The interplay of diffusional and electrophoretic transport mechanisms of charged solutes in the liquid film surrounding charged nonporous adsorbent particles employed in finite bath adsorption systems

A model that describes the diffusive and electrophoretic mass transport of the cation and anion species of a buffer electrolyte and of a charged adsorbate in the liquid film surrounding nonporous adsorbent particles in a finite bath adsorption system, in which adsorption of the charged adsorbate onto the charged surface of the nonporous particles occurs, is constructed and solved. The dynamic behavior of the mechanisms of this model explicitly demonstrates (a) the interplay between the diffusive and electrophoretic molar fluxes of the charged adsorbate and of the species of the buffer electrolyte in the liquid film surrounding the nonporous adsorbent particles, (b) the significant effect that the functioning of the electrical double layer has on the transport of the charged species and on the adsorption of the charged adsorbate, and (c) the substantial effect that the dynamic behavior of the surface charge density has on the functioning of the electrical double layer. It is found that at equilibrium, the value of the concentration of the charged adsorbate in the fluid layer adjacent to the surface of the adsorbent particles is significantly greater than the value of the concentration of the adsorbate in the finite bath, while, of course, the net molar flux of the charged adsorbate in the liquid film is equal to zero at equilibrium. This result is very different than that obtained from the conventional model that is currently used to describe the transport of a charged adsorbate in the liquid film for systems involving the adsorption of a charged adsorbate onto the charged surface of nonporous adsorbent particles; the conventional model (i) does not consider the existence of an electrical double layer, (ii) assumes that the transport of the charged adsorbate occurs only by diffusion in the liquid film, and (iii) causes at equilibrium the value of the charged adsorbate in the liquid layer adjacent to the surface of the particles to become equal to the value of the concentration of the charged adsorbate in the liquid of the finite bath. Furthermore, it was found that a maximum can occur in the dynamic behavior of the concentration of the adsorbate in the adsorbed phase when the value of the free molecular diffusion coefficient of the adsorbate is relatively large, because the increased magnitude of the synergistic interplay between the diffusive and electrophoretic molar fluxes of the adsorbate in the liquid film allows the adsorbate to accumulate (to be entrapped) in the liquid layer adjacent to the surface of the adsorbent particles faster than the concentrations of the electrolyte species, whose net molar fluxes are significantly hindered due to their opposing diffusive and electrophoretic molar fluxes, can adjust to account for the change in the surface charge density of the particles that arises from the adsorption of the charged adsorbate. The results presented in this work also have significant implications in finite bath adsorption systems involving the adsorption of a charged adsorbate onto the surface of the pores of charged porous adsorbent particles, because the diffusion and the electrophoretic migration of the charged solutes (cations, anions, and charged adsorbate) in the pores of the adsorbent particles will depend on the dynamic concentration profiles of the charged solutes in the liquid film surrounding the charged porous adsorbent particles. The results of the present work are also used to illustrate how the functioning of the electrical double layer could contribute to the development of inner radial humps (concentration rings) in the concentration of the adsorbate in the adsorbed phase of charged porous adsorbent particles.     

Numerical study of long-range surface diffusion influence on catalytic reactivity of spatially inhomogeneous planar surfaces

A phenomenological (mean-field) mathematical model of unimolecular reactions proceeding onto inhomogeneous planar surfaces is presented and investigated numerically in two-dimensional in space case taking into account the adsorption and desorption of reactant particles, long-range surface diffusion of the adsorbed particles, and an instantaneous product desorption from an adsorbent. The model also involves the bulk diffusion of the reactant from the bounded vessel towards the adsorbent and the product bulk one from the adsorbent into the same vessel. Simulations were performed using the finite difference technique. The influence of the long-range surface diffusion of adsorbed particles on the kinetics for processes catalyzed by inhomogeneous surfaces with a different arrangement of reactive and non-reactive adsorption sites is studied.     

Product desorption rate influence on catalytic reactivity of spatially inhomogeneous surfaces

We investigate numerically a phenomenological mathematical model of unimolecular reactions proceeding on inhomogeneous planar surfaces in the two-dimensional space case taking into account: the bulk diffusion of the reactant from the bounded vessel toward the adsorbent and the product bulk one from the adsorbent into the same vessel, the adsorption and desorption of reactant particles, long-range surface diffusion of the adsorbate, and a slow product desorption from the adsorbent. Simulations were performed using the finite difference technique. The influence of the long-range surface diffusion and product desorption rate on the kinetics of processes catalysed by inhomogeneous surfaces with different arrangements of reactive and nonreactive adsorption sites are studied.     

ADSORPTION DYNAMICS OF MACROPOROUS POLYMERIC ADSORBENT I. The Studies on the Particle Diffusion Mass-Transfer Process

1 INTRODUCTIONBoyd et al established the foundation of ion-exchange dynamics based on the Fick's Law intothe process of ion-exchange diffusion at firstll]. At present time, most of studies for themacroporous adsorption resin are focus on the synthesis of new adsorbent, observing the effectof some conditions on the adsorption capacity and adsorption selectivity. But there are nopedicular studies on the aspect of adsorption dynamics, such as mass-transfer rate, mass-transfermechanism and so…     

Analysis of mass transport models for protein adsorption to cation exchanger by visualization with confocal laser scanning microscopy

The mass transfer of bovine serum albumin (BSA) to a cation exchanger, SP Sepharose FF, has been studied by finite batch adsorption experiments. The uptake curve was simulated with three mass transport models (i.e., effective pore diffusion model, surface diffusion model and Maxwell-Stefan model) incorporating the particle size distribution of the adsorbent particles. All the three models can simulate the uptake curves reasonably well. However, how well these models could simulate the real concentration profile within the adsorbent particle cannot be verified by the fitness of the models to the uptake curve. Thus, confocal laser scanning microscopy (CLSM) was used to visualize protein uptake to the porous adsorbent particles during the batch experiments. Using a fluorescent dye-labeled bovine serum albumin (BSA) for the dynamic adsorption experiments, the radial concentration profiles of the labeled BSA molecules into individual adsorbent particles at different times were obtained from the CLSM images. The protein distribution profiles within various particle diameters at different time were compared with the radial protein distributions predicted from the models. It reveals that surface diffusion model describes the intraparticle protein concentration profiles better than the other two models.     

Comparative study between a CMS membrane and a CMS adsorbent: Part II. Water vapor adsorption and surface chemistry

The adsorption/desorption equilibria of water vapor in a carbon molecular sieve (CMS) membrane and a commercial CMS adsorbent were determined, exhibiting S-shaped, type V isotherms. The fits of several models found in the literature to the experimental data were evaluated. The results obtained led to the development of a new model accounting for both adsorption and desorption and essentially based on the work of Lagorsse et al. (2005) [15]. Furthermore, the adsorption kinetics was also assessed for both materials and well described by a linear driving force model. The existence of hydrophilic groups responsible for water vapor adsorption in such carbonaceous materials has been related to the surface chemistry by means of X-ray microanalysis and by thermogravimetry. It was concluded from X-ray microanalyses that the carbon membrane presents a lower C/O ratio and is thus more sensitive towards water vapor exposure, as evidenced by the measured water adsorption at lower relative pressures. It was also observed that the diffusion rates are higher for the CMS membrane than for the CMS adsorbent.     

Characteristic and mechanism of Cr(Ⅵ) adsorption by ammonium sulfamate-bacterial cellulose in aqueous solutions

A new adsorbent, ammonium sulfamate-bacterial cellulose (ASBC), was prepared through chemical modifications of bacterial cellulose. The process of adsorbing Cr(Ⅵ) including its isotherm and kinetics, was measured and studied. The results showed that pH value was a very important parameter to the adsorbing efficiency. The adsorption kinetics can be described by a pseudo-second rate model and a particle diffusion equation. Both physical and chemical adsorptions existed in the adsorption process, but chemical adsorption was more dominatant. And particles internal diffusion was not the only rate controlling step. The adsorption equilibrium can be described by the Langmuir type, which indicated that a typical single-molecule layer adsorption of Cr(Ⅵ) by ASBC could be described. And the rate of adsorption followed the Slips model well, which indicated that ASBC had some multiphase and asymmetry. The coordination adsorption and ion exchange effect were the main mechanisms of chemical adsorption. The absorbed Cr(Ⅵ) can be desorbed effectively by 0.5 mol/L EDTA or HCl from the adsorbent, which could make it be reusable.     

Preparation, Properties and Mechanism of Inhomogeneous Calcium Alginate Ion Cross-linking Gel Microspheres

Inhomogeneous calcium alginate ion cross-linking gel microspheres,a novel ion absorbent,were prepared by dropping a sodium alginate solution to a calcium chloride solutioin via an electronic droplet generator.Calcium alginate microspheres have uniform particle sizes.a smooth surface and a microporous structure.The electrode probe reveals the inhomogeneous distribution of calcium ions with the highest concentration on the surface,and the lowest concentration in the cores of the spheres.As a novel ion adsorbent,calcium alginate gel microspheres have a lower limiting adsorption mass concentration,a higher enrichment capacity and a higher adsorption capacity for Pb^2 than usual ion exchange resins.The highest percentage of the adsorption is 99.79%.The limiting adsorption mass concentration is 0.0426mg/L.The adsorption capacity for Pb^2 is 644mg/g,Calcium alginate gel microspheres have a much faster ion exchange velocity than D418 chelating resin and D113 polyacrylate resin.The moving boundary model was employed to interpret the ion exchange kinetics process,which indicates that the ion exchange process is controlled by intraparticle diffusion of adsorbable ions.So the formation of inhomogeneous gel microspheres reduces the diffusion distance of adsorbable ions within the spheres and enhances the ion exchange velocity.Alginate has a higher selectivity for pb^2 than for Ca^2 and the selectivity coefficient KCa^Pb is 316. As an ion cross-linking gel,calcium alginate inhomogeneous microspheres can effectively adsorb heavy metal Pb^2 at a higher selectivity and a higher adsorption velocity.It is a novel and good ion adsorbent.     

Pore network modelling: determination of the dynamic profiles of the pore diffusivity and its effect on column performance as the loading of the solute in the adsorbed phase varies with time

A three-dimensional pore network model for diffusion in porous adsorbent particles was employed in a dynamic adsorption model that simulates the adsorption of a solute in porous particles packed in a chromatographic column. The solution of the combined model yielded the dynamic profiles of the pore diffusion coefficient of beta-galactosidase along the radius of porous ion-exchange particles and along the length of the column as the loading of the adsorbate molecules on the surface of the pores occurred, and, the dynamic adsorptive capacity of the chromatographic column as a function of the design and operational parameters of the chromatographic system. The pore size distribution of the porous adsorbent particles and the chemistry of the adsorption sites were unchanged in the simulations. It was found that for a given column length the dynamic profiles of the pore diffusion coefficient were influenced by: (i) the superficial fluid velocity in the column, (ii) the diameter of the adsorbent particles and (iii) the pore connectivity of the porous structure of the adsorbent particles. The effect of the magnitude of the pore connectivity on the dynamic profiles of the pore diffusion coefficient increased as the diameter of the adsorbent particles and the superficial fluid velocity in the column increased. The dynamic adsorptive capacity of the column increased as: (a) the particle diameter and the superficial fluid velocity in the column decreased, and (b) the column length and the pore connectivity increased. In preparative chromatography, it is desirable to obtain high throughputs within acceptable pressure gradients, and this may require the employment of larger diameter adsorbent particles. In such a case, longer column lengths satisfying acceptable pressure gradients with adsorbent particles having higher pore connectivity values could provide high dynamic adsorptive capacities. An alternative chromatographic system could be comprised of a long column packed with large particles which have fractal pores (fractal particles) that have high pore connectivities and which allow high intraparticle diffusional and convective flow mass transfer rates providing high throughputs and high dynamic adsorptive capacities. If large scale monoliths could be made to be reproducible and operationally stable, they could also offer an alternative mode of operation that could provide high throughputs and high dynamic adsorptive capacities.     

The simple procedure of the calculation of diffusion coefficient for adsorption on spherical and cylindrical adsorbent particles--experimental verification

A recently proposed simplified procedure for calculating the effective diffusion coefficient (D(e)) for adsorption on spherical and cylindrical adsorbent particles is now experimentally verified for adsorption systems: paracetamol-activated carbon. Adsorption kinetics was measured on nine carbons; for seven of them, measurements were taken at three temperatures. Since for adsorption on spherical adsorbent particles the approximate methods of D(e) calculation are already available in literature, only two systems have been studied, and the results of the new procedure are compared with those calculated from previously published methods. However, for cylinders the proposed method is the first simplification of this kind available in literature, thus, we focus our attention on the comparison of the results of the analytical approach with the simplified approaches for the systems where an adsorbent possesses cylindrically shaped granules. It is shown that for adsorption on spherical as well as on cylindrical adsorbent granules the proposed simplification leads to satisfactory results that, taking into account an experimental error, are practically the same as those obtained from exact time-consuming and mathematically advanced numerical fitting procedure. It is also shown that, for the studied carbons, the surface diffusion process dominates, and this explains the recently obtained correlation between the effective diffusion coefficient and the enthalpy of carbon immersion in water.     

Spillover in monomer–monomer reactions on supported catalysts: dynamic mean-field study

The kinetics of a $A_1+A_2\rightarrow A_1A_2$ reaction on supported catalysts is investigated numerically using a phenomenological model which includes: the bulk diffusion of reactants from a bounded vessel towards the adsorbent and the product bulk one into the same vessel, adsorption and desorption of reactants molecules, and surface diffusion of adsorbed particles. The model is based on the Langmuir–Hinshelwood surface reaction mechanism coupled with the Eley–Rideal step. The model based only on the Langmuir–Hinshelwood mechanism is also studied. Simulations were performed using the finite difference technique. Three cases of reactants adsorption are considered: each reactant can adsorb on the active in reaction catalyst surface and inactive support, one of reactants adsorbs on the catalyst surface while the other one adsorbs on the support, both reactants adsorb only on the support. The surface diffusion and catalytic surface size influence on the catalytic reactivity of a supported catalyst is studied.     

Kinetics of sodium dodecyl benzene sulfonate adsorption on hematite and its interaction with polyacrylamide

This article describes the adsorption of sodium dodecyl benzene sulfonate, an anionic surfactant, on a hematite surface and that when the surface is preadsorbed with polyacrylamide. The adsorption of surfactant on a hematite surface has been studied through equilibration and during kinetics measurements at three pH levels, viz. 4.0, 7.0, 8.9. The surfactant adsorbs strongly on the hematite surface. The adsorption density at equilibrium as well as the rate of adsorption are dependent on the suspension pH. The maximum adsorption density has been observed at pH 4, which reflects strong adsorption of negatively charged sulfonate ions on the oppositely charged Fe₂O₃ surface (point of zero charge, 6.4). The adsorption density reaches its equilibrium value sooner in the case of an alkaline suspension and later in the case of acidic pH. The polymer surfactant interaction has been noticed in the present study and is also a function of pH. The hematite mineral when preadsorbed with the polymer draws fewer of the surfactant molecules at lower surface coverage (during the initial period of the kinetics measurement) irrespective of the pH. When the adsorption of the surfactant reaches a value which is near the equilibrium one, the pH effect is evident. In the case of acidic pH, the surfactant adsorbs more on the hematite surface when preadsorbed with the polymer compared to the bare surface. In the case of neutral or alkaline pH, however, the density of surfactant adsorption remains lower throughout the kinetics measurement when the surface is preadsorbed with the flocculant compared to the bare surface. The particles also remain flocculated till the end of the experiment, whereas at pH 4 the particles are deflocculated. In addition to pH, the electrostatic nature of the adsorbent and the presence of anionic surfactant have an influence on the flocculation–deflocculation phenomena. The polymer–surfactant interaction has been schematically represented. The surfactant is bound with polymeric chains as a combination of its monomeric form as well as in the form of association in the case of acidic media and in competition with polymer in the case of alkaline media. Received: 18 April 2000/Accepted: 2 August 2000     

SURFACE MODIFICATION OF POLYPROPYLENE MICROPOROUS MEMBRANES BY THE ADSORPTION OF NON-IONIC SURFACTANTS

Surface modification by physical adsorption of a series of non-ionic surfactants including Tween 20, Tween 40, Tween 60, Tween 80 and Tween 85, was accomplished on polypropylene microporous hollow fiber and flat membranes. The adsorption curve of the membrane surface was analyzed by weight measurements and the typical results showed a twoplatform character similarly. Differences in the degree and curve shape of adsorption resulting from such factors as concentration, temperature, as well as water cleaning time were observed for Tween 85 among other Tweens. Attenuated total reflection - Fourier transform infrared spectroscopy analysis and field emission scanning electron microscopy observation showed that the adsorption of Tween on polypropylene microporous membrane （PPMM） is effective and occurs mainly in the pores of PPMMs at low adsorption amount, and on the membrane surface also at high adsorption value.     

In situ determination of the adsorption characteristics of a zeolite membrane

A methodology based on adsorption-branch porosimetry is described for in situ measurement of the adsorption of condensable gases within the pore structure of inorganic membranes. The method is applied to the study of n-hexane and p-xylene adsorption in a high-silica, MFI zeolite membrane. The results, interpreted in terms of a simple model for competitive adsorption effects on the permeance of a non-adsorbing gas, yield Langmuir adsorption constants and Henry’s law constants for n-hexane and p-xylene that are in excellent agreement with measurements on bulk materials. The method is proposed for the fundamental study of fouling characteristics of inorganic membranes, especially in cases where a true bulk surrogate is not available.     

Removal of zinc metal ion (Zn) from its aqueous solution by kaolin clay mineral: A kinetic and equilibrium study

A laboratory batch study has been performed to study the effect of various physic-chemical factors such as initial metal ion concentration, solution pH, and amount of adsorbent, contact time and temperature on the adsorption characteristics of zinc (Zn²⁺) metal ions onto kaolin. It has been found that the amount of adsorption of zinc metal ion increases with initial metal ion concentration, contact time, solution pH but decreases with the amount of adsorbent and temperature of the system. Kinetic experiments clearly indicate that adsorption of zinc metal ion (Zn²⁺) on kaolin is a two steps process: a very rapid adsorption of zinc metal ion to the external surface is followed by possible slow decreasing intra-particle diffusion in the interior of the adsorbent which has also been confirmed by intra-particle diffusion model. The equilibrium time is found to be in the order of 60 min. Overall the kinetic studies showed that the zinc adsorption process followed pseudo-second-order kinetics among pseudo-first-order and intra-particle diffusion model. The different kinetic parameters including rate constant are determined at different initial metal ion concentration, solution pH, amount of adsorbent and temperature respectively. The equilibrium adsorption results are analyzed by both Langmuir and Freundlich models to determine the mechanistic parameters associated with the adsorption process. The value of separation factor, R_L from Langmuir equation also gives an indication of favorable adsorption. Finally thermodynamic parameters are determined at three different temperatures and it has been found that the adsorption process is exothermic due to negative ΔH° accompanied by decrease in entropy change and Gibbs free energy change (ΔG°).     

Numerical study of the kinetics of unimolecular heterogeneous reactions onto planar surfaces

In this paper we investigate two-dimensional in space mathematical models of the kinetics of unimolecular heterogeneous reactions proceeding onto planar surfaces. The models are based on Langmuir-type kinetics of the adsorption, desorption, and reaction including the surface diffusion of the adsorbate, surface diffusion of the product before its desorption, and slow desorption of the product from the adsorbent. It is also assumed that the reactant diffuses towards an adsorbent from a bounded vessel and the product diffuses from the adsorbent into the same vessel. Diffusivity of all species and kinetic coefficients are constants. The numerical simulation was carried out using the finite difference technique for four models: one model neglects the surface diffusion of the adsorbate and product, the second one includes the surface diffusion of the adsorbate and product, the third of them includes the surface diffusion of the adsorbate and neglects diffusion of the product along the surface, and the last one neglects the surface diffusion of the adsorbate and includes diffusion of the product along the adsorbent. By changing input parameters effects of the surface diffusion of the adsorbate and product and the slow desorption of the product are studied numerically.     

ND-100超高交联吸附树脂对水中苯酚的吸附行为研究

通过静态吸附试验，研究了ND－100超高交联树脂对水溶液中苯酚的吸附动力学和热力学特性，探讨了初始浓度对吸附过程的影响。结果表明 ND－100树脂对苯酚的吸附速率同时受液膜扩散和颗粒内扩散过程控制。吸附符合Langmuir和Freundlich等温吸附方程，吸附量随着温度的升高而降低，随着平衡浓度的增大而增大，吸附表现为放热的物理吸附过程。     

Analysis and parametric sensitivity of the behavior of overshoots in the concentration of a charged adsorbate in the adsorbed phase of charged adsorbent particles: practical implications for separations of charged solutes

In this work, an analysis of the parametric sensitivity of the overshoot in the concentration of the adsorbate in the adsorbed phase, which occurs under certain conditions during an ion-exchange adsorption process, is presented and used to suggest practical implications of the concentration overshoot phenomenon on operational policies and configurations of chromatographic columns and finite bath adsorption systems. The results presented in this work demonstrate and explain how the development of an overshoot in the concentration of the adsorbate in the adsorbed phase could be enhanced or suppressed by (i) varying the diffusion coefficient, D3, of the adsorbate relative to the diffusion coefficients, D1 and D2, of the cations and anions, respectively, of the background/buffer electrolyte, (ii) altering the initial surface charge density, delta0, of the charged adsorbent particles, (iii) varying the Debye length, lambda, and (iv) changing the initial concentration, Cd3(0), of the adsorbate in the bulk liquid of the finite bath. The influence of the pH and ionic strength, Iinfinity, of the liquid solution on the development of an overshoot in the concentration of the adsorbate in the adsorbed phase is also presented and discussed through the relationships of these parameters to delta0 and lambda, respectively. Furthermore, a detailed explanation of the effects of each parameter on the interplay between the diffusive and electrophoretic molar fluxes, as well as on the structure and functioning of the electrical double layer, which are responsible for the concentration overshoot phenomenon, is presented.     

Tailoring the Asymmetric Structure of NH2-UiO-66 Metal-Organic Frameworks for Light-promoted Selective and Efficient Gold Extraction and Separation

Designing adsorption materials with high adsorption capacities and selectivities is highly desirable for precious metal recovery. Desorption performance is also particularly crucial for subsequent precious metal recovery and adsorbent regeneration. Herein, a metal–organic framework (MOF) material (NH₂-UiO-66) with an asymmetric electronic structure of the central zirconium oxygen cluster has an exceptional gold extraction capacity of 2.04 g g⁻¹ under light irradiation. The selectivity of NH₂-UiO-66 for gold ions is up to 98.8 % in the presence of interfering ions. Interestingly, the gold ions adsorbed on the surface of NH₂-UiO-66 spontaneously reduce in situ, undergo nucleation and growth and finally achieve the phase separation of high-purity gold particles from NH₂-UiO-66. The desorption and separation efficiency of gold particles from the adsorbent surface reaches 89 %. Theoretical calculations indicate that -NH₂ functions as a dual donor of electrons and protons, and the asymmetric structure of NH₂-UiO-66 leads to energetically advantageous multinuclear gold capture and desorption. This adsorption material can greatly facilitate the recovery of gold from wastewater and can easily realize the recycling of the adsorbent.     

吸附质大小对吸附树脂粒内扩散行为的影响(Ⅰ)——大孔聚苯乙烯型吸附树脂粒内扩散机制的考察

本文详细考察了大孔聚苯乙烯型吸附树脂对不同大小吸附质分子的吸附动力学行为,当吸附过程为粒扩散控制时,树脂孔径与分子尺寸的相对大小不仅决定了粒扩散速度的大小,也影响了粒扩散的控制机制.随着吸附质分子尺寸的增加,决定粒扩散速度的控速步骤也逐渐由表面扩散转向孔扩散。此外,还利用建立的扩散方程,测定了树脂吸附不间大小的吸附质时的粒扩散常数B和有效粒扩散系数De。