Dependence on effective saturation of numbers of singlet peaks in one- and two-dimensional separations

The average numbers of singlet peaks in one-dimensional (1D) and two-dimensional (2D) separations of randomly distributed peaks are predicted by statistical-overlap theory and compared against the effective saturation. The effective saturation is a recently introduced metric of peak crowding that is more practitioner-friendly than the usual metric, the saturation. The effective saturation absorbs the average minimum resolution of statistical-overlap theory, facilitating the comparison of 1D and 2D separations by traditional metrics of resolution and peak capacity. In this paper, singlet peaks are identified with maxima produced by a single mixture constituent. Their effective saturations are calculated from published equations for the average minimum resolution of 1D singlet peaks, and from equations derived here for the average minimum resolution of 2D singlet peaks. The fractions of peaks that are singlets in 1D and 2D separations are predicted by statistical-overlap theory as functions of saturation but are compared as functions of effective saturation. The two fractions differ by no more than 0.033 at any effective saturation between 0 and 6, when the distribution of peak heights is exponential and the edge effect is neglected. This result shows that 1D and 2D separations of randomly distributed peaks are about the same in their ability to separate singlet peaks as maxima, when assessed relative to effective saturation. Empirical equations in effective saturation are reported for the fractions of peaks that are singlets. It is argued that the effective saturation is a good metric for comparing separations having different average minimum resolutions.     

Fluidization in tapered vessels

Methods for the prediction of bed height and pressure drop in tapered air-fluidized beds are proposed. A comparison was made with measurements in slugging fluidized beds in the slow bubble regime over a wide range of apex angle from 0° (rectangular) to 45°. The bed height and pressure drop are well predicted by each of the proposed methods using the same constant values of bubble rise velocity and fluctuation ratio as for the rectangular fluidized bed with the same distributor geometry.     

Efficiency of preparative and process column distribution systems

An analytical method for computing the residence time distribution of the liquid distribution system in chromatography columns is described. The impact of the distributor design on the separation efficiency is predicted as a function of media properties and packed bed dimensions. The efficiency loss due to the distributor when increasing column diameter during scale-up is quantified. It is shown that this loss can be compensated by modulating the local bed height via a moderate inclination of the bed support. It is concluded that the selection of an appropriate distributor design concept with optimised dimensions enables a scale-up of chromatographic separations without any significant loss of chromatographic efficiency due to the distribution system.     

Surface anchoring and the saturation behaviour of a NLC cell under external electric and magnetic fields

Based on the modified Rapini-Papoular formula for surface anchoring energy, the saturation behaviour of a weak anchoring nematic liquid crystal cell under electric and magnetic fields has been studied by the methods of analytical derivation and numerical calculation. The results show that the transition at saturation point may be second order, as many authors have predicted. However, it may also be first order. The condition for the first order transition is deduced; it is related to the anchoring parameters. The influence of anchoring on the saturation field strength is also discussed, both for second and for first orders; the results are shown by graphically.     

Fluidisation and dispersion behaviour of small high density pellicular expanded bed adsorbents

The fluidisation and dispersion properties of various agarose-based expanded bed matrices--small high density stainless steel cored prototypes and standard commercial types--were studied in 1-cm diameter expanded bed contactors in which fluid entering the column base is locally stirred. In all cases, fluidisation behaviour was poorly predicted from the Richardson-Zaki correlation, with experimentally determined values of the expansion index being considerably higher than the theoretical values. The resons for these discrepancies are discussed in detail and the validity of applying this widely used correlation for characterisation of expanded bed systems is questioned. Residence time distribution studies using acetone tracers, demonstrated that in comparison to existing commercial supports, the small pellicular prototype materials generally possessed far superior hydrodynamic properties, which augurs well for their future employment in expanded bed chromatographic separations.     

Evaluation of tertiary pyridine resin for the separation of lanthanides by simulated moving‐bed chromatography

Lanthanide separation by simulated moving‐bed chromatography was studied as a model system for separating lanthanide fission products and minor actinides from used nuclear fuels. The simulated moving‐bed system was modeled for a tertiary pyridine anion‐exchange resin supported on silica particles as the stationary phase and a mixture of methanol and 1M nitric acid as the mobile phase. Pulse injection tests using a single packed column were used to obtain chromatographic parameters for mathematical modeling of the simulated moving‐bed system. Higher concentrations of methanol improved the separation, but the chromatograms showed evidence of nonlinearity of the isotherms. The mathematical model of the simulated moving‐bed process predicted a production rate of purified samarium and neodymium at 118 g solute/L resin/day and a purity of 99.5%. The optimal methanol ratio for the production rate for various product purities was determined from the model. The excellent separation of Nd and Sm suggests that the simulated moving‐bed system could be applied to the separation of minor actinides such as americium and curium.     

Modeling of an immobilized-cell three-phase fluidized-bed bioreactor

A mathematical model of a three-phase, tapered, fluidized-bed bioreactor has been developed. This model includes the effects of the tapered bed, a variable dispersion coefficient, and the concentration profile inside the biocatalyst bead on the reaction rate within the bed. Parameters in this model were obtained by adjusting them, within a realistic range, such that the square of the difference between the values predicted by the model and those obtained experimentally was minimized. The model was found to predict experimentally obtained concentration profiles quite accurately. It also demonstrates the need to include the effects of variable dispersion in three-phase systems where the gas phase is being generated inside the reactor, as the dispersion coefficient varied by more than an order of magnitude across the bed.     

Designing Fixed Bed Column and Batch Studies of Chitosan Nanoparticles for Defluoridation of Drinking Water

The aim of present investigation was to prepare nanoparticles of chitosan and perform batch and column studies with them to study their defluoridation capacity. The nanoparticles of chitosan were characterized by techniques like FTIR, SEM, TEM, etc. Effect of initial fluoride concentration, adsorbent dose, pH and temperature were studied in the batch studies. Effect of bed height, flow rate, and inlet concentration on the column performance were studied. Performance of packed columns were described through the concept of breakthrough curves and column parameters were predicted as a function of bed heights. The breakthrough curves were defined by the Adams-Bohart and Wolborska models.     

Backfill Cycle of a Layered Bed H2 PSA Process

The backfill cycle of two-bed PSA process using activated carbon beds, zeolite 5A beds, and layered beds was studied experimentally and theoretically to recover high purity H₂ from coke oven gas. In a layered bed PSA, a comparison was made between two PSA processes with/without a backfill step before the feed pressurization step. Since the backfill step made the adsorption bed rich in H₂ and this led to a rather steep concentration wave front at the feed pressurization step, incorporating a backfill step resulted in an increase in product purity with a decrease in recovery. Each step of the single-adsorbent and layered bed PSA processes with a backfill step was simulated with a dynamic model incorporating mass, energy, and momentum balances. The model agreed well with the experimental results in predicting the product H₂ purity and recovery, thus giving a basic understanding of the bed dynamics of a backfill cycle. While the concentration and temperature profiles of a layered bed in each step showed characteristic behavior of each adsorbent in each layer, the product purity of a layered bed was not between the limits of two single-adsorbent bed processes. The concentration profiles predicted by simulation showed that CO and N₂ played an important role in obtaining high H₂ purity.     

Measurements and particle resolved modelling of the thermo- and fluid dynamics of a packed bed

The objective of this study is to investigate experimentally and numerically into heat-up, drying and pyrolysis of a packed bed consisting of large single particles. The novelty of the current approach is that the numerical model contrary to continuum mechanic approaches considers a packed bed as an ensemble of a finite number of particles, which may have different material properties or sizes. The heat-up, drying and pyrolysis process of each particle is described sufficiently accurate by a set of one-dimensional and transient differential conservation equations for mass and energy. Applying this model to all particles, including interactions between them, of a packed bed forms the entire backed bed process as a sum of individual particle processes. The arrangement of particles within a bed defines a void space between the particles. The flow through the void space of a packed bed is modelled as a flow through a porous media taking into account interaction between the solid and the gaseous phase by heat and mass transfer. Experiments for drying and pyrolysis of a packed bed were carried out for validation in a temperature range of T=120–530 °C. The temperatures and the mass loss due to drying and pyrolysis were recorded during the experiments. The measured mass loss of the packed bed due to drying were well predicted by the constant evaporation temperature model of the particles and thus, indicating, that the drying process is transport limited by heat transfer for large wood particles in a temperature range of T=120–530 °C. A comparison between experiments and predictions of pyrolysis yielded reasonable agreement for temperatures above T=300 °C. For temperatures of T≈200 °C the deviations were not acceptable. However, the results show, that a particle resolved approach is well suited to describe packed bed processes.     

Optimization of simulated moving bed plants with low efficient stationary phases: separation of fructose and glucose

An optimization procedure for simulated moving bed (SMB) plants with low efficient stationary phases is presented. The new aspect is that the desorbent consumption can be cut by 70% by running the plant with lower internal liquid flows and a corresponding larger switch time while the productivity is kept constant. This concept was validated by the separation of fructose and glucose in water on a calcium resin with an eight-column SMB plant. The separation can be predicted well by a true moving bed (TMB) and a simulated moving bed simulation. Adsorption isotherms were determined up to 300 kg/m3 for glucose and 500 kg/m3 for fructose from 25 to 80 degrees C. Experimental SMB runs were performed over a wide range of feed concentrations (10-350 kg/m3) and temperatures (25-80 degrees C). The strong influence of the delay volume is pointed out. For an experimental run with high feed concentration a complete set of data is presented. To reduce biological growth separation at 80 degrees C is recommended.     

流化床气化炉带出细粉非机械返料机构研究

对非机械返料机构（流动密封阀式）在流化床气化炉上的应用进行了研究。结果表明，流动密封阀式返料机构同样可以在流化床气化炉上应用；在返料室截面积、供料室截面积、水平孔口面积比为1∶1∶0.5时，通过流化风、松动风或侧吹风的组合充气获得了良好的开启、运行及调节性能；同时考察了压力对返料机构运行的影响；最后得到了适合流化床气化炉非机械返料机构操作的经验公式，试验值和计算值符合较好。对改进流化床气化炉循环返料系统和提高气化炉碳转化率提供了理论指导和设计参考。     

Electrokinetic coupling in unsaturated porous media

We consider a charged porous material that is saturated by two fluid phases that are immiscible and continuous on the scale of a representative elementary volume. The wetting phase for the grains is water and the nonwetting phase is assumed to be an electrically insulating viscous fluid. We use a volume-averaging approach to derive the linear constitutive equations for the electrical current density as well as the seepage velocities of the wetting and nonwetting phases on the scale of a representative elementary volume. These macroscopic constitutive equations are obtained by volume-averaging Ampère's law together with the Nernst-Planck equation and the Stokes equations. The material properties entering the macroscopic constitutive equations are explicitly described as functions of the saturation of the water phase, the electrical formation factor, and parameters that describe the capillary pressure function, the relative permeability functions, and the variation of electrical conductivity with saturation. New equations are derived for the streaming potential and electro-osmosis coupling coefficients. A primary drainage and imbibition experiment is simulated numerically to demonstrate that the relative streaming potential coupling coefficient depends not only on the water saturation, but also on the material properties of the sample, as well as the saturation history. We also compare the predicted streaming potential coupling coefficients with experimental data from four dolomite core samples. Measurements on these samples include electrical conductivity, capillary pressure, the streaming potential coupling coefficient at various levels of saturation, and the permeability at saturation of the rock samples. We found very good agreement between these experimental data and the model predictions.     

Adsorption of water vapour from humid air in carbon molecular sieves: carbosieve S-III and carboxens 569, 1000 and 1001

The adsorption of water vapour in carbon molecular sieves (CMS) used to determine volatile organic compounds (VOCs) in air was investigated. The CMS mass in the trap was found not to affect the mass of retained water under conditions of incomplete saturation of the adsorbent bed with water. Thus, the restrictions commonly imposed on the CMS mass are not necessary. The usefulness of four different CMSs to sample large volumes of humid air was estimated. Carboxen 1000 exhibited the best performance. To assess the magnitude of CMS mass in the trap in dependence on the volume, the relative humidity and the temperature of the sample, the use of a novel parameter, called the water vapour interference factor, was suggested.     

Effect of Operation Symmetry on Pressure Swing Adsorption Process

In a multi-bed pressure swing adsorption (PSA) process, cycle steps with gas flow transferring from one bed to another such as equalization, purge, etc. are generally practiced to enhance the product recovery. However, if the flows for the connected beds in these steps are not balanced, the PSA process may not operate in a symmetrical manner. In the modeling of the PSA process, most of the simulations consider only one bed and assume that the rest of the beds would behave in a same way. In order to assess the impact of bed symmetry on the PSA performance, a new PSA model capable of studying bed symmetry in a two-bed system is developed. Experimental results from this paper show that uneven equalization flow can result in a lower product purity and a peculiar purity curve at different equalization levels. This phenomenon can be successfully predicted by this model. Simulation results also show that in large-scale PSA units, asymmetrical operation can cause drastically different temperature profiles in different adsorbers and hence a much lower performance. This paper demonstrates the importance of maintaining operation symmetry in PSA processes.     

ODMR saturation techniques in the study of line broadening

The lineshapes of optically detected magnetic resonance (ODMR) spectra from two different, but complementary methods, are predicted using the geometrical model of Breiland and Harris. The ODMR spectra by differential saturation method of van der Velden and Veeman and the pre-saturation pulse technique are examined. Of particular interest are the ODMR spectra for which narrow dips upon a broad background are observed.     

稀土在土壤中运移数值模拟研究

９种不同性质土壤Ｃｅ和Ｎｄ吸附和度达５０％时，用同位素示踪法和数值模拟法对ＲＥ运移进行比较，发现两者对极大多数土壤有较好的拟合性。说明该数值模拟程序对预测稀土长期在土壤中运移具有一定的可靠性。预测结果表明，在自然降雨量情况下，ＲＥ吸附饱和度１０％时，在吸附容量小的酸性土壤中，ＲＥ下移约每年１ｃｍ，吸附容量中等的中性、策酸性土壤，每两年约下移１ｃｍ而吸附容量较大的碱性土壤，ＲＥ很难被雨水运移。     

The first order Freedericksz transition at saturation point for weak anchoring NLC cells

On the basis of the modified Rapini-Papoular expression for the anchoring energy, the properties of the transition at saturation point for weak anchoring NLC cells has been studied analytically. We find that this transition may be of second order, as is usually predicted by many authors; however, it may also be first order. Whether it is first or second order is determined by the material, anchoring energy and thickness of the cell. The conditions for first order transition are deduced by an analytical method, and the results of calculation are shown by graph for κ(= K 11 / K 33 ) values 0.8, 0.6 and 0.4. The saturation field strengths for the first order transition case are calculated and shown in the table.