Axial Diffusion Model Research Articles

Breakthrough Model of Recombinant Human-Like Collagen in Immobilized Metal Affinity Chromatography

The adsorption of recombinant human-like collagen by metal chelate media was investigated in a batch reactor and in a fixed-bed column. The adsorption equilibrium and kinetics had been studied by batch adsorption experiments. Equilibrium parameters and protein diffusivities were estimated by matching the models with the experimental data. Using the parameters of equilibrium and kinetics, various models, such as axial diffusion model, linear driving force model, and constant pattern model, were used to simulate the breakthrough curves on the columns. As a result, the most suitable isotherm was the Langmuir-Freundlich model, and the ionic strength had no effect on the adsorption capacity of chelate media. In addition, the pore diffusion model fitted very well to the kinetic data. The pore diffusivities decreased with increasing the initial protein concentration, however had little change with the ionic strength. The results also indicated that the models predict breakthrough curves reasonably well to the experimental data, especially at low initial protein concentration (0.3 mg ml(-1)) and low flow rate (34 cm h(-1)). By the results, we optimized the experimental conditions of a chromatographic process using immobilized metal affinity chromatography to purify recombinant human-like collagen.

A simple technique to characterize proximal and peripheral nitric oxide exchange using constant flow exhalations and an axial diffusion model

The most common technique employed to describe pulmonary gas exchange of nitric oxide (NO) combines multiple constant flow exhalations with a two-compartment model (2CM) that neglects 1) the trumpet shape (increasing surface area per unit volume) of the airway tree and 2) gas phase axial diffusion of NO. However, recent evidence suggests that these features of the lungs are important determinants of NO exchange. The goal of this study is to present an algorithm that characterizes NO exchange using multiple constant flow exhalations and a model that considers the trumpet shape of the airway tree and axial diffusion (model TMAD). Solution of the diffusion equation for the TMAD for exhalation flows >100 ml/s can be reduced to the same linear relationship between the NO elimination rate and the flow; however, the interpretation of the slope and the intercept depend on the model. We tested the TMAD in healthy subjects (n = 8) using commonly used and easily performed exhalation flows (100, 150, 200, and 250 ml/s). Compared with the 2CM, estimates (mean +/- SD) from the TMAD for the maximum airway flux are statistically higher (J'aw(NO) = 770 +/- 470 compared with 440 +/- 270 pl/s), whereas estimates for the steady-state alveolar concentration are statistically lower (CA(NO) = 0.66 +/- 0.98 compared with 1.2 +/- 0.80 parts/billion). Furthermore, CA(NO) from the TMAD is not different from zero. We conclude that proximal (airways) NO production is larger than previously predicted with the 2CM and that peripheral (respiratory bronchioles and alveoli) NO is near zero in healthy subjects.

Modeling of the linear-gradient dye-ligand affinity chromatography with a binary adsorption isotherm

A mathematical model for the linear gradient elution chromatography of a binary protein system was established based on the axial dispersion theory and pore diffusion model. Bovine serum albumin (BSA) and hemoglobin (Hb) were used as model proteins and Cibacron blue 3GA (CB) modified Sepharose CL-6B (CB-Sepharose) was used as adsorbent. The binary adsorption isotherms of the proteins were expressed by the steric mass-action (SMA) formulism, and its parameters were determined by batch adsorption equilibrium experiments of each protein. With all the model parameters determined by independent experiments or calculated from available correlations, model simulations were performed and compared with the chromatograms of the single-component and binary protein systems. It was found that the model predictions agreed reasonably well with the experimental data obtained under various conditions. The results indicate that the binary SMA formulism with its parameters determined by single-component equilibrium experiments was useful for simulation of nonlinear chromatography.

Membrane extraction for sulfanilic acid removal from waste water

The flow characteristics in hollow fiber modules (HFMs) were studied using resident time distribution (RTD) curves, which showed that the actual flow was nonideal and conformed to neither the ideal plug flow nor the complete mixed-flow models. Axial dispersion was found to decrease with an increase in flow velocity on the tube side and to increase with an increase in flow velocity on the shell side. Good agreement between the curves calculated using an axial diffusion model and experimentally determined RTD curves showed that the diffusion model can be used to describe the mass transfer characteristics in HFMs. In the study using 20% trioctylamine+30% octanol+50% kerosene–sulfanilic acid–water as actual extraction process, it was found that axial dispersion was the cause of the significant decrease in mass transfer performance. The resistance to mass transfer is located mainly in the boundary layer of aqueous phase. The large amount of treatment suggested that sulfanilic acid removal from its wastewater by HFM was an efficient process.

Boundary conditions for column flotation —A study by transfer function representation of an axial diffusion model

The boundary conditions for an axial diffusion model were overviewed and then modified concerning the pulp layer boundaries in a flotation column. It has been confirmed through the transfer function representation that the four general boundary conditions for an axial diffusion model correspond to the particular cases of Wehner and Wilhelm's, which considers not only the reaction section itself but also those of its top and bottom sides. Various mathematical models have been proposed for the pulp layer in a flotation column and the most popular one may be an axial diffusion with first order reaction model of one stage. They are, however, unable to estimate the behaviors of free particles which have not attached to bubbles at the pulp-froth interface. In this study, therefore, the authors, represented the transportation of free particles in the pulp layer of a flotation column by the two-stage axial diffusion with first order reaction model. The Wehner and Wilhelm's, as well as Danckwerts' boundary conditions have been partly modified and then applied to the feed point, the pulp-froth interface and the tailing discharge point of the flotation column. The proposed models and their boundary conditions made it possible to estimate the behaviors of free particles at the pulp-froth interface.

カラム浮選における境界条件について 一軸拡散モデルの伝達関数表示による考察

Abstract The boundary conditions for an axial diffusion model were overviewed and then modified concerning the pulp layer boundaries in a flotation column. It has been confirmed through the transfer function representation that the four general boundary conditions for an axial diffusion model correspond to the particular cases of Wehner and Wilhelm's, which considers not only the reaction section itself but also those of its top and bottom sides. Various mathematical models have been proposed for the pulp layer in a flotation column and the most popular one may be an axial diffusion with first order reaction model of one stage. They are, however, unable to estimate the behaviors of free particles which have not attached to bubbles at the pulp-froth interface. In this study, therefore, the authors, represented the transportation of free particles in the pulp layer of a flotation column by the two-stage axial diffusion with first order reaction model. The Wehner and Wilhelm's, as well as Danckwerts' boundary conditions have been partly modified and then applied to the feed point, the pulp-froth interface and the tailing discharge point of the flotation column. The proposed models and their boundary conditions made it possible to estimate the behaviors of free particles at the pulp-froth interface.

実操業カラム浮選プロセスの機能分析 ２段一軸拡散モデルを利用した考察

実操業カラム浮選プロセスの機能分析 ２段一軸拡散モデルを利用した考察

Neutral pumping in a helicon discharge

At powers of 500-800 W of 13.56 MHz rf power in a 1 kG axial magnetic field, the neutral pressure in the bulk of a helicon discharge with electron densities of and electron temperatures of eV in argon decreased by a factor of ten compared to the pressure before the discharge. These experimental results are compared with a simple axial diffusion model of ionization and neutral transport and agree qualitatively with calculated axial profiles of neutral pressure. The effects of cusped fields on neutral density profiles and plasma confinement are also examined.

Effective mass diffusion over cell boundaries in a Taylor-Couette flow system

Effective mass diffusion over cell boundaries in a Taylor-Couette flow system was investigated ranging from singly periodic wavy vortex flow to weakly turbulent wavy vortex flow by a salt-solution tracer technique. In order to determine experimentally the intercell mixing coefficient k CB between the neighbouring pairs of vortices, an appropriate model was formulated. As a result, k CB depends not only on Taylor number but also on axial wavelength with fluid viscosity. In the singly periodic wavy vortex flow region, the intermixing is enhanced by periodic fluctuations resulting from azimuthally travelling waves on the cell boundaries. With increasing Taylor number in the doubly periodic wavy vortex flow and weakly turbulent wavy vortex flow regions, the mixing characteristics go toward axial turbulent diffusion. In these two flow regions, the correlation between k CB and effective diffusion coefficient D z based on an axial diffusion model has been obtained as D z = 2 λk CB .

A study of fluid dispersion in oscillatory flow through a baffled tube

AbstractPrevious studies show that axial dispersion in steady laminar flow can be substantially reduced by superimposing fluid oscillation in a baffled tube. In this paper, experimental observations on fluid dispersion for oscillatory flow in a baffled tube are obtained in a series of concentration measurements using high spatial resolution local conductivity probes, and two models—the continuous stirred tank (CST) with feedback and the plug flow with axial dispersion—are used to analyse the concentration curves and determine the fluid dispersion for such a system. The CST with feedback model combines the algorithms from Mecklenburgh and Hartland with the evaluations of unbiased moments from Anderssen and White to determine the dimensionless dispersion coefficient, D/uL, and the backmixing coefficient, F. The plug flow with axial dispersion model, on the other hand, utilises the axial diffusion model by replacing the molecular diffusion coefficient to the axial dispersion coefficient. This model uses an upstream concentration measurement together with an imperfect pulse technique to predict a downstream concentration profile, and thereby determine a best fit value for the dispersion coefficient D/uL. The axial dispersion results show that there is generally more dispersion predicted using the plug flow with axial dispersion model than when using the CST with feedback model for all the oscillatory Reynolds numbers and Strouhal numbers tested. The difference in the calculated D/uL between the two models is discussed.

SIZE DISTRIBUTION OF CRYSTALS FROM CLASSIFIED BED TYPE CRYSTALLIZER

The concentration of particular size throughout the bed was experimentally studied on a fluidized bed of glass beads with an acrylic column of 50 mm diameter and 1000 mm height, and analyzed by the application of the axial diffusion model for particles of two sizes. From the experimental results, it was found that the axial distribution of void fraction might become that calculated by the assumption of perfect classification for the range of present conditions. The estimation method of size distribution of crystals from a classified-bed crystallizer is proposed on the axial diffusion model, using the relation between crystal size and bed height under the assumption of perfect classification in the author''s previous report. It is shown that the size distribution of sodium chlorate crystals from a test plant and sodium sulfate from pilot and industrial plants of this type agree with the calculated results from the model.

The dynamics of a packed gas absorber by the pulse response technique

AbstractThe dynamic response of a packed gas absorber to inlet gas composition changes was investigated by the pulse response technique for the case where absorption was accompanied by pseudo first‐order irreversible chemical raction.The solute‐carrier‐solvent system was carbon dioxide‐air‐0.07 normal aqueous sodium hydroxide solution. The column used was 6.5 in. I.D. Plexiglass packed to a height of 6.15 ft. with either ¼‐in. Raschig rings or ¾‐in. Berl Saddles. Gas flow rates ranged from 1.5 to 10 lb.‐moles/hr./sq.ft. and liquid flow rates ranged from 0 to 200 lb.‐moles/hr./sq.ft. A pulse of carbon dioxide was injected into the inlet air stream and monitored as it entered the packed section. The outlet gas and liquid phase concentrations were continuously monitored as the resulting pulses left the packed section. The pulse response data were reduced to frequency response by digital computer calculations. Reliable data could be obtained over the frequncy range 0 to 5 radians/second.The experimental results were compared with theoretical predictions from the slug flow, axial diffusion, and mixing cell models. Both the mixing cell model and the axial diffusion model satisfactorily predicted the experimental frequency responses over the entire frequency range covered. The slug flow model was found unsatisfactory for predicting gas‐phase amplitude ratios at high frequencies, where axial mixing affected the amplitude ratios. Gas‐phase particle Peclet numbers and overall mass transfer coefficients based on the gas‐phase driving force determined in the present absorption system were in reasonable agreement with the values reported in the literature.

On the applicability of the Taylor—Aris axial diffusion model to tubular reactor calculations

The relationship between the one dimensional Taylor—Aris model and the more detailed diffusion model for the steady state behavior of a tubular reactor is studied for the case of laminar flow and a first order reaction. It is shown that: (1) the Taylor—Aris model is valid provided that ka 2/3·8 2 D < 1; (2) the mean concentration computed using the Taylor—Aris model should be identified as the mean in the plane, C m , and the net flux across any plane perpendicular to the axis of the reactor is C m −[( a 2 U 2/48 D) + D] (∂ C m /∂ z); for large N pe the inlet condition. C m (0) = 1−( ka 2/ D)(1/48+1/ N 2 Pe ), seems to yield better results than the Wehner—Wilhelm boundary condition; and the zero gradient boundary condition is not the proper one to use at the outlet end of the reactor. It seems to be more appropriate to simply truncate a semi-infinite solution.

The influence of axial dispersion on carbon dioxide absorption tower performance

AbstractCarbon dioxide was absorbed from mixtures with nitrogen by countercurrent contact with water in an experimental packed tower. Radial and axial gas concentration profiles were determined from measurements made within the packing. Substantial gas phase channeling was observed. Characterizing the gas flow regime by both piston flow and axial diffusion models yielded mass transfer data and computed axial gas concentration profiles. Differences between the mass transfer results for the two models allowed the influence of axial dispersion to be assessed. Comparison of the piston flow and axially dispersed profiles with the experimental profiles enabled conclusions to be drawn regarding the applicability of the axial diffusion model and the accuracy of available dispersion parameter values.The axial diffusion model appears to be a satisfactory representation of the process. The dispersion coefficients used were found to be too high, which emphasizes shortcomings in the transient response experiments yielding dispersion coefficients. The influence of dispersion on the performance was found to be only moderately adverse. The effect increases with increasing liquid rate, decreasing gas rate, and decreasing packing height. It is improbable that the effect is large enough to account for the difference between industrial scale performance and that predicted from available mass transfer correlations.