Simple Mass Transfer Model Research Articles

Uptake, efflux, and mass transfer coefficient of fluorescent PAMAM dendrimers into pancreatic cancer cells

Targeted delivery of imaging agents to cells can be optimized with the understanding of uptake and efflux rates. Cellular uptake of macromolecules is studied frequently with fluorescent probes. We hypothesized that the internalization and efflux of fluorescently labeled macromolecules into and out of mammalian cells could be quantified by confocal microscopy to determine the rate of uptake and efflux, from which the mass transfer coefficient is calculated. The cellular influx and efflux of a third generation poly(amido amine) (PAMAM) dendrimer labeled with an Alexa Fluor 555 dye was measured in Capan-1 pancreatic cancer cells using confocal fluorescence microscopy. The Capan-1 cells were also labeled with 5-chloromethylfluorescein diacetate (CMFDA) green cell tracker dye to delineate cellular boundaries. A dilution curve of the fluorescently labeled PAMAM dendrimer enabled quantification of the concentration of dendrimer in the cell. A simple mass transfer model described the uptake and efflux behavior of the PAMAM dendrimer. The effective mass transfer coefficient was found to be 0.054±0.043μm/min, which corresponds to a rate constant of 0.035±0.023min−1 for uptake of the PAMAM dendrimer into the Capan-1 cells. The effective mass transfer coefficient was shown to predict the efflux behavior of the PAMAM dendrimer from the cell if the fraction of labeled dendrimer undergoing non-specific binding is accounted for. This work introduces a novel method to quantify the mass transfer behavior of fluorescently labeled macromolecules into mammalian cells.

Adsorption kinetics, isotherms and thermodynamics of atrazine removal using a banana peel based sorbent

Atrazine removal from water by treated banana peels was studied. The effect of pH, contact time, initial atrazine concentration, and temperature were investigated. Batch experiments demonstrated that 15 g L(-1) adsorbent dosage removed 90-99% of atrazine from 1-150 ppm aqueous solutions. The removal was both pH and temperature dependent with the most atrazine removed between pH 7 and 8.2 and increased with increasing temperature. Equilibrium data fitted well to the Langmuir and Redlich-Peterson models in the concentration and temperature ranges investigated, with a maximum adsorption capacity of 14 mg g(-1). Simple mass transfer models were applied to the experimental data to examine the adsorption mechanism and it was found that both external mass transfer and intraparticle diffusion played important roles in the adsorption mechanisms. The enthalpy of atrazine adsorption was evaluated to be 67.8 ± 6.3 kJ mol(-l) with a Gibbs free energy of -5.7 ± 1.2 kJ mol(-1).

The Effect of the CO32- to Ca2+ Ion activity ratio on calcite precipitation kinetics and Sr2+ partitioning.

BackgroundA proposed strategy for immobilizing trace metals in the subsurface is to stimulate calcium carbonate precipitation and incorporate contaminants by co-precipitation. Such an approach will require injecting chemical amendments into the subsurface to generate supersaturated conditions that promote mineral precipitation. However, the formation of reactant mixing zones will create gradients in both the saturation state and ion activity ratios (i.e., ). To better understand the effect of ion activity ratios on CaCO3 precipitation kinetics and Sr2+ co-precipitation, experiments were conducted under constant composition conditions where the supersaturation state (Ω) for calcite was held constant at 9.4, but the ion activity ratio was varied between 0.0032 and 4.15.ResultsCalcite was the only phase observed, by XRD, at the end of the experiments. Precipitation rates increased from 41.3 ± 3.4 μmol m-2 min-1 at r = 0.0315 to a maximum rate of 74.5 ± 4.8 μmol m-2 min-1 at r = 0.306 followed by a decrease to 46.3 ± 9.6 μmol m-2 min-1 at r = 1.822. The trend was simulated using a simple mass transfer model for solute uptake at the calcite surface. However, precipitation rates at fixed saturation states also evolved with time. Precipitation rates accelerated for low r values but slowed for high r values. These trends may be related to changes in effective reactive surface area. The ratios did not affect the distribution coefficient for Sr in calcite (DPSr2+), apart from the indirect effect associated with the established positive correlation between DPSr2+ and calcite precipitation rate.ConclusionAt a constant supersaturation state (Ω = 9.4), varying the ion activity ratio affects the calcite precipitation rate. This behavior is not predicted by affinity-based rate models. Furthermore, at the highest ion ratio tested, no precipitation was observed, while at the lowest ion ratio precipitation occurred immediately and valid rate measurements could not be made. The maximum measured precipitation rate was 2-fold greater than the minima, and occurred at a carbonate to calcium ion activity ratio of 0.306. These findings have implications for predicting the progress and cost of remediation operations involving enhanced calcite precipitation where mineral precipitation rates, and the spatial/temporal distribution of those rates, can have significant impacts on the mobility of contaminants.

Carbon Dioxide Removal from Flue Gases by Absorption/Desorption in Aqueous Diethanolamine Solutions

The carbon dioxide (CO2) desorption rate from CO2-loaded aqueous diethanolamine (DEA) solutions was measured using a stirred cell with a flat gas-liquid interface. The measurements were performed in the temperature range of 293.15–313.15 K and an amine concentration range of 10–20% mass DEA. Measurements were based on a semibatch isothermal absorption of the gas until the equilibrium state was reached, followed by desorption, which was initiated by the pressure release in the system. A simplified mass transfer model based on the film theory coupled with CO2 mass balance was developed to interpret the experimental data. On the basis of the proposed model, the initial mass transfer rates were calculated from the experimental results. The calculated initial desorption rates enabled estimation of the enhancement factor for CO2 mass transfer from aqueous DEA solutions. Analysis of the experimental data showed that desorption took place in the diffusive mass transfer regime.

Mass transfer in pervaporation: The key component approximation for the solution-diffusion model

A simple mass transfer model for the pervaporation process, the key component model, is described. In pervaporation the selectivity is often of the sorption type, which means that at the upstream side of the membrane, one of the components is much more sorbed than the others. The diffusivity of each component in this model does only depend on the volume fraction occupied by the key component. With this approximation when to solvents are involved in the pervaporation process the classical 6-parameter model becomes a four-parameter model. We develop the mass transfer equations in a special case where the diffusivity of each pure component follows Long's equation with a common plastization coefficient. The key component model is checked with data concerning pervaporation of ethanol–water mixtures through a PVA based membrane that follows these conditions. The limiting diffusivities and plastization coefficient are obtained from equilibrium and pervaporation data (at nil downstream pressure). The model allows the prediction of the pervaporation fluxes at growing downstream pressure.

Microwave-assisted extraction of tea phenols: A phenomenological study

In this paper, aqueous microwave-assisted extraction (MAE) of total phenols from black tea powder was investigated in an ordinary household microwave oven. Influence of microwave power (450–600–900 W) and irradiation duration (30–210 s) on total phenols concentration and antioxidant activity was investigated. MAE allowed higher recoveries compared to conventional brewing technique, without altering the antioxidant potential of the extracts. Experimental data indicated to follow first-order kinetics. Total phenols diffusion at different water to tea ratios was studied, and the results varied depending on how the ratio was modified (that is at either constant tea mass or water volume), due to the characteristics of microwave heating. In trials at constant solvent volume, infusion temperature resulted constant and experimental data could be successfully predicted by a simplified mass transfer model. MAE process can then be predicted and controlled for industrial application, but attention must be paid to both sample size and solvent to solid ratio.

Why do we have a bronchial tree with 23 levels of bifurcation?

A simple one-dimensional mass transfer model has been proposed for the oxygen transport through a bronchial tree to alveolar tissues as well as the carbon dioxide removal from the tissues in the human respiratory system. The proposed model mathematically describes the mass transfer between the airway inlet and the red blood cell interior in the pulmonary capillaries. The quasi steady one-dimensional analysis based on the model reveals that the bronchial tree is constructed such that it promotes the easiest access to the external air. Naturally, there exists the optimal number of the bifurcation levels, namely, 23, that yields the minimum overall mass transfer resistance for the mass transport from the external air to the red blood cells.

Potential use of cotton plant wastes for the removal of Remazol Black B reactive dye

In this study, the potential use of cotton plant wastes – stalk (CS) and hull (CH) – as sorbents for the removal of Remazol Black B (RB5), a vinyl sulfone type reactive dye, was investigated. The results indicated that adsorption was strongly pH-dependent but slightly temperature-dependent for each sorbent-dye system. The Freundlich, Langmuir, Redlich–Peterson and Langmuir–Freundlich adsorption models were used for the mathematical description of adsorption equilibrium and isotherm constants were evaluated at 25 °C. All models except the Freundlich model were applicable for the description of dye adsorption by both sorbents in the concentration range studied. According to the Langmuir model, CS and CH sorbents exhibited the highest RB5 dye uptake capacities of 35.7 and 50.9 mg g −1, respectively, at an initial pH value of 1.0. Simple mass transfer and kinetic models were applied to the experimental data to examine the mechanisms of adsorption and potential rate-controlling steps. It was found that both external mass transfer and intra-particle diffusion played an important role in the adsorption mechanisms of dye, and adsorption kinetics followed the pseudo second-order type kinetic model for each sorbent. Using the Langmuir model parameters, thermodynamic constant Δ G° was also evaluated for each sorption system.

Continuous Biosorption in Rotating Packed-Bed Contactor

Biosorption process has been studied in fixed-bed contactors where terrestrial gravity dictates attainable mass transfer rates. This work explored the mass transfer characteristics of continuous biosorption under centrifugal acceleration (many times earth’s gravity) in a rotating packed-bed (RPB) contactor. The system studied was copper(II) ion adsorption on the packing of the contactor constituted by scales of Catla catla fish. Experiments were performed by continuously recycling a fixed volume of solution through the bed. The uptake of copper by the biosorbent increases with centrifugal force and liquid flow rate, but compaction of the bed negates the advantages of using high values of these. A low-packing-density bed demonstrated comparable efficiency in adsorbing copper as a bed nearly twice its packing density. Mass transfer rate per unit volume of packed bed was enhanced in the RPB by about 2.4 times compared to the fixed bed. A simple mass transfer model predicted the continuous biosorption experim...

Effects of organic compounds and recycling on ozone absorption in a portable water purification unit

The absorption of ozone gas in a portable bubbling unit was investigated. First, six types of bubblers were tested under identical operating conditions with a gas flow rate of 1 L/min and a water volume of 1.5 L. A simple mass transfer model with the liquid phase assumed to be completely mixed and the axial ozone gas concentration gradient neglected was used to obtain the overall mass transfer coefficient, KLa, by fitting experimental data. The effect of organic compounds in the water on ozone absorption and liquid ozone concentration buildup was investigated experimentally using phenol as a model compound. It was found that the existence of phenol significantly reduced the liquid ozone concentration because absorbed ozone is consumed for the destruction of phenol, leading to the delay in liquid phase ozone concentration buildup. The implication is that the disinfection time was prolonged when water of high organic compounds concentration is to be purified. Using the completely stirred tank reactor model, the gas recycling is simulated and demonstrated to be effective for enhancing ozone utilization efficiency in the small portable water purification unit.

Study on the reactive extraction and stripping kinetics of certain β-lactam antibiotics

The extraction equilibrium and stripping of certain β-lactam antibiotics such as 7-aminocephalosporanic acid (7-ACA), 7-aminodeacetoxy cephalosporanic acid (7-ADCA), 6-aminopenicillanic acid (6-APA), cephalosporin-C (CPC) and cephalexin from aqueous solution of phosphate and carbonate buffers were studied with Aliquat-336 (tricaprylylmethylammonium chloride) dissolved in n-butylacetate as the solvent over an aqueous phase pH range of 5–10. The extraction equilibrium constant K p was found to increase with aqueous phase pH, which is attributed to the increase in ionisation of the β-lactam. A systematic study on kinetic of stripping or re-extraction of 7-ADCA and cephalexin from the extracted phase was carried out using an aqueous solution of citrate buffer at different pH values and was found to be pH dependent which is also attributable to ionisation behaviour of the β-lactams. Such observation is considered important, as re-extraction at an appropriate pH value is possible. The rate of stripping was found to be weakly dependent on Cl − concentration of the aqueous phase and the same was analysed with a simple mass transfer model based on film theory.

Study of As(V) transfer through a supported liquid membrane impregnated with trioctylphosphine oxide (Cyanex 921)

This paper presents a study of As(V) transfer through a supported liquid membrane (SLM) with trioctylphosphine oxide (Cyanex 921) in kerosene. Transport of As(V) from 2 M H 2SO 4 aqueous solutions was studied as a function of parameters such as the nature of the stripping solution, extractant concentration and stirring rate. Of the stripping solutions studied, Na 2SO 4 presents the highest As(V) transfer (close to 94%) in 120 min at concentrations where the ionic strengths of the feed and stripping solutions are equal. Additionally, when the extractant concentration was increased from 0.05 to 0.12 M, higher As(V) transfer values were obtained. The highest As(V) transfer was found at a Cyanex concentration of 0.12 M. The study of stirring rate influence indicates that at 16.66 Hz (1000 rpm) the thickness of the limit layer reaches a minimum; thus, we consider that at this point the mass transfer coefficient is essentially constant. Finally, a simple mass transfer model (based on the stationary state) was developed to determine the mass transfer coefficients at the feed solution–membrane and membrane–stripping solution interfaces.

Use of agricultural waste sugar beet pulp for the removal of Gemazol turquoise blue-G reactive dye from aqueous solution

The potential use of dried sugar beet pulp, an agricultural solid waste by-product, as an biosorbent for Gemazol turquoise blue-G, a copper–pthalocyanine reactive dye commonly used in dyeing of cotton, was investigated in the present study. Batch adsorption studies were carried out to examine the influence of various parameters such as initial pH, temperature and initial dye concentration. The results indicated that adsorption was strongly pH-dependent and slightly temperature-dependent. At 800mgl−1 initial Gemazol turquoise blue-G concentration, dried sugar beet pulp exhibited the highest Gemazol turquoise blue-G uptake capacity of 234.8mgg−1 at 25°C and at an initial pH value of 2.0. The Freundlich, Langmuir, Redlich–Peterson and Langmuir–Freundlich, the two and three parameters adsorption models were used for the mathematical description of the biosorption equilibrium and isotherm constants were evaluated depending on temperature. Both the Langmuir and Redlich–Peterson models were applicable for describing the dye biosorption by dried sugar beet pulp in the concentration (100–800mgl−1) and temperature (25–45°C) ranges studied. Simple mass transfer and kinetic models were applied to the experimental data to examine the mechanisms of biosorption and potential rate controlling steps such as external mass transfer, intraparticle diffusion and biosorption process. The sorption process was found to be controlled by both surface and pore diffusion with surface diffusion at the earlier stages followed by pore diffusion at the later stages. Pseudo first-order, pseudo second-order and saturation type kinetic models described the biosorption kinetics accurately at all concentrations and temperatures studied. The thermodynamic analysis indicated that the sorption process was exothermic and the biosorption of dye on dried sugar beet pulp might be physical in nature.

Experimental Validation of an Improved Squish Velocity Model for Bowl-in-Piston Combustion Chambers

A simple two-zone mass transfer model was used to predict the mean squish velocity history at the rim of a conventional bowl-in-piston combustion chamber. The chamber’s geometry produces gas flow that converges radially inwards (“squish”) as TDC (top dead center) is approached. The squish flow generates turbulence, which can be used to enhance the combustion rate. When compared with PIV (particle image velocimetry) measurements, the peak squish velocity at the bowl rim was 12% less than the value predicted by the simple mass transfer model. After a thorough examination, the assumption of uniform density in the simple model was strongly suspected to be the cause of this discrepancy. Improvements were made to the simple model to account for density variations that are caused by nonuniform heat transfer in the combustion chamber. The revised model yielded velocities that were in close agreement with PIV measurements.

Ozone transfer and design concepts for NOM decolourization in tubular membrane contactor

Ozonation membrane contact was carried out with a tubular membrane module to study the effects of the flow rates and the temperatures of the liquid phase on ozone transfer and on the enhancement of mass fluxes. Changes in liquid temperature gave both positive and negative effects on the ozone fluxes for the nitrite solutions. The increase of the ozone fluxes with temperature was observed until the temperature approached approximately 40 degrees C. Ozonation membrane contact was also applied to decolorize Norwegian natural organic matter (NOM) at typical color concentrations in the range of 15-20 mg Pt/L. The ozone consumption for NOM decolourization tended to decrease with the liquid flow rates. A simple mass transfer model was proposed for the ozonation membrane contactor for the NOM decolourization studied here. The model was developed based on the concepts of the ozone consumption and the enhancement factor and can be used to describe the influence of mass transfer on the effluent colour concentration of the NOM. The experimental results validated the proposed model with deviations in the range of -9 to + 7%. The decolourization rate constants obtained from the concentration-time (C-tau) model for the ozonation membrane contactor were found to be in the range of 139.44-298.81 M-1 s(-1). Simple concept to design ozonation membrane contactor for NOM decolourization was proposed. The kinetic characteristics for the NOM decolourization in ozonation membrane contactor are discussed in this paper. (c) 2005 Elsevier B.V. All rights reserved.

Removal of copper(II) ions from aqueous solution by biosorption onto agricultural waste sugar beet pulp

Dried sugar beet pulp, an agricultural solid waste by-product, was used as an biosorbent for the removal of copper(II) from aqueous solution. A series of experiments were conducted in a batch system to assess the effect of the system variables, i.e. initial pH, temperature and initial metal ion concentration. The results indicated that at 250 mg l −1 initial copper(II) concentration dried sugar beet pulp exhibited the highest copper(II) uptake capacity of 28.5 mg g −1 at 25 °C and at an initial pH value of 4.0. The equilibrium data were analyzed using the Freundlich, Langmuir, Redlich–Peterson and Koble–Corrigan isotherm models depending on temperature. The Langmuir model was found to best describe the data in the concentration and temperature ranges studied. Simple mass transfer and kinetic models were applied to the experimental data to examine the mechanisms of biosorption and potential rate-controlling steps such as external mass transfer, intraparticle diffusion and biosorption process. It was found that the intraparticle diffusion played an important role in the biosorption mechanisms of copper(II), and biosorption kinetics followed pseudo first- and pseudo second-order kinetic models rather than the saturation type kinetic model for all temperatures studied. The activation energy of biosorption ( E A) was determined as −58.47 kJ mol −1 using the Arrhenius equation. Using the thermodynamic equilibrium coefficients obtained at different temperatures, the thermodynamic constants of biosorption (Δ G°, Δ H° and Δ S°) were also evaluated.

A reversible surface reaction model with an effectiveness factor and its application to sorption kinetics of cupric ions on corncob particles

A novel reversible surface reaction model with an effectiveness factor was developed. To avoid uncertainty of nonlinear regression, an experimental procedure was designed to determine the following four constants in the model: the effectiveness factor, the maximum sorption capacity, and the intrinsic forward and backward rates. In this procedure first the intrinsic forward and backward rate constants for copper sorption were estimated to be 1.082 l/(mmol min) and 0.472 min −1 based on the elimination of the effect of the intraparticle and external mass transfers, and then the other two constants, the effectiveness factor and the maximum sorption capacity, were regressed as a function of the corncob particle size. Their values increased with decreasing the particle size. The simple external mass transfer model can describe only the solute change in solution for an initial 5 min period of time, which suggests that sorption of copper on corncob particles is controlled first by the external mass transfer, and then by the intraparticle mass transfer. The external mass transfer coefficients increased with increasing the modified Reynolds number, and then reached a maximum at higher values of the number. Studying the effects of the agitation speed and size of corncob particle on the kinetics of cupric ions sorption, it was found that the uptake of cupric ions on corncob particles increased with decreasing particle size and with increasing the agitation speed.

Sources of Non‐ideal Flow Distribution and Their Effect on the Performance of Hollow Fiber Gas Separation Modules

Hollow fiber membrane gas separation modules are used predominantly in membrane gas separation processes. The performance of these modules is often captured by simple flow and mass transfer models. However, as processes are pushed to the limits of their commercial viability, non‐ideal performance is often observed. Potential sources of this non‐ideality due to non‐uniform flows through the module are summarized and their effect on module performance evaluated.

Initial evaluation of simple mass transfer models to describe hemicellulose hydrolysis in corn stover.

The uncatalyzed hydrolysis and removal of xylan from corn stover is markedly enhanced when operation is changed from batch to continuous flowthrough conditions, and the increase in hemicellulose removal with flow rate is inconsistent with predictions by widely used first-order kinetic models. Mass transfer or other physical effects could influence the hydrolysis rate, and two models reported in the literature for other applications were adapted to investigate whether incorporation of mass transfer into the kinetics could explain xylan removal in both batch and continuous flowthrough reactors on a more consistent basis. It was found that a simple leaching model and a pore diffusion/leaching model could describe batch and flowthrough data with accuracy similar to that of conventional batch models and could provide a more rational explanation for changes in performance with flow rate.

Batch adsorption of 2,4-dichlorophenoxy-acetic acid (2,4-D) from aqueous solution by granular activated carbon

Abstract Adsorption equilibrium, kinetics and thermodynamics of 2,4-dichlorophenoxy-acetic acid (2,4-D), one of the most commonly used phenoxy acid herbicides, onto granular activated carbon were studied in aqueous solution in a batch system with respect to pH, temperature and initial 2,4-D concentration. At 600 mg l −1 initial 2,4-D concentration activated carbon exhibited the highest 2,4-D uptake capacity of 518.0 mg g −1 at 45 °C and at an initial pH value of 2.0. Freundlich, Langmuir, Redlich-Peterson and Koble-Corrigan isotherm models were applied to experimental equilibrium data of 2,4-D adsorption depending on temperature. Equilibrium data fitted very well to the Freundlich and Koble-Corrigan equilibrium models in the studied concentration range of 2,4-D at all the temperatures studied. Some simple mass transfer and kinetic models were applied to the experimental data to examine the mechanisms of adsorption and potential rate controlling steps such as external mass transfer, intraparticle diffusion and adsorption process. It was found that both the boundary layer and intraparticle diffusion played important roles in the adsorption mechanisms of 2,4-D, and adsorption kinetics followed a pseudo first-order kinetic model rather than pseudo second-order and saturation type kinetic models for all temperatures studied. The activation energy of adsorption ( E A ) was determined as 8.46 kJ mol −1 using the Arrhenius equation. Using the thermodynamic equilibrium coefficients obtained at different temperatures, the thermodynamic constants of adsorption (Δ G °, Δ H ° and Δ S °) were also evaluated.