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An analysis of particle motion in rapidly oscillating flows provides a simple conceptual basis for particle retardation, hovering, and levitation. The method of averaging from nonlinear mechanics is the major mathematical toolin this analysis. The results provide a conservative design basis for particle motion modification in fluctuating flows, a phenomenon which may find application in flotation, settling, and multiphase contacting operations.

The interaction between imperfect mixing and cyclic operation is examined for several continuous polymerizations in stirred-tank reactors. The reactor is represented by a mixed model involving two interconnected ideal stirred vessels. Cyclic fluctuations in the concentration of a chain transfer agent during Ziegler-catalyzed olefin polymerization can yield molecular weight distributions significantly different from those of a conventional steady state reactor. This result is consistent with the available experimental data. It is especially interesting that the cyclic reactor effluent with a modified molecular weight distribution is of approximately time-invariant composition when the period of cycling is on the order of the reactor holding time. Imperfect mixing has a lesser effect on cycled reactors for free-radical and polycondensation polymerization than it has on cycled olefin polymerization reactors.

The selectivity for a complex heterogeneously catalyzed reaction is examined for steady and periodic control of reactant concentration at the exterior catalyst surface. Cycling alters the selectivity by creating waves of concentrations within the catalyst which interact favorably in this instance. This new phenomenon in periodic processing is revealed by an analytical perturbation solution for the reaction-limited regime, a technique which can be extended to other reaction mechanisms. Numerical simulations employing an orthogonal collocation technique reproduce the perturbation solution in the reaction-limited regime and show that favorable effects of cycling persist when mass transfer limits the overall reaction.

(1974). PERIODIC OPERATION OF CHEMICAL REACTORS: A REVIEW. Chemical Engineering Communications: Vol. 1, No. 3, pp. 111-124.

When a periodic process is disturbed, control action may be necessary to maintain satisfactory performance. Regulating controls to achieve this objective can be synthesized by solving a linear-quadratic optimization problem with periodic coefficient's. Generalized proportional and proportional-integral feedback regulators developed in this manner are tested by simulating a cyclic reactor. Very satisfactory control is achieved for 10% step disturbances in reactor feed conditions although the results are sensitive to the choice of manipulated variables.

Many enzyme-catalyzed reactions involve the liberation or consumption of hydrogen ions. In this paper a mathematical model is employed to investigate how such reactions behave when the enzyme is immobilized. Shifted pH optima, disappearance of an optimum pH, insensitivity to bulk pH, and very large effectiveness factors are some of the phenomena which appear as a result of pH coupling between the reaction and the enzyme's activity. Several of the qualitative features revealed by the model are consistent with earlier experimental observations. In addition, preliminary guidelines for optimal choice of enzyme support are suggested.

Several techniques for investigating the multiplicity and stability of open isothermal enzymatic reactors are discussed and some of the pitfalls in previous thinking pointed out. The example which is used to illustrate these methods exhibits several interesting features. Among these is the existence of a stable oscillatory state which surrounds a unique steady state which is asymptotically stable to certain finite disturbances.

Systematic application of Pontryagin's maximum principle to a general class of nonlinear mixed boundary value control problems yields necessary conditions for optimal control. Also, the features of certain pathological situations including the abnormal case and singular control are clearly revealed in this treatment.

The relaxed steady state operation of a tubular fixed-bed catalytic reactor under control of the inlet composition is investigated. It is shown that the performance of such a reactor can be improved under certain conditions by periodically varying inlet concentrations rather than keeping these concentrations time invariant.

When a chemical reaction occurs on the exterior surfaces of a catalytic nonporous slab, stable asymmetric steady states may exist. The number of the asymmetric solutions is a complex function of the Biot number of the system. A graphical technique is presented for determination of these solutions for uniform as well as nonuniform environments. Our method provides a rapid determination of the qualitative features of all the solutions and their stability. The procedure enables the determination of the stable steady states from the results of a simple experiment without the need for any information about the functional form of the rate expression or about the kinetic parameters. The results indicate several suprising patterns of solutions. When the temperature of the reactant streams are not equal, a stable steady state may exist for which the heat flux in the slab is against the external temperature driving force.

The oxidation stage in the production of carbon fibres from acrylics is time-consuming. Here we describe why oxidation is necessary.

Using standard methods, the polypeptide α-chain of human haemoglobin A, with the haem group attached, has been prepared and purified. The spectra of the met form and its derivatives have been characterised. The spectrum of the met form of the α-chain is distinctly different from that of methaemoglobin A and closely similar to that of methaemoglobin Norfolk and these spectra shown to be consistent with the existence of two forms of methaemoglobin. Possible structural differences between the two forms are discussed. The formation constant of the azide complex of met α-chain has been measured under different conditions of pH and temperature. The thermodynamic data for the reaction are comparable with those for other methaemoglobins.

The approximation theorem of relaxed control has an interesting application in the field of heterogeneous catalysis. For some reaction mechanisms, the selectivity of a catalyst can be increased significantly by operating the catalyst dynamically rather than in the steady state.

The properties of haemoglobin Zurich have been examined. The peak positions of the spectra of most derivatives are at lower wavelengths than those for haemoglobin A. The haems attached to the abnormal β-polypeptide chains have a higher redox potential than methaemoglobin A, and the affinity for hydroxyl ion of these haems is about thirty times greater than that of methaemoglobin A. Haemoglobin Zurich, in which all the haems are in the acid met form, denatures rapidly. These observations are interpreted in terms of the known structue of haemoglobin Zurich.

Whenever multiple symmetric steady states exist for a single reaction in a porous catalyst slab with uniform catalytic activity, asymmetric state can be constructed in a slab with symmetric, nonuniform catalytic activity. This construction yields asymmetric states even in the relatively simple case of an isothermal catalyst with equilibrium boundary conditions at the external surfaces.

Electron microscope observations on the dislocation structure of cold-worked polycrystalline silver and on the processes occurring during annealing are described. In silver deformed 25% in tension the dislocations are arranged in a cell structure and the stored energy is released in two stages, a recovery stage followed by recrystallization. During the recovery stage there is no observable change in the dislocation distribution but there is a possibility of small-scale dislocation rearrangements within the cell boundaries. Recrystallization occurs by the migration of the grain boundaries originally present in the metal and this process is discussed in some detail. Observations made on heavily rolled silver annealed either inside the electron microscope on a heating stage or outside the microscope are also described.

Distribution and densities of dislocations, determined by electron transmission microscopy, flow stress and stored energy measurements (by microcalorimetry) on cold-worked polycrystalline silver are correlated with each other, The dislocations are arranged in dense networks forming the boundaries of an otherwise relatively dislocation-free cell structure. The flow stress is explained quantitatively in terms of the forest intersection mechanism at the boundaries. The stored energy after recovery is of the same order as the total self-energy of the dislocation arrangement, so that the long-range stresses must be largely relaxed. The considerable energy release during the recovery stage produces no observable change in dislocation distribution. This recovery stage is thought to be due to the relief of long-range stresses or to the removal of point defects. While the values of flow stress and stored energy can be accounted for in terms of the observed non-uniform distribution of dislocations (cell st...

An X-ray powder diffraction method is described which can determine the phases present in hydrogen–zirconium alloys containing ≥ 100 p.p.m. hydrogen. The method is applied to show that γ- and δ-hydrides are formed when hydrogen–zirconium alloys are cooled from the α-phase field. It is shown that quenching favours the formation of the γ phase.

A transmission electron microscopy study has been made of the monoclinic to tetragonal phase transformation in thin films of zirconia. The films were prepared by the oxidation and subsequent recrystallization of zirconium foils. The transformation, which is rapid and reversible, is generally accompanied by twinning on (100) and {110} planes. The orientation relations between the two phases and the shape change accompanying transformation have been determined. The twinning shears have also been measured. Stacking faults on several low index planes have been observed in monoclinic zirconia and dislocations are present in both phases. Cracks occur in the films on transformation from the tetragonal to the monoclinic phase.

Using variational techniques, a computationally efficient procedure is developed for determining the sensitivity of the observed reaction rate in a porous catalyst with external transport resistances. Derivatives of the observed rate with respect to bulk fluid conditions or any other parameters in the mathematical model of the catalyst may be easily calculated for slab, cylindrical, or spherical catalyst geometry.

The relationships between the dislocation density, flow stress and stored energy in polycrystalline copper have been determined experimentally. The stored energy can be predicted from the observed density and distribution of dislocations. The flow stress–stored energy and flow stress–dislocation density relationships can be accounted for if the flow stress is attributed either to the stress required for a dislocation to penetrate the forest of dislocations, or to the stress required to move jogged dislocations.

Electron microscope observations on some polycrystalline metals suggest that after small to moderate deformation, recrystallization occurs by the migration of the original grain boundaries. A theory based on this mechanism can account for the known form of the recrystallization kinetics without necessarily introducing any anisotropy of grain boundary mobility. For this mechanism the so-called recrystallization activation energy is identical to the activation energy for grain boundary migration.

Uniaxial fibre-reinforced epoxy resin composites have been produced containing up to Vf=08 of type I, II, III and IV carbon fibres in both untreated and surface-treated conditions. Their mechanical properties have been determined, and it has been shown that the fibre-matrix interface is strongest when the type II and III treated fibres are employed and weakest for the type I untreated fibres. The strength and stiffness of the composites approach that predicted by a rule of mixtures law at low Vf, but tend to fall below this when Vf>06. This fall off is greater in the case of composites of low fibre-matrix interface strength. The impact resistance (unnotched) is related to the strain energy potential of the fibre, Vf, and to a lesser extent to the fibre-matrix interface strength. A parameter U*=σf2Vf/Ef is proposed as an indicator of impact resistance performance. The principal effect of the interface strength is to modify the mode of failure. At high levels of strength the failure is brittle and relatively little energy is absorbed. At low levels of strength a multiple delamination occurs, energy absorption is about three times as high as in the brittle case, but extensive disintegration of the specimen occurs. At intermediate values of interface strength a progressive failure occurs which appears to be the best practical compromise; energy absorption is relatively high and disintegration is avoided. The composites having the best impact resistance were those containing 06 Vf type II or III untreated fibre. These gave impact energies of similar 100 kJ m−2 and had interlaminar shear strengths of 50-60 MN m−2.

Topological methods are applied in a study of the periodic operation of plug-flow processes. Attention is focused on periodic processes, but the results are shown to apply to other important situations. Three combinations of control options are considered and compared. Attainable sets for each case are characterized. The theory describes comparisons between steady state and time-varying controls and the a priori structure of optimal control. On applique des methodes topologiques a I'etude du fonctionnement periodique des procedes d'ecoulement a bouchon (plug). On considere particulierement les procedes periodiques, mais on demontre que les resultats s'appliquent aussi a d'autres cas importants. On examine et compare trois sortes de contro'le qu'on peut utiliser et caracterise les resultats qu'on peut obtenir dans chaque cas. La theorie decrit des comparaisons entre les contro'les en regime permanent et a duree variable et la structure a priori du contro'le optimal.

This article describes analysis by infrared spectroscopy of the reactions occurring during the oxidation stage of the formation of carbon fibres.

Free, bound, and total plasma tryptophan (F.P.T., B.P.T., and T.P.T.) levels have been measured throughout the night in six young female volunteers. All-night polygraphic sleep recordings were also made. No direct temporal relationship was found between plasma tryptophan levels and specific sleep stages. The mean F.P.T. levels, however, were found to have a positive correlation with rapid-eye-movement (R.E.M.) sleep and a negative correlation with non-R.E.M. sleep. An inverse relationship existed between the F.P.T. and B.P.T. levels. There appeared to be a diurnal variation in F.P.T. levels, with high readings in the first half of the night.

It is shown that the perturbation of the ultraviolet absorption spectra of the tyrosine and tryptophan chromophores in aqueous solutions by addition of solvents of lower polarity leads not only to red shifts but also to changes in peak intensity, and oscillator strength. The effect is much greater in tyrosine than in tryptophan, and can be as large as 30% (transfer from water to ethanol). It is shown that observed difference spectra can be reasonably reproduced by the addition of two calculated curves, one corresponding to a shift, the other to a change in intensity, i.e. an admixture of shift difference spectrum and absolute spectrum. Similar intensity changes are seen to accompany the denaturation of several proteins. The changes of the characteristic parameters of difference spectra with the concentration of perturbant are analyzed. The relation between the difference spectra generated by aromatic chromophores near 230 mμ and those in the 280 mμ region are considered, and their relative magnitudes have been estimated for a variety of perturbants. It is shown that in denaturation of a number of proteins, the difference spectra near 230 mμ cannot be satisfactorily accounted for solely in terms of the model compounds containing aromatic chromophores. Possible contributions to difference spectra of proteins in this region are considered.

Alumina gels, also known as gelatinous boehmite or pseudo-boehmite are a mono-hydrate of alumina having orthorhombic crystal structure. They are prepared by precipitation from aluminium salts by treatment with bases. The properties and appearance of the precipitate vary according to the reaction condition, but all gelatinous boehmites have extremely small particle and crystallite size (1,2,3). On calcination they lose their water of hydration and are converted to transition oxides of very high surface area (2,4,5,5,6). The present interest in alumina gels arises from their ability to form highly extrudable pastes. The possibility of enhanced sintering in such ‘reactive’ powders has been recognised in the past, but little experimental work has been undertaken. The purpose of this paper, therefore, is to present the results of some studies of the sintering behaviour of alumina gels, with particular regard to the influence of phase transformations, which have formed part of a more technological research programme (7,8,9).

Continuous filament reinforcement of nickel base alloy turbine blades with SiC, W, or Al203 has been considered as a means of improving creep resistance at high temperatures (up to 1200°0). SiC is readily available in fibre form, but reacts chemically with the matrix; tungsten wires are excessively dense; and alumina fibres have not been available until recently. Extrusion or pulling of molten alumina was tried but abandoned at an early stage. Extrusion and sintering of a very concentrated aqueous dispersion of hydrated alumina has been moderately successful. Bend strengths of about 80 x 103 psi at 85% theoretical density are better than most commercially available sintered alumina rods of larger diameter and are capable of withstanding stresses >10 x 103 psi for 100 hr at 1100°C, Fabrication of composite blades using polycrystalline alumina (or continuous sapphire single crystal) fibres has not proved successful by liquid infiltration since severe damage is caused to the fibres.

Carbon fiber-epoxy resin composites containing up to 0. 80 Vf of unidirectionally disposed fibers have been developed with flexural moduli and strengths very close to the theoretical values. However, the fiber-matrix interface is relatively weak resulting in low interlaminar shear strength. Attempts to raise the shear strength have led to brittleness problems. The fracture behavior of a variety of fiber-resin systems has been studied in the flexural and shear modes under static and repeated loading (fatigue), and under sustained loading (creep). Mechanical test data is correlated with fracture mode and morphology.

The standard free-energies and enthalpies of formation of the azide complex of three human abnormal methaemoglobins, human fetal methaemoglobin FII, and five animal methaemoglobins have been determined as a function of pH. For all the methaemoglobins –ΔH° passes through a maximum at a pH, pHch, characteristic of the particular methaemoglobin. There is a correlation between pHch and a simple function of the number of lysine, arginine, glutamic acid, and aspartic acid residues in the molecules. The pK values of ionization of methaemoglobins FII, DIbadan, and NBaltimore have been determined as a function of temperature and ionic strength. The variation of pK with ionic strength and the difference between the values of the pK values at zero ionic strength are shown to be consistent with the dielectric cavity model for the protein used in earlier papers in the series.