Adsorption behavior and prediction of the band profiles of the enantiomers of 3-chloro-1-phenyl-1-propanol. Influence of the mass transfer kinetics

The single-component and competitive adsorption isotherms of the enantiomers of 3-chloro-1-phenyl-1-propanol were measured by frontal analysis. The stationary phase was a cellulose tribenzoate coated on silica, the mobile phase an n-hexane-ethyl acetate (95:5) solution. The adsorption data measured fitted well to the Langmuir isotherm model. The band profiles of single components and of their mixtures were calculated using the equilibrium-dispersive model. These profiles were found to match quite satisfactorily the experimental band profiles. However, the agreement between calculated and experimental band profiles was significantly improved when a more complex model taking into account the mass transfer kinetics was used. The mass transfer rate coefficients, k(f), for both single components were determined by using the transport-dispersive model of chromatography. The coefficients obtained were used to predict the band profiles of mixtures of the two enantiomers to good agreement.     

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.     

Influence of the particle porosity on chromatographic band profiles

The mass transfer kinetics of butyl benzoate, eluted on a monolithic RPLC column with methanol-water (65:35, v/v) as the mobile phase was investigated, using the perturbation method to acquire isotherm data and the mobile phase velocity dependence of the height equivalent to a theoretical plate of perturbation peaks to acquire kinetics data. The equilibrium isotherm of butyl benzoate is accounted for by the liquid-solid extended multilayer BET isotherm model. The total porosity of the column varies much with the butyl benzoate concentration, influencing strongly the parameters of its mass transfer kinetics and the profiles of the breakthrough curves. Using all these parameters, the general rate model of chromatography predicts band profiles and Van Deemter curves that are in excellent agreement with experimental results provided the influence of concentration on the porosity is properly taken into account. This agreement confirms the validity of the models selected for the isotherm and for the mass transfer kinetics.     

Extraction and re-extraction of phenylalanine by cationic reversed micelles in hollow fibre contactors

This work reports the extraction of phenylalanine with a reversed micellar system consisting of TOMAC/hexanol/n-heptane using hydrophobic hollow fibre modules. Extraction studies were performed under different hydrodynamic conditions and mass transfer correlations for the shell and tube sides were developed. The correlations were determined using a one-step calculation method and the results obtained are in agreement with the literature for the range of Reynolds numbers studied.Based on the obtained correlations and on the resistance in series model, a transport model was developed in which the phenylalanine concentration in the feed phase can be predicted during the experimental run. For the extraction process the model developed describes satisfactorily the evolution of phenylalanine concentration with time under different hydrodynamic conditions. The re-extraction process was found to be kinetically controlled due to the higher dynamic stability of reversed micelles when contacting a stripping phase with high ionic strength. The experimental results obtained were described using a kinetic model developed.Simultaneous extraction/stripping of phenylalanine was also accomplished using two hollow fibre modules in series, using different volume phase ratios. The mass transfer process was modelled and compared with the experimental results.     

Biosorption of Chromium(III) by Biomass of Seaweed Sargassum sp. in a Fixed-Bed Column

This work aimed at modeling chromium biosorption using the biomass of seaweed Sargassum sp. in a fixed-bed column. The mathematical model used was obtained from the mass balance of the component in the liquid phase and in the biosorbent material. The effects of both axial dispersion in the column and the resistance to mass transfer in the solid were considered for the solution of the partial differential equations of the model, using the Galerkin method on finite elements. To represent the equilibrium data of the batch system the Langmuir isotherm were used. The chromium ion adsorption capacity of the seaweed Sargassum sp., at a temperature of 30°C and pH 3.5, was 2.61 mmol/g. The model performance was evaluated from experimental data obtained at 30°C for flow rates of 2, 6 and 8 mL/min. The parameters of the model, mass transfer and axial dispersion coefficients, were adjusted from these experimental data. The model proved adequate to describe chromium biosorption dynamics in fixed-bed columns.     

Mathematical modelling for extraction of oil from Dracocephalum kotschyi seeds in supercritical carbon dioxide

Extraction of oil from Dracocephalum kotschyi Boiss seeds using supercritical carbon dioxide was designed using central composite design to evaluate the effect of various operating parameters including pressure, temperature, particle size and extraction time on the oil yield. Maximum extraction yield predicted from response surface method was 71.53% under the process conditions with pressure of 220 bar, temperature of 35 °C, particle diameter of 0.61 mm and extraction time of 130 min. Furthermore, broken and intact cells model was utilised to consider mass transfer kinetics of extracted natural materials. The results revealed that the model had a good agreement with the experimental data. The oil samples obtained via supercritical and solvent extraction methods were analysed by gas chromatography. The most abundant acid was linolenic acid. The results analysis showed that there was no significant difference between the fatty acid contents of the oils obtained by the supercritical and solvent extraction techniques.     

Evaluation of nonlinear chromatographic performance by frontal analysis using a simple multi-plate mathematical model

A multi-plate (MP) mathematical model was proposed by frontal analysis to evaluate nonlinear chromatographic performance. One of its advantages is that the parameters may be easily calculated from experimental data. Moreover, there is a good correlation between it and the equilibrium-dispersive (E-D) or Thomas models. This shows that it can well accommodate both types of band broadening that is comprised of either diffusion-dominated processes or kinetic sorption processes. The MP model can well describe experimental breakthrough curves that were obtained from membrane affinity chromatography and column reversed-phase liquid chromatography. Furthermore, the coefficients of mass transfer may be calculated according to the relationship between the MP model and the E-D or Thomas models.     

Influence of protein–protein interactions on bulk mass transport during ultrafiltration

Bulk mass transfer limitations can have a significant effect on the flux and selectivity during membrane ultrafiltration. Most previous studies of these phenomena have employed the simple stagnant film analysis, but this model is unable to account for the effects of solute–solute interactions on mass transport. We have developed a generalized framework for multicomponent mass transfer that includes both thermodynamic and hydrodynamic (frictional) interactions. Thermodynamic (virial) coefficients were evaluated from osmotic pressure data for albumin (BSA) and immunoglobulins (IgG), while hydrodynamic interaction parameters were determined from filtrate flux data obtained in a stirred cell using fully retentive membranes. The protein concentration profiles in the bulk solution were evaluated by numerical solution of the governing continuity equations incorporating the multicomponent diffusive flux. This model was used to analyze flux and protein transmission data obtained for the filtration of BSA and IgG mixtures through partially permeable membranes. The model accurately predicted the large reduction in flux and BSA transmission upon addition of IgG. These effects were due to the coupling between BSA and IgG mass transfer caused by protein–protein interactions.     

Analysis of model polyurethane thermolysis products by direct mass spectrometer sampling

The results obtained using a molecular beam direct sampling mass spectrometer system to determine the thermolysis products and investigate the decomposition kinetics of two model linear polyurethanes are reported. The polyurethanes are shown to degrade in this system strictly to the polycondensation reactants. These results conflict with previous research which indicated that the model polymers degraded by different mechanisms and yielded different degradation products. Kinetic analysis of results obtained from rapid thermolysis of the polymer in the ion source chamber of the pyrolysis mass spectrometer using the activation energy and frequency factor parameters deduced from thermogravimetric analysis of the same polymers reproduced the experimental data on decomposition as a function of time and temperature quite satisfactorily.     

加温加压条件下气液固三相鼓泡塔体积传质系数的测定

气液固三相鼓泡塔反应器被广泛地应用于化工、石油化工、煤化工、化工冶金、环境工程等领域,如石油馏分的加氢、煤的脱硫与脱氮、对二甲苯氧化、费托合成、甲醇合成、二甲醚合成以及含有机物废水的湿式氧化等工业过程[1.2].     

Theoretical background of short chromatographic layers. Optimization of gradient elution in short columns

Although linear salt gradient elution ion-exchange chromatography (IEC) of proteins is commonly carried out with relatively short columns, it is still not clear how the column length affects the separation performance and the economics of the process. The separation performance can be adjusted by changing a combination of the column length, the gradient slope and the flow velocity. The same resolution can be obtained with a given column length with different combinations of the gradient slope and the flow velocity. This results in different separation time and elution volume at the same resolution. Based on our previous model, a method for determining the separation time and the elution volume relationship for the same resolution (iso-resolution curve) was developed. The effect of the column length and the mass transfer rate on the iso-resolution curve was examined. A long column and/or high mass transfer rate results in lesser elution volume. The resolution data with porous bead packed columns and monolithic columns were in good agreement with the calculated iso-resolution curves. Although the elution volume can be reduced with increasing column length, the pressure drop limits govern the optimum conditions.     

Influence of microwave irradiation on the intraparticle diffusion of an insulin variant in reversed-phase liquid chromatography under linear conditions

The influence of microwave irradiation on the mass transfer kinetics of an insulin variant in reversed-phase liquid chromatography (RPLC) was investigated. The elution band profiles of insulin were obtained by the pulse-response method, under linear conditions. The RPLC column was placed in a microwave oven and the incremental change in the temperature of the column effluent stream at various microwave energies and mobile phase flow rates were measured. The microwave energy dissipated in the column was set at 15 and 30 W and the mobile phase flow rate was varied from 1.0 to 2.5 mL/min at a mobile phase composition of acetonitrile, water, and trifloroacetic acid (31:69:0.1, v/v/v). The experimental data were analyzed using the conventional method of moment analysis and the lumped pore diffusion model. Regardless of mobile flow rates, the effluent temperatures measured at 15 and 30 W microwave power input were 25+/-1 and 30+/-1 degrees C, respectively. The effect of microwave irradiation on the mass transfer of the variant insulin was determined by comparing the band profiles obtained under the same experimental conditions, at the same column temperature, with and without irradiation. The calculated intraparticle diffusion coefficient, D(e), at 30 W (30+/-1 degrees C) microwave irradiation was ca. 20% higher than without irradiation at 30+/-1 degrees C. These preliminary results suggest that microwave irradiation may have a significant influence on the intraparticle diffusion of insulin in RPLC.     

Investigation of the concentration dependence of mass transfer coefficients in reversed-phase liquid chromatography

In order to investigate the concentration dependence of mass transfer coefficients in RPLC, experimental breakthrough curves obtained by staircase frontal analysis (FA) were fitted to the simplified models such as multiplate (MP) model, equilibrium dispersive (ED) model, and transport model, and the sophisticated models such as lumped pore diffusion (POR) model and general rate (GR) model. The MP model was used to obtain the initial guesses of the parameters of the ED and the transport models. Then the best values were obtained by minimizing the differences between theoretical and experimental values with a nonlinear fitting procedure. The values of the parameters of the POR and the GR models can be calculated by using the expressions derived from the plate height equations, which was further validated by using the fitting method. It was found that the mass transfer coefficients would depend on the solute concentration. This can be ascribed to the surface diffusivity, which correlates with the concentration and is lumped into the mass transfer coefficients for both simplified and sophisticated models.     

Batch and continuous fixed-bed column biosorption of thorium(IV) from aqueous solutions: equilibrium and dynamic modeling

Biosorption of thorium(IV) from aqueous solution by Cystoseira indica alga was investigated in batch and fixed-bed column experiments. In the batch study the effects of pH and initial concentration were investigated. The optimum pH for Th(IV) biosorption was found to be 3.5. The experimental isotherms obtained at different pH conditions were analyzed using three two-parameter models and three three-parameter models. Among the two-parameter models the Langmuir model and among the three-parameter models the Redlich–Peterson model vividly described the equilibrium data. The results showed that C. indica alga is a homogeneous biosorbent and Th(IV) biosorption is a favorable and physical process. The maximum biosorption capacity from the Langmuir model was 151.3, 195.7 and 120.6 mg/g at pH 2.5, 3.5 and 4.5, respectively. The continuous isotherm obtained from the column data was modeled by the Langmuir model and the maximum biosorption capacity was 283.8 mg/g. The experimental data were fitted by the use of an analytical and a numerical model, namely Clark and mass transfer models. The results showed that the mass transfer model adequately described the experimental data. Sensitivity analysis revealed that the value of k _in has more effect than the axial dispersion coefficient (D _z) on the shape of breakthrough curve.     

Thermodynamic functions and intra-particle mass transfer kinetics of structural analogues of a template on molecularly imprinted polymers in liquid chromatography

The parameters of the thermodynamics and mass transfer kinetics of the structural analogues (L-enantiomers) of the template were measured on an Fmoc-L-tryptophan (Fmoc-L-Trp) imprinted polymer, at different temperatures. The equilibrium isotherm data and the overloaded band profiles of these compounds were measured at temperatures of 298, 313, 323, and 333 K. The isotherm data were modeled. The thermodynamic functions of the different adsorption sites were derived from the isotherm parameters, using van't Hoff plots. The mass transfer parameters were derived by comparing the experimental peak profiles and profiles calculated using the lumped pore diffusion (POR) model for chromatography. These data show that (1) the strength between the substrate molecules and the MIP increases with increasing number of functional groups on the substrates; (2) enthalpy is the driving force for the affinity of the substrates for the MIP; (3) surface diffusion is the dominant mass transfer mechanism of the substrates through the porous MIP. For those substrate molecules that have the same stereochemistry as the template, the energetic surface heterogeneity needs to be incorporated into the surface diffusion coefficients. Heterogeneous surface diffusivities decrease with increasing affinity of the substrates for the MIP.     

Integration of scale-down experimentation and general rate modelling to predict manufacturing scale chromatographic separations

Chromatography is an essential downstream processing step in the production of biopharmaceuticals. Here we present an approach to chromatography scale-up using scale-down experimentation integrated with general rate modelling. This type of modelling takes account all contributions to the mass transfer kinetics providing process understanding. The model is calibrated using a 2.5 cm height, 1 ml column and used to predict chromatograms for 20 cm height columns from 40 ml to 160 L volume. Simulations were found to be in good agreement with experimental results. The envisaged approach could potentially reduce the number of experiments, shorten development time and reduce costs.     

Shell-side mass transfer of hollow fibre modules in osmotic distillation process

The effect of packing density of hollow fibre modules on mass transfer in the shell side of osmotic distillation process was studied. The osmotic distillation experiments were carried out with several modules of the packing densities ranging from 30.6 to 61.2%. It was found that the Reynolds number was a function of packing density and packing density affected mass transfer performance. The shell-side mass transfer coefficient increased with the brine velocity. The membrane permeability can be predicted from the experimental flux at the maximum brine velocity. The mass transfer correlation was proposed in order to determine the shell-side mass transfer coefficient in the randomly packed modules for osmotic distillation process. The empirical correlation proposed was fitted to the experimental results and it was found that the mass transfer coefficients calculated from the proposed correlation were in good agreement with those from the experimental data. Comparison of the results obtained from the proposed correlation with other correlations in the literature was discussed.     

Simultaneous determination of two‐component isotherm parameters and lumped mass transfer coefficients in RPLC with the 0‐1 model‐inverse method

The 0‐1 model‐inverse method of nonequilibrium nonlinear chromatography was developed to simultaneously determine the isotherm parameters and the lumped mass transfer coefficients of the two‐component systems in RPLC. By comparing the simulated elution curves with experimental curves with regard to profiles and areas, the suitable isotherm parameters and the lumped mass transfer coefficients were obtained with the 0‐1 model‐inverse method. With a solute cell unit width of cm, the average errors of the peak areas were 0.178% for one component and ?0.40% for two components, and the numerical diffusions of the 0‐1 model for the contribution to band broadening may be negligible. In addition, the results showed that the lumped mass transfer coefficients decrease as the solute concentration increases. The 0‐1 model‐inverse method has not only the advantages of high calculation speed (less than 10 min for one‐component systems or approximately 3 h for two‐component systems using an ordinary computer) and high accuracy in simultaneously obtaining thermodynamic parameters and kinetic parameters of two‐component systems, but this method also possesses the potential to optimally design and control the time‐variant preparative chromatographic system due to the thermodynamic state recursion and the Lagrangian‐Eulerian presentation of the 0‐1 model.     

Mathematical modeling of seeded miniemulsion copolymerization for oil-soluble initiator

A mathematical model of seeded miniemulsion copolymerization of styrene-methyl methacrylate for oil-soluble initiator is presented. The mathematical model includes the mass transfer, from the miniemulsion droplets to the polymer particles, by both molecular diffusion and collision between miniemulsion droplets and the polymer particles. The mathematical model also includes the calculation of both the distribution of partices with i radicals and the average number of radicals per particle in the miniemulsion copolymerization using oil-soluble initator. Studies were carried out on the mass transfer coefficients of monomers across the interface between the miniemulsion droplet and the aqueous phase, hexadecane concentration in the miniemulsion droplets, the miniemulsion droplet sizes, and the collision between miniemulsion droplets. The results indicated that the copolymerization of styrene-methyl methacrylate was not a mass transfer controlled process. The mass transfer by collision between miniemulsion droplets and polymer particles plays an important role and was included in the model in order to predict the experimental data of seeded miniemulsion copolymerization.