Adsorption Kinetics and Dynamic Behavior of a Carbon Monolith

The zero length column (ZLC) method has been applied to study the adsorption and diffusion of CO₂ in a carbon monolith adsorbent. ZLC desorption curves, measured over a wide range of flow rates, are shown to be very well accounted for assuming a linear equilibrium isotherm with the kinetics controlled by diffusion into a parallel sided slab. The data, at all flow rates, are characterized by a single pair of parameters (K and D _s). Diffusivities for a He carrier are about double those for a N₂ carrier reflecting both the difference in molecular diffusivities and some contribution from Knudsen diffusion. Breakthrough curves for CO₂-He and CO₂-N₂ were also measured for columns packed with the monolith adsorbent. Both the equilibrium and diffusion parameters derived from analysis of the breakthrough curves in accordance with the Golay/Spangler models are consistent with the values derived from the ZLC measurements. Dispersion in the monoliths is shown to be controlled by mass transfer resistance rather than axial mixing.     

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.     

Determination of the intraparticle electroosmotic volumetric flow-rate, velocity and Peclet number in capillary electrochromatography from pore network theory

The results obtained from the pore network model employed in this work, clearly show that the magnitudes of the intraparticle electroosmotic volumetric flow-rate, Qintrap, and velocity, (v(intrap,x)), in the pores of the charged porous silica particles considered in this study are greater than zero. The intraparticle Peclet number, Pe(intra, of a solute in these charged porous silica particles would be greater than zero, and, in fact, the magnitude of the intraparticle Peclet number, Pe(intrap), of lysozyme is greater than unity for all the values of the pore connectivity, nT, of the intraparticle pores and of the applied electric potential difference per unit length, Ex, along the axis of the capillary column considered in this work. Furthermore, the values of the intraparticle electroosmotic volumetric flow-rate, Qintrap, and velocity, (v(intrap,x)), as well as the magnitude of the pore diffusion coefficient, Dp, of the solute increase as the value of the pore connectivity, nT, of the intraparticle pores increases. The intraparticle electroosmotic flow can contribute significantly, if the appropriate chemistry is employed in the mobile liquid phase and in the charged porous particles, in (i) decreasing the intraparticle mass transfer resistance, (ii) decreasing the dispersive mass transfer effects, and (iii) increasing the intraparticle mass transfer rates so that high column efficiency and resolution can be obtained.     

Modeling equilibrium and kinetics of metal uptake by algal biomass in continuous stirred and packed bed adsorbers

Physical and chemical characterization of algae Gelidium particles shows a gel structure, with two major binding groups, carboxylic and hydroxyl groups, with an affinity constant distribution for protons, well described by a Quasi-Gaussian distribution suggested by Sips. A continuous model, considering a heterogeneous distribution of the carboxylic groups, determined by potentiometric titration experiments, was able to predict equilibrium data at different pH. The metal uptake capacity decreases with the solution pH, suggesting that competition exists between hydrogen ions, present in high concentrations for low pH values, and metal ions. For high ionic strengths, adsorption sites will be surrounded by counter ions and partially lose their charge, which weakens the contribution of the electrostatic binding and decreases the overall adsorption. A small influence of the temperature in the adsorption process was observed. Batch kinetic experiments were also performed, at different pH values, and results were well fitted by a mass transfer model, considering the intraparticle diffusion resistance given by the linear driving force model (LDF). Continuous stirred adsorber (CSTA) and packed bed column configurations were also tested for metal adsorption. The biosorbent regeneration was achieved by contacting it with strong acid (0.1 M HNO₃). A mass transfer model was applied with success to describe the biosorption/desorption process in CSTA and packed bed column, considering the equilibrium given by the Langmuir equation/mass action law and film and intraparticle diffusion resistances.     

Diffusion mechanism of water vapour in a zeolitic tuff rich in clinoptilolite

The adsorption kinetics of H₂O in a clinoptilolite rich zeolitic tuff was experimentally investigated at 18°C. In the identification of the diffusion mechanism the isothermal adsorption model equation was used. It was found out that the intraparticle mass transfer becomes more dominant over the heat transfer with increase in particle size and the adsorptive dose pressure. Although initially intraparticle mass transfer was the controlling resistance later external heat transfer also contributes to the transfer mechanism.     

Single component and binary diffusion of n-heptane and toluene in SBA-15 materials

In this work, the diffusion properties of single component n-heptane and toluene as well as their binary mixtures in two SBA-15 samples with different structural characteristics were studied by the standard Zero Length Column (ZLC) technique under three different concentration levels. A theoretical ZLC desorption model considering the Generalized Maxwell-Stefan (GMS) formulation was developed. Using the independently measured single component equilibrium and kinetic parameters, the model was able to reasonably predict experimental binary ZLC desorption curve for countercurrent diffusion of toluene in the presence of n-heptane. However, there was a significant deviation between model prediction results and experimental data for countercurrent desorption of n-heptane in the presence of toluene. The diffusion of n-heptane is reduced by the presence of toluene, regardless of the relative content of micropores in the intrawall pores, while that of toluene is virtually unaffected by the counter-diffusion of n-heptane. The observed phenomena cannot be addressed by the simple model considering the cross term diffusion effect. The structural property of material and the molecular characteristics of probe molecules were used to account for the difference in the behavior between n-heptane and toluene.     

Transport Properties of Ethane, Butanes and Their Binary Mixtures in MFI-Type Zeolite and Zeolite-Membrane Samples

Transport properties of ethane, butane and their binary mixtures in large crystals of silicalite-1, ZSM-5, and an MFI-zeolite membrane as well as agglomerates (pellets) of silicalite zeolites have been investigated by the Zero Length Column (ZLC) method. It was found that in the large crystals of silicalite-1 and ZSM-5, and in the membrane sample desorption of iso-butane was controlled by micropore diffusion, while in the case of pelleted silicalite sample it was controlled by macropore diffusion. The effective thickness of the zeolite membrane can be reasonably evaluated by comparing the diffusivity data obtained from the ZLC and gas permeation measurements. Desorption of ethane and n-butane in the large crystals of silicalite-1 and ZSM-5 and the membrane sample is attributed to both equilibrium effects and micropore diffusion. The diffusivity of ethane is significantly reduced in the presence of iso-butane giving rise to a micropore diffusion-controlled process. Furthermore, diffusion of iso-butane in the zeolite samples is affected by the counter flow of ethane.     

Kinetic study of the mass transfer of S-Tr?ger's base in the system cellulose triacetate and ethanol.

A recent study of the mass transfer kinetics of (-)- or S-Tr?ger's base (TB) between ethanol and microcrystalline cellulose triacetate (CTA) allows an analysis of the concentration dependence of the mass transfer rate coefficient (k(m)). S-TB elutes before R-TB. The retention time of the both compounds decreases with increasing temperature. In this study, experimental data measured between 30 and 50 degrees C were analyzed to provide information on the kinetics of several mass transfer processes which take place in the chromatographic column, i.e., axial and intraparticle dispersion, the fluid-to-particle mass transfer, and the kinetics of adsorption/desorption at the actual adsorption sites. Intraparticle diffusion has the dominant contribution to band broadening at high flow-rates. Both intraparticle diffusivity and the surface diffusion coefficient exhibit a small concentration dependence. The positive dependence of k(m) on the concentration of S-TB seems to result from the properties of the adsorption/desorption kinetics and can be interpreted by considering the phase equilibrium properties. A quantitative analysis of the activation energy of the mass transfer kinetics of S-TB in the CTA column was also attempted.     

Comparison of the mass transfer in totally porous and superficially porous stationary phases in liquid chromatography

The characterization of mass-transfer processes in a chromatographic column during a separation process is essential, since the influence of the mass-transfer kinetics on the shape of the chromatographic band profiles and on the efficiency of the separation is crucial. Several sources of mass transfer in a chromatographic bed have been identified and studied: the axial dispersion in the stream of mobile phase, the external mass-transfer resistance, intraparticle diffusion, and the kinetics of adsorption–desorption. We measured and compared the characteristics and performance of a new brand of shell particles and those of a conventional brand of totally porous silica particles. The shell stationary phase was made of 2.7-μm superficially porous particles (a 1.7-μm solid core is covered with a 0.5-μm-thick shell of porous silica). The other material consisted of totally porous particles of conventional 3.5-μm commercial silica. We measured the first and second central moments of the peaks of human insulin over a wide range of mobile phase velocities (from 0.02 to 1.3 mL/min) at 20°C. The plate height equations were constructed and the axial dispersion, external mass transfer, as well as the intraparticle diffusion coefficients were calculated for the two stationary phases.     

Kinetic study of the mass transfer of bovine serum albumin in anion-exchange chromatography

A kinetic study was made on the mass transfer phenomena of bovine serum albumin (BSA) in two different anion-exchange columns (Resource-Q and TSK-GEL-DEAE-5PW). The analysis of the concentration dependence of the lumped mass transfer rate coefficient (km,L) provided the information about the kinetics of the several mass transfer processes in the columns and the anion exchangers, i.e., the axial dispersion, the fluid-to-particle mass transfer, the intraparticle diffusion, and the adsorption/desorption. In the Resource-Q column, the intraparticle diffusion had a dominant contribution to the band broadening compared with those of the other processes. The surface diffusion coefficient (Ds) of BSA showed a positive concentration dependence, by which the linear dependence of km,L on the BSA concentration seemed to be interpreted. On the other hand, in the TSK-GEL-DEAE-5PW column, the contribution of the adsorption/desorption was also important and almost same as that due to the intraparticle diffusion. There are some differences between the intrinsic properties of the mass transfer kinetics inside the two anion exchangers. It was likely that the positive concentration dependence of Ds was explained by the heterogeneous surface model.     

The development of a new LDF mass transfer correlation for adsorption in fixed beds

In this study, a general LDF model has been introduced to predict mass transfer rate through adsorbents with the macropore diffusion as the controlling step. Using this relation eliminates the need for solving the time-consuming diffusion equation to find mass transfer rate through the porous adsorbent. The proposed relation was successfully applied in the general mathematical model for an adsorption fixed bed. This correlation was adjusted to be capable of predicting the mass transfer rate in a wide range of gas adsorption systems reported in the literature. This correlation was used in 21 different adsorbent and adsorbate systems. The results demonstrated an excellent agreement between the correlation results and those obtained using Fickian diffusion equation. By applying the developed LDF model instead of diffusion model, a great deal of CPU time can be saved. The latter characteristic will be very important when this model is employed in commercial software such as Aspen Adsorption or Prosim Dynamic Adsorption Column.     

Effect of macropore convection on mass transfer in a bidisperse adsorbent particle

The importance of adsorption induced convection in the macropores of a bidisperse adsorbent particle is studied for a step change in mole fraction or total pressure at the surface of the particle. Material balance equations for a binary gas mixture are written for both the macropores and the macropores with allowance for convection in the macropores, which is described by Darcy's law. The coupled set o1' partial differential equations is solved by orthogonal collocation. The enhancement in mass transfer as a result of convection is assessed by comparing the fractional uptake curves obtained with and without allowance for convection. Both equilibrium-based and kinetic-based separation processes are considered. The effect of the presence of convection in determining the controlling diffusional resistance (macropore or micropore) is also examined. Due to inclusion of convection no single non-dimensional group alone can determine the relative importance of macropore and micropore resistances. Results show that convection can significantly affect the performance of an equilibrium-based macropore diffusion controlled process and that the enhancement in mass transfer is more for a particle with a high value of Darcy permeability.     

Patterns of protein adsorption in chromatographic particles visualized by optical microscopy

A new method is presented to image transient patterns of protein adsorption in individual spherical chromatographic particles under strong binding conditions. The method takes advantage of the difference in refractive index between the protein-free and protein-saturated adsorbent matrix. When the particles are viewed with an ordinary microscope using white light illumination, the adsorption front appears as a bright ring that moves in time from the surface of the particle to its center. Experimental data are obtained for the proteins lysozyme and albumin with a commercial agarose-based cation exchanger. Sharp rings are observed in both cases confirming that protein mass transfer within the particles occurs via a shell-progressive diffusion mechanism. Quantitative analysis based on the shrinking core model provides an accurate and precise way of determining the intraparticle diffusivity for individual particles as a function of protein concentration and mobile phase composition.     

Heat Transfer Enhancement on the Adsorber of Adsorption Heat Pump

Three methods for improving the heat transfer of the adsorber have been developed in this paper. First, an electrically conductive polyaniline was applied for enhancing the thermal conductivity of adsorbent bed. A thermally conductive composite of polyaniline and adsorbent was prepared by chemical oxidative in situ polymerization of aniline onto the surface of adsorbent particles. A thin thermal conducting net on the surface of the adsorbent particles was grown. The experimental results indicated that the thermal conductivity of this composite could be increased to approximately 4 times that of the raw adsorbent. Second, the adsorbent bed was shaped by a compressing process. This process can reduce the thermal resistance among the adsorbent particles and the contact thermal resistance between the adsorbent bed and the heat exchanger. The thermal conductivity of the shaped adsorbent bed itself from the tests can be increased 30% when the density of the solid adsorbent bed is 1.5 times that of its original density. Furthermore, the adsorption capacity of the above treated adsorbent did not decrease obviously. Third, a proper design of adsorber has been introduced and analyzed. Further tests of this design will be conducted soon.     

Hypercross-linked polystyrene and its potentials for liquid chromatography: a mini-review

A recently introduced method [Biotechnol. Prog. 13 (1997) 429] for determining intraparticle mass transfer parameters in high speed liquid chromatography is considered in the present study for the case where the eluite adsorbs onto the stationary phase. The validity of the method was verified theoretically using simulated elution profiles and then applied to experimental data obtained using columns packed with either a macroporous or a gel-filled gigaporous stationary phase. For this purpose, experimental measurements were made using alpha-lactalbumin and bovine serum albumin as eluites at several retention factors. Apparent intraparticle diffusivities measured for the gel-filled gigaporous stationary phase were seen to increase with the retention factor, which indicates that for this material surface diffusion is a significant mechanism of mass transfer under retained conditions. Data obtained on the macroporous stationary phase revealed that the intraparticle diffusivity was independent of the retention factor, which suggests that pore diffusion remains the principal mass transfer mechanism even under conditions where proteins are adsorbed on the column packing.     

Sorption of basic dyes onto granulated pillared clays: thermodynamic and kinetic studies

Effect of the granulation process onto the thermodynamic and kinetic sorption parameters of two basic dyes (Basic Yellow 28-BY 28 and Basic Green 4-BG 4) was evaluated in the present work. The charge surface properties of the surfactant-modified aluminium-pillared clay (CTAB-Al-Mont-PILC) particles were not modified, and the isoelectric point remains constant after high shear wet granulation. The Gibbs free energy of both BY 28 and BG 4 sorption was negative and decreased with the granulation; the endothermic nature of the sorption process was confirmed by the positive values of ΔH°. Adsorption kinetics of the two dyes, studied at pH 6 and 150 mg L(-1), follow the pseudo-first order kinetic model with observed rate constants of 2.5-4.2×10(-2) min(-1). The intraparticle diffusion model, proposed by Weber and Morris, was applied, and the intraparticle plots revealed three distinct sections representing external mass transfer, intraparticle diffusion and adsorption/desorption equilibrium. Diffusion coefficients, calculated from the Boyd kinetic equation, increased with the granulation and the particle size. Pseudo-first order kinetic constants, intraparticle diffusion rate constants and diffusion coefficients were determined for two other initial concentrations (50 and 100 mg L(-1)) and include in a statistical study to evaluate the impact of granulation and initial concentration on the kinetic parameters. Kruskal-Wallis tests, Spearman's rank order correlation and factor analysis revealed a correlation between (i) the diffusion coefficients and granulation, and between (ii) the intraparticle diffusion rate constants and initial concentration.     

STOCHASTIC MODEL OF PERIODIC OPERATION PERFORMANCE FOR THE CONTINUOUS COUNTER—CURRENT ADSORPTION PROCESS

A stochastic model is developed to predict the periodic operation per formance of the continuous counter-current adsorption process.The model takes into account the effects of random backmixing of particles,axial dispersion of liquid phase,liquid-film mass transfer,intraparticle diffusion and particle shape,and can reveal clearly the behavior of solid and liquid phase in adsorption process.The simulation results agree with the experimental data rather well.     

Direct Red 28 Adsorption on Amosil and <Emphasis Type="Italic">Avena sativa </Emphasis> L.: Mass Transfer and Kinetics Modelling on the Solid/Solution Interface

Adsorption kinetics is a key issue for successful sorbent selection and the proper design of batch and fixed-bed adsorption systems. The aim of the present study was to determine the kinetics, mass transfer and diffusion coefficients and to establish the rate-controlling mechanism/s during Direct Red 28 adsorption on Amosil and Avena sativa L. biomass. Five kinetic models (pseudo-second order, Blanchard, Avrami, Ritchie and power function) and and four mass transfer (external diffusion, film diffusion, particle diffusion, intraparticle diffusion) mathematical models were applied to the experimental data. To confirm the best-fitting model(s), error analyses were conducted. The integrative comparative analyses of the values of the predicted model parameters, coefficients and error functions established that the intraparticle diffusion model best represented the experimental results of the dye sorption on dried A. sativa L. biomass, while for the Direct Red 28/Amosil system, the kinetic behavior is the best described by either the pseudo-second or Blanchard’s model. Boyd’s effective intraparticle diffusion coefficient (D _i ), characterizing the dye sorption on Amosil, is significantly lower than that for the system Direct Red 28/A. sativa L. biomass. The low values of the Bi number (Bi < 0.5) suggests that the mass transfer resistance, for both systems, is concentrated at the fluid/solid phase surface.     

Novel general expressions that describe the behavior of the height equivalent of a theoretical plate in chromatographic systems involving electrically-driven and pressure-driven flows

Novel general expressions are constructed and presented that describe the behavior of the height equivalent of a theoretical plate (plate height), H, as a function of the linear velocity, Vx, along the axis, x, of the column and the kinetic parameters that characterize the mass transfer and adsorption mechanisms in chromatographic columns. Open tube capillaries as well as columns packed with either non-porous or porous particles are studied. The porous particles could have unimodal or bimodal pore-size distributions and intraparticle convective fluid flow and pore diffusion are considered. The expressions for the plate height, H, presented in this work could be applicable to high-performance liquid chromatography (HPLC) and capillary electrochromatography (CEC) systems, and could be used together with experimental plate height, H, versus linear velocity, Vx, data to determine the values of the parameters that characterize intraparticle convective fluid flow and pore diffusion. Furthermore, chromatographic systems under unretained as well as under retained conditions are examined. The experimental values of the plate height, H, versus the linear velocity, Vx, for a CEC system involving charged porous silica C8 particles and an uncharged analyte are compared with the theoretical results for the plate height, H, obtained from the expressions presented in this work. The agreement between theory and experiment is good, and the results indicate that the magnitude of the intraparticle electroosmotic flow (EOF) in the pores of the particles is substantial while the pore diffusion coefficient was of small magnitude. But the overall intraparticle mass transfer resistance in these particles was low because of the significant contribution of the intraparticle EOF. Simulation results are also presented (i) for a hybrid HPLC-CEC system, and (ii) for different CEC systems involving open capillaries as well as packed columns having non-porous or porous particles. The analysis of the results indicates (a) the reasons for the superior performance exhibited by the hybrid HPLC-CEC system over the performance obtained when the system is operated only in the HPLC mode, and (b) the operational configuration and the properties that the structure of the porous particles would have to have in CEC systems involving uncharged or charged analytes under unretained or retained conditions in order to obtain high CEC efficiency (low values of the plate height, H).