Modeling of phase equilibrium and vapor adsorption on carbon black based on a combination of a lattice theory and equation of state

A thermodynamic approach is developed in this paper to describe the behavior of a subcritical fluid in the neighborhood of vapor-liquid interface and close to a graphite surface. The fluid is modeled as a system of parallel molecular layers. The Helmholtz free energy of the fluid is expressed as the sum of the intrinsic Helmholtz free energies of separate layers and the potential energy of their mutual interactions calculated by the 10-4 potential. This Helmholtz free energy is described by an equation of state (such as the Bender or Peng-Robinson equation), which allows us a convenient means to obtain the intrinsic Helmholtz free energy of each molecular layer as a function of its two-dimensional density. All molecular layers of the bulk fluid are in mechanical equilibrium corresponding to the minimum of the total potential energy. In the case of adsorption the external potential exerted by the graphite layers is added to the free energy. The state of the interface zone between the liquid and the vapor phases or the state of the adsorbed phase is determined by the minimum of the grand potential. In the case of phase equilibrium the approach leads to the distribution of density and pressure over the transition zone. The interrelation between the collision diameter and the potential well depth was determined by the surface tension. It was shown that the distance between neighboring molecular layers substantially changes in the vapor-liquid transition zone and in the adsorbed phase with loading. The approach is considered in this paper for the case of adsorption of argon and nitrogen on carbon black. In both cases an excellent agreement with the experimental data was achieved without additional assumptions and fitting parameters, except for the fluid-solid potential well depth. The approach has far-reaching consequences and can be readily extended to the model of adsorption in slit pores of carbonaceous materials and to the analysis of multicomponent adsorption systems. (C) 2002 Elsevier Science (USA).

Study on diffusion and flow of benzene, n-hexane and CCl4 in activated carbon by a differential permeation method

In this paper the diffusion and flow of carbon tetrachloride, benzene and n-hexane through a commercial activated carbon is studied by a differential permeation method. The range of pressure is covered from very low pressure to a pressure range where significant capillary condensation occurs. Helium as a non-adsorbing gas is used to determine the characteristics of the porous medium. For adsorbing gases and vapors, the motion of adsorbed molecules in small pores gives rise to a sharp increase in permeability at very low pressures. The interplay between a decreasing behavior in permeability due to the saturation of small pores with adsorbed molecules and an increasing behavior due to viscous flow in larger pores with pressure could lead to a minimum in the plot of total permeability versus pressure. This phenomenon is observed for n-hexane at 30degreesC. At relative pressure of 0.1-0.8 where the gaseous viscous flow dominates, the permeability is a linear function of pressure. Since activated carbon has a wide pore size distribution, the mobility mechanism of these adsorbed molecules is different from pore to pore. In very small pores where adsorbate molecules fill the pore the permeability decreases with an increase in pressure, while in intermediate pores the permeability of such transport increases with pressure due to the increasing build-up of layers of adsorbed molecules. For even larger pores, the transport is mostly due to diffusion and flow of free molecules, which gives rise to linear permeability with respect to pressure. (C) 2002 Elsevier Science Ltd. All rights reserved.

Modeling of gas adsorption equilibrium over a wide range of pressure: A thermodynamic approach based on equation of state

A thermodynamic approach based on the Bender equation of state is suggested for the analysis of supercritical gas adsorption on activated carbons at high pressure. The approach accounts for the equality of the chemical potential in the adsorbed phase and that in the corresponding bulk phase and the distribution of elements of the adsorption volume (EAV) over the potential energy for gas-solid interaction. This scheme is extended to subcritical fluid adsorption and takes into account the phase transition in EAV The method is adapted to gravimetric measurements of mass excess adsorption and has been applied to the adsorption of argon, nitrogen, methane, ethane, carbon dioxide, and helium on activated carbon Norit R I in the temperature range from 25 to 70 C. The distribution function of adsorption volume elements over potentials exhibits overlapping peaks and is consistently reproduced for different gases. It was found that the distribution function changes weakly with temperature, which was confirmed by its comparison with the distribution function obtained by the same method using nitrogen adsorption isotherm at 77 K. It was shown that parameters such as pore volume and skeleton density can be determined directly from adsorption measurements, while the conventional approach of helium expansion at room temperature can lead to erroneous results due to the adsorption of helium in small pores of activated carbon. The approach is a convenient tool for analysis and correlation of excess adsorption isotherms over a wide range of pressure and temperature. This approach can be readily extended to the analysis of multicomponent adsorption systems. (C) 2002 Elsevier Science (USA).

The interaction of water flow and nutrients on aquatic plant growth

A long-term experiment was conducted to compare the effects of flowing and still water on growth, and the relationship between water flow and nutrients, in Aponogeton elongatus, a submerged aquatic macrophyte. A. elongatus plants were grown for 23 weeks with three levels of nutrition (0, 0.5 and 1g Osmocote Plus(R) fertiliser pot(-1)) in aquaria containing stirred or unstirred water. Fertilized plants grew much better than non-fertilized. The highest fertilizer level produced 29% wider leaves and 58% higher total dry weight in stirred water. Stirred water increased leaf area by 40% and tuber size by 81%, but only with the highest level of nutrition. These results suggest that this plant depends on its roots for mineral uptake, rather than from the open water, and the major limitation to growth in still water is the supply of dissolved inorganic carbon. It was the combined effects of nutrient availability and stirring that produced the strongest response in plant growth, morphology and composition. This study provides some explanation for the observations of others that these plants grow best in creeks or river systems with permanently flowing water.

Slurry flow in mills: grate-pulp lifter discharge systems (Part 2)

Pulp lifters, also known, as pan lifters are an integral part of the majority of autogenous (AG), semi-autogenous (SAG) and grate discharge ball mills. The performance of the pulp lifters in conjunction with grate design determines the ultimate flow capacity of these mills. Although the function of the pulp lifters is simply to transport the slurry passed through the discharge grate into the discharge trunnion, their performance depends on their design as well as that of the grate and operating conditions such as mill speed and charge level. However, little or no work has been reported on the performance of grate-pulp lifter assemblies and in particular the influence of pulp lifter design on slurry transport. Ideally, the discharge rate through a grate-pulp lifter assembly should be equal to the discharge rate through at a given mill hold-up. However, the results obtained have shown that conventional pulp lifter designs cause considerable restrictions to flow resulting in reduced flow capacity. In this second of a two-part series of papers the performance of conventional pulp lifters (radial and spiral designs) is described and is based on extensive test work carried out in a I m diameter pilot SAG mill. (C) 2003 Elsevier Science Ltd. All rights reserved.

Slurry flow in mills: grate-only discharge mechanism (Part-1)

Discharge grates play an important role in determining the performance of autogenous, semi-autogenous and grate discharge ball mills. The flow capacity (grinding capacity) of these mills is strongly influenced by the discharge grate design-open area and position of apertures, as well as the performance of the pulp lifters. As mill sizes have progressively increased and closed-circuiting has become more popular the importance of grate and pulp lifter design has grown. Unfortunately very few studies have concentrated on this aspect of mill performance. To remedy this a series of laboratory and pilot-scale tests were undertaken to study both the performance of grates on their own and in conjunction with pulp lifters. In this first paper of a two-part series the results from the grate-only experiments are presented and discussed, whilst the performance of the grate-pulp-lifter system is covered in the second paper. The results from the grate-only experiments have shown that the build-up of slurry (hold-up) inside the mill starts from the shoulder of the charge, while the toe position of the slurry progressively moves towards the toe of the charge with increasing flowrate. Besides grate design (open area and position of apertures), charge volume and mill speed were also found to have a strong influence on mill hold-up and interact with grate design variables. (C) 2003 Elsevier Science Ltd. All rights reserved.

Capillaries within compartments: Microvascular interpretation of dynamic positron emission tomography data

Measurement of exchange of substances between blood and tissue has been a long-lasting challenge to physiologists, and considerable theoretical and experimental accomplishments were achieved before the development of the positron emission tomography (PET). Today, when modeling data from modern PET scanners, little use is made of earlier microvascular research in the compartmental models, which have become the standard model by which the vast majority of dynamic PET data are analysed. However, modern PET scanners provide data with a sufficient temporal resolution and good counting statistics to allow estimation of parameters in models with more physiological realism. We explore the standard compartmental model and find that incorporation of blood flow leads to paradoxes, such as kinetic rate constants being time-dependent, and tracers being cleared from a capillary faster than they can be supplied by blood flow. The inability of the standard model to incorporate blood flow consequently raises a need for models that include more physiology, and we develop microvascular models which remove the inconsistencies. The microvascular models can be regarded as a revision of the input function. Whereas the standard model uses the organ inlet concentration as the concentration throughout the vascular compartment, we consider models that make use of spatial averaging of the concentrations in the capillary volume, which is what the PET scanner actually registers. The microvascular models are developed for both single- and multi-capillary systems and include effects of non-exchanging vessels. They are suitable for analysing dynamic PET data from any capillary bed using either intravascular or diffusible tracers, in terms of physiological parameters which include regional blood flow. (C) 2003 Elsevier Ltd. All rights reserved.

Determination of regional flow by use of intravascular PET tracers: Microvascular theory and experimental validation for pig livers

Today, the standard approach for the kinetic analysis of dynamic PET studies is compartment models, in which the tracer and its metabolites are confined to a few well-mixed compartments. We examine whether the standard model is suitable for modern PET data or whether theories including more physiologic realism can advance the interpretation of dynamic PET data. A more detailed microvascular theory is developed for intravascular tracers in single-capillary and multiple-capillary systems. The microvascular models, which account for concentration gradients in capillaries, are validated and compared with the standard model in a pig liver study. Methods: Eight pigs underwent a 5-min dynamic PET study after O-15-carbon monoxide inhalation. Throughout each experiment, hepatic arterial blood and portal venous blood were sampled, and flow was measured with transit-time flow meters. The hepatic dual-inlet concentration was calculated as the flow-weighted inlet concentration. Dynamic PET data were analyzed with a traditional single-compartment model and 2 microvascular models. Results: Microvascular models provided a better fit of the tissue activity of an intravascular tracer than did the compartment model. In particular, the early dynamic phase after a tracer bolus injection was much improved. The regional hepatic blood flow estimates provided by the microvascular models (1.3 +/- 0.3 mL min(-1) mL(-1) for the single-capillary model and 1.14 +/- 0.14 min(-1) mL(-1) for the multiple-capillary model) (mean +/- SEM mL of blood min(-1) mL of liver tissue(-1)) were in agreement with the total blood flow measured by flow meters and normalized to liver weight (1.03 +/- 0.12 mL min(-1) mL(-1)). Conclusion: Compared with the standard compartment model, the 2 microvascular models provide a superior description of tissue activity after an intravascular tracer bolus injection. The microvascular models include only parameters with a clear-cut physiologic interpretation and are applicable to capillary beds in any organ. In this study, the microvascular models were validated for the liver and provided quantitative regional flow estimates in agreement with flow measurements.

The modeling of turbulent reactive flows based on multiple mapping conditioning

A new modeling approach-multiple mapping conditioning (MMC)-is introduced to treat mixing and reaction in turbulent flows. The model combines the advantages of the probability density function and the conditional moment closure methods and is based on a certain generalization of the mapping closure concept. An equivalent stochastic formulation of the MMC model is given. The validity of the closuring hypothesis of the model is demonstrated by a comparison with direct numerical simulation results for the three-stream mixing problem. (C) 2003 American Institute of Physics.

Numerical investigation of turbulent flow around a rotating stepped cylinder for corrosion study

Direct numerical simulation has been carried out for turbulent flow set up by a rotating cylinder with two backward-facing steps axisymmetrically mounted in the circumferential direction. This flow geometry creates a qualitatively similar flow pattern as observed near, a sudden, pipe expansion or a plane backward-facing step, characterized by flow separation and reattachment. A region of intense turbulence intensity and high wall-shear-stress fluctuations is formed in,the recirculating I region downstream of the step, where high mass-transfer capacity was also experimentally observed. Since, corrosion is frequently mass-transfer., controlled, our findings, put forward this apparatus as useful tool for future corrosion research.

Heat transfer and flow behind a step in high enthalpy superorbital flow

Heat transfer levels have been investigated behind a rearward-facing step in a superorbital expansion tube. The heat transfer was measured along a flat plate and behind 2 and 3mm steps with the same length to step height ratio. Results were obtained with air as the test gas at speeds of 6.76kms(-1) and 9-60kms(-1) corresponding to stagnation enthalpies of 26MJ/kg and 48MJ/kg respectively. A laminar boundary layer was established on the flat plate and measured heat transfer levels were consistent with classical empirical correlations. In the case of flow behind a step, the measurements showed a gradual rise in heat transfer from the rear of the step to a plateau several step heights downstream for both flow conditions. Reattachment distance was estimated to be approximately 1.6 step heights downstream of the 2mm step at the low enthalpy condition through the use of flow visualisation.

An electromagnetic-field method modeling of a radial line planar antenna with coupling probes

This communications describes an electromagnetic model of a radial line planar antenna consisting of a radial guide with one central probe and many peripheral probes arranged in concentric circles feeding an array of antenna elements such as patches or wire curls. The model takes into account interactions between the coupling probes while assuming isolation of radiating elements. Based on this model, computer programs are developed to determine equivalent circuit parameters of the feed network and the radiation pattern of the radial line planar antenna. Comparisons are made between the present model and the two-probe model developed earlier by other researchers.

Direction of Causation Modeling Between Cross-Sectional Measures of Parenting and Psychological Distress in Female Twins

Under certain conditions, cross-sectional analysis of cross-twin intertrait correlations can provide important information about the direction of causation (DOC) between two variables. A community-based sample of Australian female twins aged 18 to 45 years was mailed an extensive Health and Lifestyle Questionnaire (HLQ) that covered a wide range of personality and behavioral measures. Included were self-report measures of recent psychological distress and perceived childhood environment (PBI). Factor analysis of the PBI yielded three interpretable dimensions: Coldness, Overprotection, and Autonomy. Univariate analysis revealed that parental Overprotection and Autonomy were best explained by additive genetic, shared, and nonshared environmental effects (ACE), whereas the best-fitting model for PBI Coldness and the three measures of psychological distress (Depression, Phobic Anxiety, and Somatic Distress) included only additive genetic and nonshared environmental effects (AE). A common pathway model best explained the covariation between (1) the three PBI dimensions and (2) the three measures of psychological distress. DOC modeling between latent constructs of parenting and psychological distress revealed that a model which specified recollected parental behavior as the cause of psychological distress provided a better fit than a model which specified psychological distress as the cause of recollected parental behavior. Power analyses and limitations of the findings are discussed.