Fixed bed reactors with catalyst poisoning - first order kinetics.

The long performance of an isothermal fixed bed reactor undergoing catalyst poisoning is theoretically analyzed using the dispersion model. First order reaction with dth order deactivation is assumed and the model equations are solved by matched asymptotic expansions for large Peclet number. Simple closed-form solutions, uniformly valid in time, are obtained.

A finite integral transform technique for solving the diffusion-reaction equation with Michaelis-Menten kinetics

An approximate analytical technique employing a finite integral transform is developed to solve the reaction diffusion problem with Michaelis-Menten kinetics in a solid of general shape. A simple infinite series solution for the substrate concentration is obtained as a function of the Thiele modulus, modified Sherwood number, and Michaelis constant. An iteration scheme is developed to bring the approximate solution closer to the exact solution. Comparison with the known exact solutions for slab geometry (quadrature) and numerically exact solutions for spherical geometry (orthogonal collocation) shows excellent agreement for all values of the Thiele modulus and Michaelis constant.

Substrate-inhibited kinetics with catalyst deactivation in an isothermal CSTR

Analytical expressions are developed for the time-dependent reactant concentration and catalyst activity in an isothermal CSTR with Langmuir-Hinshelwood kinetics of deactivation and reaction. Several parallel and series posioning mechanisms are considered for a reactor which, without poisoning, would operate at a unique steady state. The use of matched asymptotic expansions and abandonment of the usual initial-steady-state assumption give results, valid from startup to final loss of activity, whose accuracy can be improved systematically.

Substrate-inhibited kinetics with catalyst deactivation in an isothermal CSTR. II. Multiple pseudosteady states and reactor failure

Analytical expressions are derived for the time and magnitude of failure of an isothermal CSTR with substrate-inhibited kinetics, caused by slow catalyst deactivation under three types of parallel and series mechanisms. Reactors operating at high space velocity are found to be most susceptible to early failure and poisoning by product is more dangerous than by reactant. The magnitude of the jump across steady states depends solely on the Langmuir-Hinshelwood kinetic parameters and a detailed analysis of reactor behavior during the jump itself is given.

Using the level set method to model endogenous lava dome growth

Modeling volcanic phenomena is complicated by free-surfaces often supporting large rheological gradients. Analytical solutions and analogue models provide explanations for fundamental characteristics of lava flows. But more sophisticated models are needed, incorporating improved physics and rheology to capture realistic events. To advance our understanding of the flow dynamics of highly viscous lava in Peléean lava dome formation, axi-symmetrical Finite Element Method (FEM) models of generic endogenous dome growth have been developed. We use a novel technique, the level-set method, which tracks a moving interface, leaving the mesh unaltered. The model equations are formulated in an Eulerian framework. In this paper we test the quality of this technique in our numerical scheme by considering existing analytical and experimental models of lava dome growth which assume a constant Newtonian viscosity. We then compare our model against analytical solutions for real lava domes extruded on Soufrière, St. Vincent, W.I. in 1979 and Mount St. Helens, USA in October 1980 using an effective viscosity. The level-set method is found to be computationally light and robust enough to model the free-surface of a growing lava dome. Also, by modeling the extruded lava with a constant pressure head this naturally results in a drop in extrusion rate with increasing dome height, which can explain lava dome growth observables more appropriately than when using a fixed extrusion rate. From the modeling point of view, the level-set method will ultimately provide an opportunity to capture more of the physics while benefiting from the numerical robustness of regular grids.

Effect of Cu Toxicity on Growth of Cowpea (Vigna unguiculata)

Accurate determination of the rhizotoxicity of Cu in dilute nutrient solutions is hindered by the difficulty of maintaining constant, pre-determined concentrations of Cu (micromolar) in solution. The critical Cu2+ activity associated with a reduction in the growth of solution-grown cowpea (Vigna unguiculata (L.) Walp. cv Caloona) was determined in a system in which Cu was maintained constant through the use of a cation exchange resin. The growth of roots and shoots was found to be reduced at solution Cu2+ activities ≥ 1.7 µM (corresponding to 90 % maximum growth). Although root growth was most likely reduced due to a direct Cu2+ toxicity, it is considered that the shoot growth reduction is attributable to a decrease in tissue concentrations of K, Ca, Mg, and Fe and the formation of interveinal chlorosis. At high Cu2+ activities, roots were brown in color, short and thick, had bent root tips with cracking of the epidermis and outer cortex, and had local swellings behind the roots tips due to a reduction in cell elongation. Root hair growth was reduced at concentrations lower than that which caused a significant reduction in overall root fresh weight.

Growth Response of Various Perennial Grasses to Increasing Salinity

Although the effect of salinity on plant growth has been the focus of a substantive research effort, much of this research has failed to adequately separate the various growth limiting aspects of salinity; thus the results are confounded by multiple factors. Eight perennial grass species were grown in a sand culture system dominated by NaCl (electrical conductivities (ECs) between 1.4 and 38 dS m 1), with sufficient Ca added to each treatment to ensure that Na-induced Ca deficiency did not reduce growth. Of the eight perennial grass species examined, Chloris gayana cv. Pioneer (Rhodes grass) was the most salt tolerant species, whilst in comparison, Chrysopogon zizanioides cv. Monto (vetiver) was of only moderate tolerance. However, observed salinity tolerances tended to be lower than those expected from published values based on the threshold salinity model (bent stick model). This discrepancy may be due in part to differences in the evapotranspirational demand between studies; an increase in demand accelerating the accumulation of Na in the shoots and hence decreasing apparent salinity tolerance. It was also observed that the use of a non-saline growth period to allow seed germination and establishment results in the overestimation of vegetative salinity tolerance if not taken into consideration. This is particularly true for species of low salt tolerance due to their comparatively rapid growth in the non-saline medium compared to that at full salinity.

Bifurcation in growth patterns for arrays of parallel Griffith, edge and sliding cracks

This paper presents the recent finding by Muhlhaus et al [1] that bifurcation of crack growth patterns exists for arrays of two-dimensional cracks. This bifurcation is a result of the nonlinear effect due to crack interaction, which is, in the present analysis, approximated by the dipole asymptotic or pseudo-traction method. The nonlinear parameter for the problem is the crack length/ spacing ratio lambda = a/h. For parallel and edge crack arrays under far field tension, uniform crack growth patterns (all cracks having same size) yield to nonuniform crack growth patterns (i.e. bifurcation) if lambda is larger than a critical value lambda(cr) (note that such bifurcation is not found for collinear crack arrays). For parallel and edge crack arrays respectively, the value of lambda(cr) decreases monotonically from (2/9)(1/2) and (2/15.096)(1/2) for arrays of 2 cracks, to (2/3)(1/2)/pi and (2/5.032)(1/2)/pi for infinite arrays of cracks. The critical parameter lambda(cr) is calculated numerically for arrays of up to 100 cracks, whilst discrete Fourier transform is used to obtain the exact solution of lambda(cr) for infinite crack arrays. For geomaterials, bifurcation can also occurs when array of sliding cracks are under compression.

The expression of messenger RNAs coding for growth factors, their receptors, and eph-class receptor tyrosine kinases in normal and ototoxically damaged chick cochleae

Messenger RNAs coding for growth factors and receptor tyrosine kinases were measured by quantitative competitive and by semi-quantitative reverse-transcription polymerase chain reaction in whole and dissected chick inner ears. The fibroblast growth factor (FGF) receptor 1 chick embryonic kinase (CEK) 1 was expressed in all structures examined (otocyst, hatchling whole cochlea, cochlear nerve ganglion, and cochlear and vestibular sensory epithelia), although slightly more heavily in the otocyst. The related fibroblast growth factor receptors CEK 2 and 3 were preferentially expressed in the nerve ganglion and in the vestibular sensory epithelium, respectively. FGF 1 mRNA was low in early development, increasing to mature levels at around embryonic age 11 days, while FGF2, mRNA was expressed at constant levels at all ages. In response to ototoxic damage, FGF1 mRNA levels were increased in the early damaged cochlear sensory epithelium. Immunohistochemistry for CEK1 showed that normal hair cells expressed the receptor heavily on the hair cell stereocilia, while with early damage, CEK1 came to be expressed heavily on the apical surfaces of the supporting cells. In normal chicks, the CEK4 and CEK8 eph-class receptor tyrosine kinases were expressed relatively heavily by the cochlear nerve ganglion, and CEK10 was expressed relatively heavily by the cochlear hair cell sensory epithelium. The results suggest that the FGF system may be involved in the response of the cochlear epithelium to ototoxic damage. The eph-class receptor tyrosine kinase CEK10 may be involved in cell interactions in the cochlear sensory epithelium, while CEK4 and CEK8 may play a role in the cochlear innervation.