External Mass Transfer Coefficient Research Articles

Load-dependent surface diffusion model for analyzing the kinetics of protein adsorption onto mesoporous materials

The adsorption of cytochrome c in water onto organic and carbon xerogels with narrow pore size distributions has been studied by carrying out transient and equilibrium batch adsorption experiments. It was found that equilibrium adsorption exhibits a quasi-Langmuirian behavior (a g coefficient in the Redlich-Peterson isotherms of over 0.95) involving the formation of a monolayer of cyt c with a depth of ∼4nm on the surface of all xerogels for a packing density of the protein inside the pores of 0.29gcm–3. A load-dependent surface diffusion model (LDSDM) has been developed and numerically solved to fit the experimental kinetic adsorption curves. The results of the LDSDM show better fittings than the standard homogeneous surface diffusion model. The value of the external mass transfer coefficient obtained by numerical optimization confirms that the process is controlled by the intraparticle surface diffusion of cyt c. The surface diffusion coefficients decrease with increasing protein load down to zero for the maximum possible load. The decrease is steeper in the case of the xerogels with the smallest average pore diameter (∼15nm), the limit at which the zero-load diffusion coefficient of cyt c also begins to be negatively affected by interactions with the opposite wall of the pore.

Improvement of Mass Transfer by Freezing Pre-treatment and Ultrasound Application on the Convective Drying of Beetroot (Beta vulgaris L.)

The effects of freezing pre-treatment and ultrasound application during drying on microstructure, drying curves, and bioactive compounds of beetroot have been evaluated. Raw and previously frozen (at − 20 °C) beetroots were convectively dried (40 °C and 1 m/s) with and without ultrasound application using two acoustic densities (16.4 and 26.7 kW/m3), and a diffusional model was proposed to simulate the drying curves. Freezing pre-treatment and ultrasound application caused significant disruptions in the beetroot microstructure and reduced the drying time, enhancing the mass transfer. The external mass transfer coefficient significantly (p < 0.05) increased by 28–49% when ultrasound was applied; moreover, the effective diffusion coefficient significantly (p < 0.05) increased by 60–73% and 204–211%, respectively, due to the ultrasound application on the drying of raw and pre-frozen samples. Freezing caused significant (p < 0.05) increases in betalain and total polyphenol contents and antioxidant activity compared with the raw sample (16–57%), probably due to the release of free forms from the food matrix; meanwhile, drying had the opposite effect (8–54% decrease). Significantly (p < 0.05) higher decreases (32–81%) in bioactive compounds and antioxidant activity were observed when drying was assisted by ultrasound compared with dying without ultrasound. Therefore, freezing pre-treatment and ultrasound application enhanced mass transfer during drying. However, significant changes in quality parameters of the final product were observed.

Determination of external mass transfer coefficients in dynamic sorption (DVS) measurements

ABSTRACTA sorption balance is an instrument used to measure vapor uptake in a sample at controlled temperature and relative humidity. It is most commonly used to determine equilibrium values (sorption isotherms), but is also used for kinetic measurements of transport coefficients. Such measurements can be affected by the external mass transfer resistance in the gas phase around the sample. This paper presents a method to determine the external mass transfer coefficient for a given flow geometry using a water saturated sample, including corrections for temperature changes from evaporative cooling, which is found to have considerable effect on the calculated constant.

Mass transfer characteristics, rheological behavior and fractal dimension of anammox granules: The roles of upflow velocity and temperature

In this study, the mass transfer, rheological behavior and fractal dimension of anaerobic ammonium oxidation (anammox) granules in upflow anaerobic sludge blanket reactors at various temperatures (8.5–34.5°C) and upflow velocities (0.06, 0.18mh−1) were investigated. The results demonstrated that a lower temperature increased the external mass transfer coefficient and apparent viscosity and impaired the performance of anammox granules. The external mass transfer coefficient was decreased, but efficient nitrogen removal of up to 96% was achieved under high upflow velocity, which also decreased the apparent viscosity. Furthermore, a fractal dimension of up to 2.93 achieved at low temperature was higher than the previously reported values for mesophilic anammox granules. A higher upflow velocity was associated with the lower fractal dimension. Because of the disturbance in granule flaking, the effectiveness factor was less suitable than the external mass transfer coefficient for characterization of mass transfer resistance.

Novel structured catalytic systems—Cartridges on the base of fibrous catalysts

Manuscript is dedicated to the cartridges on the base of micro-fibrous catalysts. Under the strong influence of external diffusion limitations, the structured cartridges with glass-fiber catalysts (GFC) demonstrate the performance at least not worse than that of the most efficient types of conventional catalysts in volumetric apparent activity, significantly exceeding them in apparent reaction rate per unit mass of the active component or per unit pressure drop, making the GFCs one of the most efficient shapes among all existing catalytic structures. The newly proposed lemniscate-shaped GFCs demonstrate the best performance among all studied systems. The intrinsic kinetics, internal and external mass transfer intensity were studied using the model reaction of toluene deep oxidation in air at Pt-containing GFC. The elaborated criterial equation provides calculation of the external mass transfer coefficient in such catalysts with acceptable accuracy. Mass transfer enhancement in GFC cartridges is explained by flexibility of fibrous supports, resulting in the change of their shape and increase of their effective external area under the influence of the moving reaction fluid. Such systems look promising for application in fast catalytic reactions, occurring under strong influence of diffusion limitations in gas, liquid and multiphase media.

Two-structured solid particle model for predicting and analyzing supercritical extraction performance

Solid extraction process, using the supercritical fluid, is a modern science and technology, which has come in vogue regarding its considerable advantages. In the present article, a new and comprehensive model is presented for predicting the performance and separation yield of the supercritical extraction process. The base of process modeling is partial differential mass balances. In the proposed model, the solid particles are considered twofold: (a) particles with intact structure, (b) particles with destructed structure. A distinct mass transfer coefficient has been used for extraction of each part of solid particles to express different extraction regimes and to evaluate the process accurately (internal mass transfer coefficient was used for the intact-structure particles and external mass transfer coefficient was employed for the destructed-structure particles). In order to evaluate and validate the proposed model, the obtained results from simulations were compared with two series of available experimental data for extraction of chamomile extract with supercritical carbon dioxide, which had an excellent agreement. This is indicative of high potentiality of the model in predicting the extraction process, precisely. In the following, the effect of major parameters on supercritical extraction process, like pressure, temperature, supercritical fluid flow rate, and the size of solid particles was evaluated. The model can be used as a superb starting point for scientific and experimental applications.

Modeling hydrogen diffusion in hybrid activated carbon-MIL-101(Cr) considering temperature variations and surface loading changes

MIL-101(Cr) and activated carbon (AC) doped MIL-101(Cr) materials were synthesized under mild conditions, avoiding the use of hydrofluoric acid, and characterized by X-Ray Diffraction (XRD), Scanning Electron Microscopy (SEM) and physisorption. It was shown that the AC doping induced enhancements of the specific surface area and increase in the pore volume of the adsorbent. Hydrogen adsorption isotherms and kinetics were measured at 77 K up to 50 bar by using a volumetric method. A hydrogen uptake of 9.3 wt.% was measured for the hybrid material, which was significantly higher than that for pristine MIL-101(Cr) which reached an uptake of 6.2 wt.% under the same conditions of temperature and pressure. Effective diffusion coefficients were besides attempted to be extracted from experimental kinetic curves, by using the Linear Driving Force (LDF) model in a first approach. However, this model failed to describe correctly the experimental kinetic data as it does not explicitly consider the external mass transfer resistance, neither the temperature nor the surface loading effects on the intra-crystalline diffusion process. To overcome these limitations, a more detailed model was proposed, based on the evaluation of both an external mass transfer coefficient and of an internal surface diffusivity in the adsorbed phase that accounts for the effects of temperature and adsorbent surface coverage. This model was proved to predict well the hydrogen adsorption rates in both the MOF and hybrid AC-MOF material at 77 K, in the pressure range up to 20 bar.

Amides as a model system of low molar mass algal organic matter. Influence on the adsorption of p-nitrophenol on activated carbon

In this study, the adsorption equilibrium and diffusivity parameters of p-nitrophenol were estimated for water containing different concentrations of secondary amides. Commercial powdered activated carbon was used as an adsorbent. The external mass transfer coefficient (kf), the surface diffusion coefficient (Ds) and the standard free Gibbs energy were calculated for p-nitrophenol in the presence of different secondary amide concentrations. The analysis established that there are correlations between structural parameters of amides, on the one hand, and diffusion and thermodynamic parameters for p-nitrophenol adsorption process, on the other. It was noticed that voluminous hydrophobic amides decreased the adsorption capacity of p-nitrophenol on activated carbon. On the basis of the results obtained for external mass transfer coefficients, it is assumed that amides cause the reduction of adsorption capacity of p-nitrophenol onto activated carbon by concentrating at the solid/liquid interface.

Removal of phenol from wastewater by carbon sorbents at mining enterprises and coke plants

The removal of carbon from wastewater by means of carbon adsorbents is experimentally studied. The kinetics of phenol adsorption from aqueous solutions simulating its content in industrial wastewater at mining enterprises and coke plants is investigated. The kinetic curves of phenol adsorption on AG-OV-1 and ABG active carbon differ from the classic form. The time to attain equilibrium in the phenol–water–sorbent system varies in the range 30–60 min. The adsorption process is found to be limited by external diffusion. The external diffusion coefficients are calculated. On the basis of the external mass-transfer coefficients, we may expect high phenol extraction from wastewater at moderate filtration rates through the dense immobile sorbent layer.

Modeling and experimental study of vanadium adsorption by iron-nanoparticle-impregnated activated carbon

Iron-nanoparticle-impregnated activated carbon (IrAC) nanocomposite was synthesized as a new vanadium adsorbent. The vanadium adsorption rate for commercial activated carbon (AC) and IrAC nanocomposite was investigated experimentally in a batch system. The vanadium adsorption rate for AC and IrAC was then modeled using a film–pore–surface diffusion model. The resulting equations were solved numerically by the line method using MATLAB. The main parameters such as the external (film) mass transfer coefficient, pore diffusion coefficient, and surface diffusion coefficient were determined by solving the model equations for different temperatures and agitation rates. The results show that external mass transfer and pore diffusion are the important factors for vanadium adsorption using AC. However, external mass transfer and pore and surface diffusion are the important steps for vanadium adsorption on IrAC.

Vanadium separation with activated carbon and iron/activated carbon nanocomposites in fixed bed column: experimental and modelling study

In this work, iron nanoparticles were impregnated onto a commercial activated carbon surface to produce a novel adsorbent called iron-activated carbon nanocomposite (I-AC). Commercial activated carbon (CAC) and I-AC were used for vanadium separation in a fixed-bed column. The effects of various operating parameters such as inlet vanadium ion concentration, adsorbent dose and volumetric flow rate on vanadium separation performance of CAC were investigated. The performance of both adsorbents was compared in three adsorption/desorption cycles. The experimental breakthrough curves of vanadium ions in the fixed-bed column were modeled using the film-pore-surface diffusion model (FPSDM). The four mass transfer parameters characterizing this model, namely the external mass-transfer coefficient (k f ), pore and surface diffusion coefficients (D p and D s ), and axial dispersion coefficient (D L ) were evaluated through the model. Modelling and experimental results showed that the I-AC nanocomposite has a better performance for vanadium separation in comparison to AC. Sensitivity analysis on the FPSDM showed that the pore and surface diffusion, external mass transfer and axial dispersion play a significant role in vanadium separation using the I-AC. On the other hand, surface diffusion resulted to be relatively less important when CAC was used.

Equilibrium and kinetics of adsorption of ruthenium on activated charcoal from nitric acid solutions

Equilibrium and kinetics of adsorption of ruthenium on activated charcoal were investigated experimentally using batch method under different conditions. The Freundlich isotherm model was used to describe the partitioning behaviour of ruthenium between the solution and adsorbent phase. A pore diffusion model, coupled with Freundlich isotherm equation was used to interpret the experimentally obtained adsorption kinetic curves at different concentrations of ruthenium. The model was found to fit with the experimental data fairly well. The effective diffusivity and external mass transfer coefficient were estimated to be in the range 10−8cm2s−1 to 10−4cms−1 respectively.

Adsorption rate of Reactive Black 5 on chitosan based materials: geometry and swelling effects

The overall adsorption rate of Reactive Black 5 dye (RB5) on chitosan based materials was elucidated using diffusional models. Fundamental aspects, such as, geometry of the adsorbents and swelling effects were considered. Chitosan based materials (powder and film) were prepared from shrimp wastes and characterized regarding to the fundamental features for adsorption. Experimental decay curves were obtained under different conditions of stirring rate and initial dye concentration. The data were modeled according to the external mass transfer and diffusional models. The kL (external mass transfer coefficient), Dep (effective pore diffusion coefficient) and Ds (surface diffusion coefficient) values were estimated. For both adsorbents, it was found that the surface diffusion was the intraparticle diffusion mechanism governing the adsorption rate of RB5, since its contribution was higher than 92 % regardless the position and time. The Ds values ranged from 2.85 × 10−11 to 5.78 × 10−11 for chitosan powder and from 4.15 × 10−11 to 12.12 × 10−11 cm2 s−1 for chitosan films. The RB5 adsorption was faster when chitosan powder was used, mainly at higher stirring rates and initial dye concentrations. The swelling effect was most pronounced for the chitosan films, where, provided an increase of about 65 times in the Ds value.

Dynamic characterization of external and internal mass transport in heterotrophic biofilms from microsensors measurements

Knowledge of mass transport mechanisms in biofilm-based technologies such as biofilters is essential to improve bioreactors performance by preventing mass transport limitation. External and internal mass transport in biofilms was characterized in heterotrophic biofilms grown on a flat plate bioreactor. Mass transport resistance through the liquid-biofilm interphase and diffusion within biofilms were quantified by in situ measurements using microsensors with a high spatial resolution (<50 μm). Experimental conditions were selected using a mathematical procedure based on the Fisher Information Matrix to increase the reliability of experimental data and minimize confidence intervals of estimated mass transport coefficients. The sensitivity of external and internal mass transport resistances to flow conditions within the range of typical fluid velocities over biofilms (Reynolds numbers between 0.5 and 7) was assessed. Estimated external mass transfer coefficients at different liquid phase flow velocities showed discrepancies with studies considering laminar conditions in the diffusive boundary layer near the liquid-biofilm interphase. The correlation of effective diffusivity with flow velocities showed that the heterogeneous structure of biofilms defines the transport mechanisms inside biofilms. Internal mass transport was driven by diffusion through cell clusters and aggregates at Re below 2.8. Conversely, mass transport was driven by advection within pores, voids and water channels at Re above 5.6. Between both flow velocities, mass transport occurred by a combination of advection and diffusion. Effective diffusivities estimated at different biofilm densities showed a linear increase of mass transport resistance due to a porosity decrease up to biofilm densities of 50 g VSS·L−1. Mass transport was strongly limited at higher biofilm densities. Internal mass transport results were used to propose an empirical correlation to assess the effective diffusivity within biofilms considering the influence of hydrodynamics and biofilm density.

Isotherms and Kinetics of Water Vapor Sorption/Desorption for Surface Films of Polyion-Surfactant Ion Complex Salts.

Thin films of "complex salts" (CS = ionic surfactants with polymeric counterions) have recently been shown to respond to humidity changes in ambient air by changing their liquid crystalline structure. We here report isotherms and kinetics of water sorption/desorption for ∼10-100 μm films of alkyltrimethylammonium polyacrylate CS, measured in a dynamic gravimetric vapor sorption instrument over a 0-95% relative humidity (RH) range. The sorption per ion pair was similar to that observed for common ionomers. A kinetic model for the water exchange is presented, assuming that the "external" transport between the vapor reservoir and the film surface is rate-determining. The model predicts that the water content, after a small stepwise change of the reservoir RH, should vary exponentially with time, with a time constant proportional to both the slope of the sorption isotherm and the film thickness. These predictions were confirmed for our films over large RH ranges, and the external mass transfer coefficient in our setup was calculated from the experimental data. Expressions derived for the Biot number (ratio of characteristic times for internal and external water transport) for the considered limiting case strongly indicate that external water transport should quite generally affect, or even dominate, the measured kinetics for similarly thin hydrated films.

THE USER OF ADSORPTION FOR PURIFICATION OF WASTEWATER FROM THE PRODUCTION OF PHENOL-FORMALDEHYDE RESINS

To increase ecological safety of phenol-formaldehyde resins production of the novolac type, the adsorption technology for purification of wastewater containing mainly phenol and formaldehyde was developed. The research of organic substances adsorption (formaldehyde, phenol) from individual aqueous solutions and their mixtures on carbon sorbents grades AG-3, AG-OV-1, SKD-515, BAU, ABG, XAU was conducted, this grades differ in composition, method of producing, structure, and chemical state of the surface. The basic laws, characteristics and mechanism of adsorption of organic substances on activated carbon (AU) were established. The mechanism of mass transfer during adsorption of a mixture of phenol and formaldehyde on the investigated sorbents was showed, and the external mass transfer coefficients were calculated. There was proposed the method of optimization of parameters and continuous adsorption treatment process modes, based on the fundamental external diffusion dynamics adsorption formula using the adsorption constants of the Dubinin-Radushkevich’s equation and kinetic dependencies. The main features of the adsorption dynamics were established, which allowed to determine the duration of column operation, the amount of feed water depending on the throughput rate, the height of the fixed bed and size of the column. According to the results of experimental studies and derivatographic analysis we developed the technology of carbon sorbents regeneration after adsorption of formaldehyde and phenol mixture, which allowed to restore the AC (activated carbon) sorption capacity to 95-98%. On the basis of aggregate balance studies, kinetics and dynamics of adsorption process, optimization of the cleaning regime and the parameters of adsorption column using mathematical modeling, we recommend the technological solution for waste water purification from phenol and formaldehyde, which are formed in the process of phenol-formaldehyde resins of the novolac type production.

Influence of Flow Velocity on the Characteristics of Pseudomonas fluorescens Biofilms

AbstractThe characteristics of Pseudomonas fluorescens biofilms formed under three different linear flow velocities (u=0.1, 0.4, and 0.8 m/s; Reynolds numbers of 1,000, 4,000, and 8,000, respectively) were studied providing an extension to the studies of earlier researchers. A flow cell reactor system was used to form biofilms, and they were characterized in terms of thickness, morphological structure, mass, cell density, outer membrane protein expression, and matrix and total protein and polysaccharide content. The external mass transfer coefficients were also assessed. The biofilms developed at u=0.4 and 0.8 m/s had similar characteristics but were significantly different from those developed at 0.1 m/s. High flow velocities formed thinner biofilms with higher cell densities and contents of matrix/extracellular proteins and polysaccharides. The increase of flow velocity from 0.4 to 0.8 m/s caused a higher production of matrix proteins and polysaccharides. The external mass transfer coefficients sugg...

Film pore diffusion modeling and contact time optimization for adsorption of distillery spentwash on fly ash

The contact time in two batch adsorbers were optimized using unreacted shrinking core model for the adsorption of biopolymeric pigments in distillery spentwash by fly ash adsorbent. The total optimal contact time obtained was 40 min for 3 m3 adsorbate volume having initial biopolymer concentration of 1.5 mg/dm3. The film pore diffusion model was used to determine the external mass transfer coefficient, effective diffusion coefficient, and bed capacity for continuous adsorption process. The adsorbent bed capacities at different initial biopolymeric concentrations (2,000, 5,500, 8,700, and 12,500 mg/ml) are 69.26, 114.41, 143.64, and 172 mg/g, respectively. The effective diffusion coefficients at various bed heights were determined for continuous adsorption process.

Mass Transfer Studies on Adsorption of Phenol from Wastewater UsingLantana camara, Forest Waste

Adsorption is one of the important treatment methods for the removal of pollutants from wastewater. The determination of rate controlling step in the process is important in the design of the process. Therefore, in the present work, mass transfer studies were done to evaluate the rate-limiting step in the adsorption of phenol from aqueous solution ontoLantana camara. Different mass transfer models were used to find the rate-limiting step and also to find the values of external mass transfer coefficient and diffusion coefficient. The Biot number was found to investigate the importance of external mass transfer to intraparticle diffusion. From the various models studied and the Biot numbers obtained, it was found that the adsorption onLantana camarawas controlled by film diffusion. The sensitivity analysis was performed to study the significance of the model parameters on the adsorption process.

역상 크로마토그래피에서 모멘트 방법과 van Deemter 식을 이용한 고리형 아데노신 일인산의 분리특성 연구

The moment analysis of cyclic adenosine monophosphate (cAMP) was performed using chromatograms that were obtained with the pulse input method from an octadecyl silica (ODS) high-performance liquid chromatogra- phy (HPLC) column. The general rate (GR) model was employed to calculate the first absolute moment and the second central moment. Three important coefficients for moment analysis, which are molecular diffusivity (Dm), external mass transfer coefficient (kf), and intra-particle diffusivity (De), were estimated by the Wilke-Chang equation, Wilson-Gean- koplis equation, and comparing van Deemter equation to theoretical plate number equation, respectively. Experiments were conducted by various conditions of flow rates, methanol volume ratio of the mobile phase, and solute concentra- tion. After the moment analysis, results were organized by van Deemter plots. Also van Deemter coefficients were com- pared each other to effect Hax, Hf, and Hd on height equivalent to a theoretical plate (HETP, Htotal). The value of intra- particle diffusion (Hd) was the primary factor which makes for HETP whereas external mass transfer (Hf) was disre- gardable factor.