Adsorption Of Spherical Particles Research Articles

Nonlinear Frequency Response Analysis as a Tool for Identification of Adsorption Kinetics: Case Study—Pore-Surface Diffusion Control

In the present paper, the Nonlinear Frequency Response (NFR) analysis is applied for theoretical study of kinetics of adsorption governed by pore-surface diffusion. The concept of higher-order frequency response functions (FRFs) is used. Based on a nonlinear mathematical model for adsorption of pure gas and spherical adsorbent particles, the theoretical first- and second-order FRFs, which relate the adsorbate concentration in the particle to the surrounding pressure (F1(ω) and F2(ω,ω)), have been derived. The obtained FRFs have been simulated for different steady-state pressures and different ratios (between zero and one) of surface to pore diffusion coefficients. The results show that, unlike F1(ω), F2(ω,ω) exhibits features which unambiguously distinguish the pore-surface diffusion model from pure pore diffusion and micropore diffusion. Based on the characteristic features of F1(ω) and F2(ω,ω), a new methodology for direct estimation of the separate values of the pore and surface diffusion coefficients has been established.

Mathematical modeling of manganese adsorption onto bone char in a continuous fixed bed column incorporating backmixing and shriking core approaches

Abstract The present study investigated the dynamics of manganese adsorption onto bone char in a continuous fixed bed column using a mathematical model that incorporates: (i) the backmixing model to describe the fluid flow through the bed and (ii) the shrinking core model to describe the kinetic and mass transfer phenomena within spherical adsorbent particles. The proposed model consists of an ordinary differential equation system. Hydrodynamic, kinetic and diffusive parameters were determined by fitting the mathematical model to the experimental data obtained by Sicupira et al. (2015). For the operating conditions evaluated in this study, the intraparticle diffusion represented the controlling step of the adsorption process (Bim> 3.8). The increase in the feed rate of the column (3.0-7.5 mL min-1) and the decrease in the height of the bed (8-16 cm) resulted in a decrease in the time required for the saturation of the column bed. The model is flexible for a variety of flow conditions and adequately reproduced the behavior of the manganese adsorption process in the fixed bed column operation (R²> 0.99) with an average percentage error less than15%.

A Parametric Study on Effect of External Heat and Mass Transfer Resistance on Vapor Adsorption in a Spherical Adsorbent Particle

A Parametric Study on Effect of External Heat and Mass Transfer Resistance on Vapor Adsorption in a Spherical Adsorbent Particle

Transient Flow Induced by the Adsorption of Particles

When small particles, e.g., glass, flour, pollen, etc., come in contact with a fluid-liquid interface they disperse so quickly to form a monolayer on the interface that it appears explosive, especially on the surface of mobile liquids like water. This is a consequence of the fact that the adsorption of a particle in an interface causes a lateral flow on the interface away from the particle. In this study we use the particle image velocimetry (PIV) technique to measure the transient three-dimensional flow that arises due to the adsorption of spherical particles. The PIV measurements show that the flow develops a fraction of a second after the adsorption of the particle and then persists for several seconds. The fluid below the particle rises upwards and on the surface moves away from the particle. These latter PIV results are consistent with the surface-velocity measurements performed in earlier studies. The strength of the induced flow, and the time duration for which the flow persists, both decrease with decreasing particle size.Copyright © 2013 by ASME

Theory and applications of refractive index-based optical microscopy to measure protein mass transfer in spherical adsorbent particles

This work provides the theoretical foundation and a range of practical application examples of a recently developed method to measure protein mass transfer in adsorbent particles using refractive index-based optical microscopy. A ray-theoretic approach is first used to predict the behavior of light traveling through a particle during transient protein adsorption. When the protein concentration gradient in the particle is sharp, resulting in a steep refractive index gradient, the rays bend and intersect, thereby concentrating light in a sharp ring that marks the position of the adsorption front. This behavior is observed when mass transfer is dominated by pore diffusion and the adsorption isotherm is highly favorable. Applications to protein cation-exchange, hydrophobic interaction, and affinity adsorption are then considered using, as examples, the three commercial, agarose-based stationary phases SP-Sepharose-FF, Butyl Sepharose 4FF, and MabSelect. In all three cases, the method provides results that are consistent with measurements based on batch adsorption and previously published data confirming its utility for the determination of protein mass transfer kinetics under a broad range of practically relevant conditions.

Irreversible Adsorption of Particles on Surface Features of a Circular and Rectangular Shape

The irreversible adsorption of spherical particles on surface features of various shapes (collectors) was studied using the Random Sequential Adsorption (RSA) model. Collectors in the form of circles and rectangles were considered, including the limiting cases of squares. Numerical simulation of the Monte Carlo type enabled the particle configurations to be determined, together with their density distribution (coverage) and the saturation coverage for various collectors to particle size ratio L̅ = L/2a and collector width to particle size ratio b̅ = b/2a. An unexpected feature found in these calculations was that the local coverage distribution of adsorbed particles was highly non-uniform, exhibiting a maximum at the centre and at the periphery of these collectors. The main finding of these calculations was the averaged number of particles <Np> adsorbed at the saturation state on collectors as a function of the L̅ and b̅ parameters. It was revealed that <Np> was highest for the square collector (for a fixed value of L̅). For L̅ > 5, our numerical results could be well approximated by the analytical expression <Np> = Θ∞ L̅2 for circles, <Np> = 4Θ∞ L̅2π for squares and <Np> = Θ∞ b̅L̅2/π for rectangles. It was demonstrated that the theoretical results are in an agreement with experimental data obtained for latex particles adsorbed onto patterned surfaces obtained by a polymer-on-polymer stamping technique for gold-covered silicon and on photolithographically-patterned silane layers on silica.

Measurement of Breakthrough Curves on Pressure Swing Adsorption for Hydrogen Isotope Separation

At the National Institute for Fusion Science experimental studies on hydrogen isotope separation by a cryogenic Pressure Swing Adsorption (PSA) process have been carried out in order to apply it to the system of vacuum pumping-gas treatment for the D-D burning experiments of the Large Helical Device. Breakthrough behavior of D2 in a H2-D2 mixture flowing through a synthetic zeolite 5A-type packed-bed column at 77.4 K is examined by using a cryogenic PSA apparatus. The test column used is 40 mm inner diameter. It is filled with spherical adsorbent particles of 2 mm at an amount of 700 g on a dry basis. The hydrogen mixture including D2 at a concentration of 1 % is used in this experiment. The breakthrough curves obtained by the experiments are accurately simulated by theoretical curves calculated for the system exhibiting the Henry type adsorption. Overall effective mass transfer coefficients are obtained from the comparison of experimental curves with analytical ones. The coefficients increase monotonously with superficial velocity. The sequential operations of PSA, such as adsorption, desorption and pressurization is carried out for several times. It is confirmed that breakthrough curves are reproducible after several repetitions of operation.

Modeling chromatographic columns: Non-equilibrium packed-bed adsorption with non-linear adsorption isotherms

In this work a new mathematical model, based on non-equilibrium conditions, describing the dynamic adsorption of proteins in columns packed with spherical adsorbent particles is used to study the performance of chromatographic systems. Simulations of frontal chromatography, including axial dispersion, for non-equilibrium systems with non-linear adsorption isotherms are made and compared to those of the experimentally determined protein A affinity chromatography breakthrough curves of hIgG, gathered from the literature. The non-equilibrium model developed here combines external mass transfer and intra-particle transport by solid (surface) diffusion, and permits the prediction of (time and bed height dependent) interface and average solid concentrations, along with interface and bulk liquid concentrations. The present non-equilibrium approach significantly improved the model predictions of experimentally observed distended breakthrough fronts over local equilibrium based models, and can be used to evaluate the influence of system parameters on the performance of chromatographic packed-bed adsorption columns.

Numerical study on adsorption enhancement of rectangular adsorption bed

The present paper has dealt with the one-sidewall cooling effect of spherical adsorbent particles packed in a rectangular bed on water vapor adsorption characteristics by a 2-dimensional numerical analysis. The analysis model was considered that one-sidewall of a rectangular packed bed with homogeneous spherical silica gel particles was cooled and another walls were adiabatic. The moist air flowed into the rectangular adsorption bed packed with spherical adsorbent particles. Fuji Sylsia silica gel B was selected as a suitable adsorbent with high adsorption ability over high relative humidity. Numerical results revealed the effects of moist air inlet humidity, airflow velocity, size of spherical silica gel particles, width of the rectangular packed bed, and the side-wall cooling temperature on the amount of water vapor adsorption.

Adorption Enhancement of Rectangular Packed Bed with Spherical Adonrbent by Side Wall Cooling in a Forced Convection Flow

The present paper has dealt with the one-sidewall cooling effect of spherical adsorbent paticles packed in a rectangular bed on water vapor adsorption characteristics by a 2-dimensional numerical analysis. The analysis model was considered that one-sidewall of a rectangular packed bed with the homogeneous spherical silica-gel particles was cooled and another walls were adiabatic. The moist air flowed into the rectangular packed bed with spherical adsorbent particles. The silica-gel B with high adsorption ability over high relative humidity was selected as a suitable adsorbent. Numerical results revealed the effects of moist air inlet humidity and airflow velocity, size of spherical silica-gel particles and width of the rectangular packed bed and the sidewall cooling terperature on the amount of water vapor adsorption.

Model for parallel surface and pore diffusion of an adsorbate in a spherical adsorbent particle

A model is presented to describe the rate of uptake of a species by a spherical adsorbent particle when intraparticle transport can occur by parallel diffusion through the pore space and along the surfaces of pore walls. Although the conventional shrinking core model (SCM) has been applied to such systems previously, its use is valid only when adsorption onto the pore walls is described by a rectangular isotherm. As with the SCM, the new model differs from homogeneous models by envisaging the advance of the adsorbate to be marked by a distinct inward-moving interface, but it generalizes the SCM to allow for an incompletely saturated adsorbed shell behind the front governed by any Langmuir isotherm. The model has been applied to previously published experimental data for the uptake of bovine serum albumin by chitosan beads and compared to the results obtained when the same data are analysed using the corresponding homogeneous model. The fit of the two models to the convension-time data yields comparable results, but significant differences in the predicted absorbate concentration profiles within adsorbent particles are observed, particularly at high conversions.

607 側面冷却を受ける矩形ダクト内粒状吸着剤層の吸着特性

607 側面冷却を受ける矩形ダクト内粒状吸着剤層の吸着特性

Sardinian natural clinoptilolites for heavy metals and ammonium removal: experimental and modeling

Sardinian natural clinoptilolites are examined to evaluate their adsorption for the metals, copper, cadmium, lead and zinc, as well as ammonium removal. The natural material is either used as received or once converted into the sodium form. Equilibrium data for each species and the natural material are obtained. The corresponding behavior is quantitatively correlated using classical isotherms, whose parameters are estimated by fitting the equilibrium data. Breakthrough experiments of lead solutions are also performed. Fixed-bed runs are simulated using a mathematical model which includes axial dispersion as well as a new approximate rate law for non-linear adsorption and diffusion in spherical adsorbent particle based on an equivalent film resistance model.

Intraparticle adsorbate concentration profile for linear driving force model

The purpose of this note is to demonstrate that a very general adsorbate concentration profile within the spherical adsorbent particle can satisfy the LDF (linear driving force) model.

Spherical Zeolite-Binder Agglomerates

The aim of the present research is to prepare a drying agent adsorbent in the form of spherical particles, using locally available raw materials. This absorbent is to be used as a drying agent in the dehydration of gases. The local materials are the Iraqi synthetic zeolite (type 4A) molecular sieve as the adsorbent material and Iraqi kaolin clay as a binder. The physical and mechanical behaviour of these spherical adsorbent particles was studied, as well as the effect of binder amount and calcination temperature on their properties. In addition, a sample containing cork powder or grog (calcined kaolin clay) as materials to increase porosity has been prepared. The results obtained showed that the best conditions, which can give physical and mechanical properties comparable with the imported spherical adsorbent samples, can be obtained when the amount of binder added is 10 or 20 wt% and the calcination temperature is 823 or 923 K.

Film model approximation for non-linear adsorption and diffusion in spherical particles

A new approximate rate law for non-linear adsorption and diffusion in a spherical adsorbent particle is developed based on an equivalent film resistance model. The approximation provides a quantitatively correct description of the effect of the adsorption isotherm for parallel pore and solid diffusion as well as of the effect of a variable adsorbed-phase diffusivity. In general, uptake curves calculated with this new approximation compare favorably with the numerical solution of the adsorption–diffusion equation in spherical coordinates producing results of accuracy similar to that obtained when the LDF approximation is used for systems with a constant diffusivity.

“Perfusion chromatography”. The effects of intra-particle convective velocity and microsphere size on column performance

A mathematical model describing the dynamic adsorption in columns with spherical bidisperse perfusive or spherical bidisperse purely diffusive adsorbent particles is presented and its solution is obtained numerically. The adsorption of bovine serum albumin on spherical anion-exchange porous particles was studied for different values of the intraparticle Peclet number, Pe intra, and of the microsphere diameter, d m. The results show a departure from spherical symmetry of the isoconcentration profiles of the adsorbate in the porous adsorbent particle as Pe intra increases. This spherical asymmetry increases the adsorbate availability in the pore fluid of the macroporous region and also increases the concentration of the adsorbate in the adsorbed phase in the upstream half of the spherical adsorbent particle. If, for example, the concentration profiles of the adsorbate in the adsorbed phase of the porous adsorbent particles could be determined experimentally and if these profiles show a departure from spherical symmetry, then this result could suggest that the porous adsorbent particles may have exhibited perfusion behavior under the conditions of operation of the column. The dynamic percentage utilization of the adsorptive capacity of the column increases as Pe intra increases and d m decreases. The percentage breakthrough to be selected for column switching is influenced by the magnitude of Pe intra because of its effect on the dynamic percentage utilization of the adsorptive capacity of the column.

Molecular dynamics model of adsorbed layer at a plane fluid interface

Adsorption of spherical particles at a planar fluid interface is modelled by means of a molecular dynamics simulation of a periodic system of 500 Lennard-Jones particles in the presence of an external Gaussian potential of narrow width and adjustable depth. Numerical results are presented as a function of temperature, density and well depth for the density profile perpendicular to the interface, the pair distribution function in the adsorbed monolayer, and the lifetimes and diffusion coefficients of particles in the monolayer. The appearance of secondary layers is noted at low temperature. The simulation provides a basis for modelling the statics and dynamics of competitive adsorption at fluid interfaces.