect. Consequently, DSPM-DE aligned well with the observed salt rejection only when the membrane was strongly charged (that is, under acidic or alkaline conditions), but performed poorly in the neutral state. This observation, rarely revealed in previous research, stems from conventional desalination membranes being negatively charged in most natural water environments. Conversely, the SDM aligned well with the experimental data because it solely considered the solutes' solubility parameters and diffusion coefficient, independently of the surface charge of the desalination membranes. Given the extensive research on surface modification, our study demonstrates the limited influence of charge effects on the selective enhancement of RO membranes. [Display omitted] • Polyethyleneimine (PEI) is used to modify the surface of the SW30 membrane. • The SW30-PEI membrane shows a regulatability of the surface charge with solution pH. • SDM aligns well with the experimental data, while DSPM-DE exhibits apparent deviations. • DSPM-DE aligns well with the observed salt rejection only when the membrane is strongly charged. • The interaction between charged solutes and membrane surface minimally impacts the mass transfer. [ABSTRACT FROM AUTHOR]

Numerous experiments have demonstrated that the porous support layer limits the diffusion behavior and leads to a reduction in permeability of thin film composite (TFC) membranes. Although this geometric restriction has been described using empirical models, it is still rough and unable to describe the effect of support layer on selectivity, an accurate theoretical model to quantitatively calculate the permeation performance of TFC membranes is lacking. In this study, an equivalent theoretical model is proposed to describe the mass transfer process of TFC membrane, by properly handling the tangential diffusion at the interface between the selective layer and the support layer. Both the computational fluid dynamics (CFD) simulations performed in this work and experimental data in some literatures prove the validity of the equivalent model. Analysis of the theoretical model and CFD simulation results show that: Restriction factor Ψ is independent of the solubility coefficients but dependent of the diffusion coefficients and support layers, which would alter the TFC membrane selectivity to the diffusing species with different diffusion coefficients. Tuning the structural parameters of the support layer is an effective way to bring the performance of TFC membranes closer to that of ideal free-standing membranes. Among them, High surface porosity of the support layer is the most critical factor affecting TFC membrane performance, both for permeability and selectivity. • It reveals the selective attenuation mechanism of TFC membranes. • It provides a theoretical calculation method for the separation performance of TFC membranes. • It provides guidance for the experimental preparation of TFC membranes. [ABSTRACT FROM AUTHOR]

The kinetics of supercritical extraction from L. rivularis stalks using CO 2 were studied in terms of temperature (40−60ºC), pressure (18–30 MPa), specific CO 2 consumption (30−50 kg/kg d.s.), and particle diameter (0.5−1.1 mm). The extraction yield was found to range from 17.30 to 27.23 g/kg d.s. The highest extraction yield was obtained at 40°C, 30 MPa, 30 kg CO 2 /kg d.s., and mean particle size of 0.5 mm. The yield increased with pressure and decreased with temperature and particle size (p ≤0.05). The diffusion model based on Fick's 2nd law adequately described the cumulative extraction curves, using the effective diffusion coefficient (D e) as the adjusted parameter, which ranged between 3.50 and 19.26×10−12 m2/s. The Biot number was estimated, indicating a prevalence of internal control to mass transfer resistance. Additionally, the "apparent solubility" was obtained from the initial slope of the cumulative extraction curves. The extraction yield correlated positively with apparent solubility (p ≤0.05) and D e coefficient (p ≤0.05). [Display omitted] • Effect of supercritical conditions on yield and extraction rate was studied. • Yield and apparent solubility increased with pressure and decreased with temperature. • Extraction yield and apparent solubility correlated positively. • Diffusion model adequately described the cumulative extraction curves. • Extraction yield and effective diffusion coefficient correlated positively. [ABSTRACT FROM AUTHOR]

A novel, simple numerical method to determine the pore and surface diffusivities in adsorbents from a single experimental concentration decay curve obtained using the batch adsorption technique was investigated in this study. The pore and surface diffusion coefficients were determined based on the conventional parallel diffusion model in its dimensionless form using a theoretical model correlation. The model assumed that the film mass transfer resistance was negligible, i.e., the condition with a large Biot number, from the single concentration decay curve. The procedure for determining the kinetic parameters was investigated, and the effectiveness of the proposed simple method was validated by comparing the parameters with those reported previously. The single decay curve of p-nitrophenol, obtained by the batch adsorption system using granular activated carbon as an adsorbent, was used for validation. The diffusivities determined by the simple method corresponded fairly well with the diffusivities reported previously. [ABSTRACT FROM AUTHOR]

Modeling and simulation of batch adsorption of the organic dye methylene blue (MB) by modified metal‐organic framework‐5 (MOF‐5) were investigated. The reported data on the adsorption of MB dye onto Wells‐Dawson acids (H6P2W18O62)‐immobilized MOF‐5 were employed. The film‐pore diffusion model was developed based on external mass transfer coefficient and pore diffusion coefficient that govern the mass transfer process in batch organic dye adsorption. Applying the estimated parameters, the MB adsorption by using modified MOF‐5 was examined to evaluate the effects of MOF‐5 modification, initial dye concentration, temperature, and the dosage of adsorbent. The adsorption capacity of modified MOF‐5 (H6P2W18O62/MOF‐5) was higher than pure MOF‐5. Besides, a lower initial MB dye concentration, higher temperature, and lower adsorbent dosage resulted in higher MB dye adsorption capacity. [ABSTRACT FROM AUTHOR]

Summary: The aim of this work was to study the rule of the different concentrations on marination kinetics and mass transfer of lactic acid‐marinated pork (longissimus dorsi muscle) specimens. The marinades of lactic acid concentrations at 0.5%, 1.0%, 1.5%, 2.0%, and 2.5% (w/w) and the marination process was performed at 1, 2, 3, 4, and 5 h, respectively. The water holding capacity (WHC), water and lactic acid content of the pork specimens were measured. Mass transfer kinetic curves were fitted. Kinetic parameter values for changes in total pork mass, the content of water and lactic acid, and effective diffusion coefficient were calculated. The obtained results indicated that the values of kinetic parameters for the changes in total mass, the content of water and lactic acid, and WHC were all increased with lactic acid concentration and marination time raised. The prediction model of water and lactic acid mass transfer in pork had a good linear correlation with marination time. The apparent diffusion coefficient value was the largest and the diffusion rate was the fastest when the mass fraction of lactic acid in the marinade was 1.5%. This research could provide effective parameters for improving the efficiency and uniformly quality of lactic acid marinated meat products. [ABSTRACT FROM AUTHOR]

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Due to the increasing use of biopolymers in food formulations, introducing new hydrocolloid sources has become particularly important. Numerous researches have been done on aqueous extraction or new extraction methods such as extraction with microwave pretreatment, but in most cases, the engineering part of these processes has been neglected. In this study, the main purpose was to investigate the mass transfer in the process of microwave -assisted extraction of galactomannan from two plant seeds using a new method known as inverse numerical method. To achieve this goal, the concentration of galactomannan extracted from both plant seeds was obtained against time and the experimental data and the data predicted by the software (based on the simulation) were compared which indicated proper convergence between these data. Effective parameters in mass transfer including dispersion coefficient (E), diffusion coefficient (D) and total mass transfer coefficient (kc) were in the range of 1.12 – 1.63×10-12, 2.30 – 3.28×10-8 and 1.54 – 2.25×10-7 m²/s for fenugreek galactomannan and 1.27 – 1.76×10-12, 2.55 – 3.52×10-8 and 1.85 – 2.30×10-7 m²/s for Gleditsia caspica galactomannan. The difference between the values obtained for the two galactomannans could be attributed to the seed type, hardness or softness of the seed wall and characteristics of the target component. According to the obtained results, inverse numerical method could be introduced as an acceptable and effective method for modeling of the extraction process of both galactomannans. [ABSTRACT FROM AUTHOR]

Extraction of hydrocolloids from plant seeds is important due to the increased consumption of these compounds in the formulation of food products. Ultrasound -assisted extraction has become very popular due to its many advantages, one of the most important of which is to increase the extraction efficiency of the biopolymers. The aim of this research was to use inverse numerical method to estimate the effective parameters in mass transfer related to the ultrasound -assisted extraction of galactomannan form two plant seeds including fenugreek and Gleditsia caspica. To achieve this goal, the concentration of galactomannan extracted from both plant seeds was obtained against time and the experimental data and the data predicted by the software (based on the simulation) were compared which had proper convergence. Effective parameters in mass transfer including dispersion coefficient (E), diffusion coefficient (D) and total mass transfer coefficient (kc) were in the range of 1.21 – 1.52×10-12, 2.39 – 3.05×10-8 and 1.18 – 1.85×10-7 m²/s for fenugreek galactomannan and 1.31 – 1.54×10-12, 2.63 – 3.11×10-8 and 1.46 – 1.95×10-7 m²/s for Gleditsia caspica galactomannan. The difference between the values obtained for the two galactomannans could be attributed to the seed type, hardness or softness of the seed wall and characteristics of the target component. According to the obtained results, inverse numerical method could be introduced as an acceptable and effective method for modeling of the extraction process of both galactomannans. [ABSTRACT FROM AUTHOR]

The processes of mass transfer in the metal electrodeposition on a rotating disk electrode from the solution containing three sorts of ions (electroactive metal cation and indifferent electrolyte containing inactive cation and anion) are studied theoretically. The Nernst–Planck equations in the approximation of the solution electroneutrality reduced to a dimensionless form, which takes into account the elecrodiffusion and convective transfer of all types of ions, are used as the mathematical model. The numerical solution of the mathematical model is carried out by the finite volume method using a non-uniform grid. As a result of the numerical solution, the distributions of potential and ion concentrations are obtained with taking into account the interaction between the electric and hydrodynamic fields in the solutions with various concentrations of supporting electrolyte at various diffusion coefficients of ions of all sorts. The dependences of the limiting current of metal electrodeposition on the concentration of supporting electrolyte are obtained. When calculating the limiting current density in the absence of convection, the thickness of the Nernst diffusion layer is calculated taking into account the effective diffusion coefficient of the solution with three sorts of ions at various concentrations of supporting electrolyte. Using several examples with various ratios between the diffusion coefficients of the anion and inactive cation of the electrolyte, the error in the limiting current calculated using the Nernst diffusion layer approximation, as compared with the limiting current obtained taking into account the convective transport of ions, is estimated. [ABSTRACT FROM AUTHOR]

The adsorption properties of Aloe vera (Aloe barbadensis Miller) for the uptake of Methylene Blue (MB) from water were investigated after pre-treating the material with water–ethanol solutions at different ethanol concentrations: 0% v/v (AV0), 25% v/v (AV25), and 50% v/v (AV50). The pre-treated materials were characterized as follows: the pHZC was evaluated to be 6, 5.7, and 7.2 for AV0, AV25, and AV50, respectively; from BET-BJH analysis the mesoporous nature of the material and an increase from 108.2 (AV0) to 331.7 (AV50) m2/kg of its solid surface area was observed; TG analysis revealed a significat increase in volatile compounds from the untreated (5.4%) to the treated materials (8.9%, 10.3%, and 11.3% for AV0, AV25, and AV50, respectively). Adsorption batch tests were then performed to investigate the equilibrium, the kinetics, and the thermodynamics of the process. Results suggested that the Langmuir model was in agreement with the experimental results, and values for qmax of 199 mg/g, 311 mg/g, and 346 mg/g were calculated for AV0, AV25, and AV50, respectively. The kinetic results were used to develop a mathematical model to estimate the effective diffusion coefficient for each type of Aloe adopted. Effective diffusion coefficients of 5.43·10−7 cm2/min, 3.89·10−7 cm2/min, and 5.78·10−7 cm2/min were calculated for AV0, AV25, and AV50, respectively. It was found that pre-treatment, on the one hand, enhances the adsorption capacity of the material and on the other, reduces its affinity toward MB uptake. [ABSTRACT FROM AUTHOR]

Based on experimental pure component data for the characterization of the isostructural imidazolate framework Potsdam (IFP) series reported in Part I, a model for the simulation of non‐isothermal dynamic adsorption of CO2/CH4‐mixtures in fixed‐bed columns is presented in this Part II. The robustness of the model is examined and validated, by comparison to experimental breakthrough data at different process conditions, such as varying concentration, temperature, and pressure. Thereby, different predictive methods for the estimation of adsorption equilibria of mixtures are compared (RAST, IAST, ML). The results show that ideal behaviour can be assumed with good accuracy for the system under consideration, except for IFP‐2, which shows significant deviations at increased pressures and temperatures. A detailed kinetic analysis reveals that mass transfer is significantly influenced by micropore diffusion. Thus, only for IFP‐1 the dynamic separation of CO2 and CH4 is equilibrium‐driven, while for the remaining IFPs the kinetic regime dominates the process, which in some cases increases the separation efficiency (IFP‐2 to ‐7) but can also inhibit it (IFP‐8). The determined intracrystalline diffusion coefficients show very good agreement with values for metal organic framework (MOF) compounds of similar structure reported in the literature. [ABSTRACT FROM AUTHOR]

The functional implications of substances, such as retardation and relaxation, can be studied for magnetized diffusion coefficient based on the relative increase throughout magnetization is a well-known realization. In this context, we have explored the Oldroyd-B hybrid nanofluid flowing through a pored oscillating plate along with an inclined applied magnetics effect. The slipping effect and sinusoidal heating conditions are also supposed to be under consideration. An innovative and current classification of fractional derivatives, i.e., Prabhakar fractional derivative and Laplace transform, are implemented for the result of transformed leading equations. The graphical representation is also described to understand the physical implementation of all effecting parameters. In order to justify and physically examine the considered problem, some limiting cases, the rate of heat and mass transfer, and friction factors are also analyzed. As a result, we have concluded that the thermal enhancement can be improved more progressively with the interaction of silver-water-based nanofluid suspension compared to copper-nanoparticles mixed nanofluid. Furthermore, It has examined the impact of both parameters, i.e., time relaxation Ω 1 and retardation Ω 2 is opposite of the momentum field. [ABSTRACT FROM AUTHOR]

In 1871, Josef Stefan established the theoretical framework which allowed the design of his diffusion column. It consisted of a volatile liquid A overlaid with gases A and B. A steady gas B sweep flowed at the top, maintaining the concentration of gas A close to zero at that location. Binary gas diffusion coefficients, whose magnitudes are crucial in many mass transfer operations, were estimated with this device. This line of work was continued uninterruptedly by many research groups around the world for over eight decades. However, in the 1950s inaccuracies in the diffusivity estimates were detected mainly due to column end effects such as gas turbulence/eddy formation resulting from the sweeping stream as well as interfacial curvature. The latter affects the transport area and the path length of gas A to the top. Studies departing from the traditional Stefan column role of binary diffusivity estimation were promptly initiated to attain a better understanding of transport phenomena within the column. These efforts, which endure to this day, applied fundamental chemical engineering principles to determine the source of the diffusivity inaccuracies, the dimensionality of gas transport, the importance of interfacial curvature and nonisothermal column operation, and how liquid-phase events such as mixing affect device performance. These research initiatives have led to an in-depth description of transport phenomena within the Stefan column. Historical references are thoroughly analyzed, chemical engineering contributions to this field are highlighted, and perspectives for future theoretical and experimental work along these lines are presented. [ABSTRACT FROM AUTHOR]

Achieving the rate and the amount of mass transfer is of paramount importance in selecting optimum conditions for drying and affects the development of the quality of drying. Note that, to obtain the amount of mass transfer, the conditions of mass transfer such as temperature, pressure, geometry, and diffusion coefficient should be completely determined. In this research, an experiment is conducted in atmospheric conditions and then the amount of mass flow in a spherical body is measured. Utilizing the Newman equation and the experimental results, the diffusion coefficient is found to be in the range of 10-11 m2/s. Additionally, the experimental data reveal the linear and exponential variation of diffusion coefficient with a constant coefficient of 1306.8 and exponent of 2.0883 which is against size and time. [ABSTRACT FROM AUTHOR]