Paste Residence Time in a Spouted Bed Dryer. IV: Effect of the Inert Particle Size Distribution

The residence time distribution and mean residence time of a 10% sodium bicarbonate solution that is dried in a conventional spouted bed with inert bodies were measured with the stimulus-response method. Methylene blue was used as a chemical tracer, and the effects of the paste feed mode, size distribution of the inert bodies, and mean particle size on the residence times and dried powder properties were investigated. The results showed that the residence time distributions could be best reproduced with the perfect mixing cell model or N = 1 for the continuous stirred tank reactor in a series model. The mean residence times ranged from 6.04 to 12.90 min and were significantly affected by the factors studied. Analysis of variance on the experimental data showed that mean residence times were affected by the mean diameter of the inert bodies at a significance level of 1% and by the size distribution at a level of 5%. Moreover, altering the paste feed from dripping to pneumatic atomization affected mean residence time at a 5% significance level. The dried powder characteristics proved to be adequate for further industrial manipulation, as demonstrated by the low moisture content, narrow range of particle size, and good flow properties. The results of this research are significant in the study of the drying of heat-sensitive materials because it shows that by simultaneously changing the size distribution and average size of the inert bodies, the mean residence times of a paste can be reduced by half, thus decreasing losses due to degradation.

Kinetic analysis of vascular marker distribution in perfused rat livers after regeneration following partial hepatectomy

Background/Aims: Liver clearance models are based on information (or assumptions) on solute distribution kinetics within the microvasculatory system, The aim was to study albumin distribution kinetics in regenerated livers and in livers of normal adult rats, Methods: A novel mathematical model was used to evaluate the distribution space and the transit time dispersion of albumin in livers following regeneration after a two-thirds hepatectomy compared to livers of normal adult rats. Outflow curves of albumin measured after bolus injection in single-pass perfused rat livers were analyzed by correcting for the influence of catheters and fitting a long-tailed function to the data. Results: The curves were well described by the proposed model. The distribution volume and the transit time dispersion of albumin observed in the partial hepatectomy group were not significantly different from livers of normal adult rats. Conclusions: These findings suggest that the distribution space and the transit time dispersion of albumin (CV2) is relatively constant irrespective of the presence of rapid and extensive repair. This invariance of CV2 implies, as a first approximation, a similar degree of intrasinusoidal mixing, The finding that a sum of two (instead of one) inverse Gaussian densities is an appropriate empirical function to describe the outflow curve of vascular indicators has consequences for an improved prediction of hepatic solute extraction.

Determination of pore size distributions by regularization and finite element collocation

The problem of extracting pore size distributions from characterization data is solved here with particular reference to adsorption. The technique developed is based on a finite element collocation discretization of the adsorption integral, with fitting of the isotherm data by least squares using regularization. A rapid and simple technique for ensuring non-negativity of the solutions is also developed which modifies the original solution having some negativity. The technique yields stable and converged solutions, and is implemented in a package RIDFEC. The package is demonstrated to be robust, yielding results which are less sensitive to experimental error than conventional methods, with fitting errors matching the known data error. It is shown that the choice of relative or absolute error norm in the least-squares analysis is best based on the kind of error in the data. (C) 1998 Elsevier Science Ltd. All rights reserved.

X-ray computed tomography to quantify tree rooting spatial distributions

Poor root development due to constraining soil conditions could be an important factor influencing health of urban trees. Therefore, there is a need for efficient techniques to analyze the spatial distribution of tree roots. An analytical procedure for describing tree rooting patterns from X-ray computed tomography (CT) data is described and illustrated. Large irregularly shaped specimens of undisturbed sandy soil were sampled from Various positions around the base of trees using field impregnation with epoxy resin, to stabilize the cohesionless soil. Cores approximately 200 mm in diameter by 500 mm in height were extracted from these specimens. These large core samples were scanned with a medical X-ray CT device, and contiguous images of soil slices (2 mm thick) were thus produced. X-ray CT images are regarded as regularly-spaced sections through the soil although they are not actual 2D sections but matrices of voxels similar to 0.5 mm x 0.5 mm x 2 mm. The images were used to generate the equivalent of horizontal root contact maps from which three-dimensional objects, assumed to be roots, were reconstructed. The resulting connected objects were used to derive indices of the spatial organization of roots, namely: root length distribution, root length density, root growth angle distribution, root spatial distribution, and branching intensity. The successive steps of the method, from sampling to generation of indices of tree root organization, are illustrated through a case study examining rooting patterns of valuable urban trees. (C) 1999 Elsevier Science B.V. All rights reserved.

Habitat structure and egg distributions in the processionary caterpillar Ochrogaster lunifer: lessons for conservation and pest management

1. The spatial and temporal distribution of eggs laid by herbivorous insects is a crucial component of herbivore population stability, as it influences overall mortality within the population. Thus an ecologist studying populations of an endangered butterfly can do little to increase its numbers through habitat management without knowledge of its egg-laying patterns across individual host-plants under different habitat management regimes. At the other end of the spectrum, a knowledge of egg-laying behaviour can do much to control pest outbreaks by disrupting egg distributions that lead to rapid population growth. 2. The distribution of egg batches of the processionary caterpillar Ochrogaster lunifer on acacia trees was monitored in 21 habitats during 2 years in coastal Australia. The presence of egg batches on acacias was affected by host-tree 'quality' (tree size and foliar chemistry that led to increased caterpillar survival) and host-tree 'apparency' (the amount of vegetation surrounding host-trees). 3. In open homogeneous habitats, more egg batches were laid on high-quality trees, increasing potential population growth. In diverse mixed-species habitats, more egg batches were laid on low-quality highly apparent trees, reducing population growth and so reducing the potential for unstable population dynamics. The aggregation of batches on small apparent trees in diverse habitats led to outbreaks on these trees year after year, even when population levels were low, while site-wide outbreaks were rare. 4. These results predict that diverse habitats with mixed plant species should increase insect aggregation and increase population stability. In contrast, in open disturbed habitats or in regular plantations, where egg batches are more evenly distributed across high-quality hosts, populations should be more unstable, with site-wide outbreaks and extinctions being more common. 5. Mixed planting should be used on habitat regeneration sites to increase the population stability of immigrating or reintroduced insect species. Mixed planting also increases the diversity of resources, leading to higher herbivore species richness. With regard to the conservation of single species, different practices of habitat management will need to be employed depending on whether a project is concerned with methods of rapidly increasing the abundance of an endangered insect or concerned with the maintenance of a stable, established insect population that is perhaps endemic to an area. Suggestions for habitat management in these different cases are discussed. 6. Finally, intercropping can be highly effective in reducing pest outbreaks, although the economic gains of reduced pest attack may be outweighed by reduced crop yields in mixed-crop systems.

Modeling of hepatic elimination and organ distribution kinetics with the extended convection-dispersion model

The conventional convection-dispersion (also called axial dispersion) model is widely used to interrelate hepatic availability (F) and clearance (Cl) with the morphology and physiology of the liver and to predict effects such as changes in liver blood flow on F and Cl. An extended form of the convection-dispersion model has been developed to adequately describe the outflow concentration-time profiles for vascular markers at both short and long times after bolus injections into perfused livers. The model, based on flux concentration and a convolution of catheters and large vessels, assumes that solute elimination in hepatocytes follows either fast distribution into or radial diffusion in hepatocytes. The model includes a secondary vascular compartment, postulated to be interconnecting sinusoids. Analysis of the mean hepatic transit time (MTT) and normalized variance (CV2) of solutes with extraction showed that the discrepancy between the predictions of MTT and CV2 for the extended and conventional models are essentially identical irrespective of the magnitude of rate constants representing permeability, volume, and clearance parameters, providing that there is significant hepatic extraction. In conclusion, the application of a newly developed extended convection-dispersion model has shown that the unweighted conventional convection-dispersion model can be used to describe the disposition of extracted solutes and, in particular, to estimate hepatic availability and clearance in booth experimental and clinical situations.

Further results on the relationship between mu-invariant measures and quasi-stationary distributions for absorbing continuous-time Markov chains

This note considers continuous-time Markov chains whose state space consists of an irreducible class, C, and an absorbing state which is accessible from C. The purpose is to provide results on mu-invariant and mu-subinvariant measures where absorption occurs with probability less than one. In particular, the well-known premise that the mu-invariant measure, m, for the transition rates be finite is replaced by the more natural premise that m be finite with respect to the absorption probabilities. The relationship between mu-invariant measures and quasi-stationary distributions is discussed. (C) 2000 Elsevier Science Ltd. All rights reserved.

New methods for determining quasi-stationary distributions for Markov chains

We shall be concerned with the problem of determining quasi-stationary distributions for Markovian models directly from their transition rates Q. We shall present simple conditions for a mu-invariant measure m for Q to be mu-invariant for the transition function, so that if m is finite, it can be normalized to produce a quasi-stationary distribution. (C) 2000 Elsevier Science Ltd. All rights reserved.

Characterization of pore size distributions of mesoporous materials from adsorption isotherms

In this article, a new hybrid model for estimating the pore size distribution of micro- and mesoporous materials is developed, and tested with the adsorption data of nitrogen, oxygen, and argon on ordered mesoporous materials reported in the literature. For the micropore region, the model uses the Dubinin-Rudushkevich (DR) isotherm with the Chen-Yang modification. A recent isotherm model of the authors for nonporous materials, which uses a continuum-mechanical model for the multilayer region and the Unilan model for the submonolayer region, has been extended for adsorption in mesopores. The experimental data is inverted using regularization to obtain the pore size distribution. The present model was found to be successful in predicting the pore size distribution of pure as well as binary physical mixtures of MCM-41 synthesized with different templates, with results in agreement with those from the XRD method and nonlocal density functional theory. It was found that various other recent methods, as well as the classical Broekhoff and de Beer method, underpredict the pore diameter of MCM-41. The present model has been successfully applied to MCM-48, SBA's, CMK, KIT, HMS, FSM, MTS, mesoporous fly ash, and a large number of other regular mesoporous materials.

Determination of activation energy distributions for chemisorption of oxygen on carbon: an improved approach

The present paper proposes an approach to obtaining the activation energy distribution for chemisorption of oxygen onto carbon surfaces, while simultaneously allowing for the activation energy dependence of the pre-exponential factor of the rate constant. Prior studies in this area have considered this factor to be uniform, thereby biasing estimated distributions. The results show that the derived activation energy distribution is not sensitive to the chemisorption mechanism because of the step function like property of the coverage. The activation energy distribution is essentially uniform for some carbons, and has two or possibly more discrete stages, suggestive of at least two types of sites, each with its own uniform distribution. The pre-exponential factors of the reactions are determined directly from the experimental data, and are found not to be constant as assumed in earlier work, but correlated with the activation energy. The latter results empirically follow an exponential function, supporting some earlier statistical and experimental work. The activation energy distribution obtained in the present paper permits improved correlation of chemisorption data in comparison to earlier studies. (C) 2000 Elsevier Science Ltd. All rights reserved.

Residence time distributions of gas flowing through rotating drum bioreactors

Residence time distribution studies of gas through a rotating drum bioreactor for solid-state fermentation were performed using carbon monoxide as a tracer gas. The exit concentration as a function of time differed considerably from profiles expected for plug flow, plug flow with axial dispersion, and continuous stirred tank reactor (CSTR) models. The data were then fitted by least-squares analysis to mathematical models describing a central plug flow region surrounded by either one dead region (a three-parameter model) or two dead regions (a five-parameter model). Model parameters were the dispersion coefficient in the central plug flow region, the volumes of the dead regions, and the exchange rates between the different regions. The superficial velocity of the gas through the reactor has a large effect on parameter values. Increased superficial velocity tends to decrease dead region volumes, interregion transfer rates, and axial dispersion. The significant deviation from CSTR, plug flow, and plug flow with axial dispersion of the residence time distribution of gas within small-scale reactors can lead to underestimation of the calculation of mass and heat transfer coefficients and hence has implications for reactor design and scaleup. (C) 2001 John Wiley & Sons, Inc.

Magnetization transfer imaging for polymer gel dosimetry

Off-resonance RF pre-saturation was used to obtain contrast in MRI images of polymer gel dosimeters irradiated to doses up to 50 Gy. Two different polymer gel dosimeters composed of 2-hydroxyethyl-acryl ate or methacrylic acid monomers mixed with N, N'-methylene-bisacrylamide (BIS), dispersed in an aqueous gelatin matrix were evaluated. Radiation-induced polymerization of the co-monomers generates a fast-relaxing insoluble polymer. Saturation of the polymer using off-resonance Gaussian RF pulses prior to a spin-echo read-out with a short echo time leads to contrast that is dependent on the absorbed dose. This contrast is attributed to magnetization transfer (MT) between free water and the polymer, and direct saturation of water was found to be negligible under the prevailing experimental conditions. The usefulness of MT imaging was assessed by computing the dose resolution obtained with this technique. We found a low value of dose resolution over a wide range of doses could be obtained with a single experiment. This is an advantage over multiple spin echo (MSE) experiments using a single echo spacing where an optimal dose resolution is achieved over only very limited ranges of doses. The results suggest MT imaging protocols may be developed into a useful tool for polymer gel dosimetry.

Limiting conditional distributions for birth-death processes

In a recent paper [16], one of us identified all of the quasi-stationary distributions for a non-explosive, evanescent birth-death process for which absorption is certain, and established conditions for the existence of the corresponding limiting conditional distributions. Our purpose is to extend these results in a number of directions. We shall consider separately two cases depending on whether or not the process is evanescent. In the former case we shall relax the condition that absorption is certain. Furthermore, we shall allow for the possibility that the minimal process might be explosive, so that the transition rates alone will not necessarily determine the birth-death process uniquely. Although we shall be concerned mainly with the minimal process, our most general results hold for any birth-death process whose transition probabilities satisfy both the backward and the forward Kolmogorov differential equations.

On the validity of the dispersion model of hepatic drug elimination when intravascular transit time densities are long-tailed

The dispersion model with mixed boundary conditions uses a single parameter, the dispersion number, to describe the hepatic elimination of xenobiotics and endogenous substances. An implicit a priori assumption of the model is that the transit time density of intravascular indicators is approximated by an inverse Gaussian distribution. This approximation is limited in that the model poorly describes the tail part of the hepatic outflow curves of vascular indicators. A sum of two inverse Gaussian functions is proposed as ail alternative, more flexible empirical model for transit time densities of vascular references. This model suggests that a more accurate description of the tail portion of vascular reference curves yields an elimination rate constant (or intrinsic clearance) which is 40% less than predicted by the dispersion model with mixed boundary conditions. The results emphasize the need to accurately describe outflow curves in using them as a basis for determining pharmacokinetic parameters using hepatic elimination models. (C) 1997 Society for Mathematical Biology.