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A paper by Jottrand which deals with particle size segregation in liquid-fluidised beds is examined critically, and an attempt has been made to extend and complement his work. It is assumed that the driving force for segregation of two groups of particles in a particulately fluidised bed is the difference in bulk density of the beds formed by each group of particles separately when subjected, to the same superficial velocity of the fluid. Accordingly the following equation for the bulk density difference between two groups of particles with unequal diameters was derived and studied experimentally: [ Equation omitted ] In the above equation, the subscripts L and S refer to large and small particles respectively, m is the index of fluid régime (m = 1 in Stokes region, m = 2 in Newton region), and n is the exponent in a Richardson-Zaki type expansion equation. It was found that for equal density particles the segregation tendency increased as the overall porosity, and hence ɛL was increased and as the diameter ratio (r) was increased. The tendency either to mix or to segregate was found to be very sensitive to changes in ϒ (density difference between large particles and fluid divided by the density difference between small particles and fluid), as is the bulk density difference in the above equation. It was observed that a bed could be either mixed or completely segregated, with one or the other size of particles occupying the upper portion of the bed, depending on the relative magnitudes of r and ϒ. It was also found that, while an increase in the factor ( ρpL-ρ) increased the bulk density difference, it did not increase the tendency of the particles to segregate, provided r and ϒ were kept constant. The values of m and n were found to change sufficiently, as the fluid régime was changed from the Stokes region to the Newton region, to account for the corresponding changes in segregation tendencies. Finally it was concluded that the bulk density difference equation predicted the right trends, insofar as mixing or segregation are concerned, but that the absolute magnitude of the predicted bulk density difference was not uniquely correlated with the observed phenomena, when the particle density was varied at constant r and ϒ . The applicability of a reduced bulk density difference was suggested by the limited data available. / Applied Science, Faculty of / Chemical and Biological Engineering, Department of / Graduate

Experiments are described on the possibility of developing a gas luminescence chamber for the observation of particle tracks. A brief review of devices currently available for obtaining ionizing particle tracks, particularly those capable of time resolutions in the microsecond region, is included. Attempts were made to detect scintillations in several gas and vapour mixtures. For some gas mixtures the possibility of using ionizing radiation to initiate a light producing chain reaction was investigated. These experiments were performed in the temperature range from 25 to 220° centigrade. Results obtained were not of such a nature to encourage further work towards the development of a gas luminescence chamber. As a background of non-radiation induced photon emission was observed for several reactions, it is possible that the methods employed in the experiment may be adopted to measure the onset and rate of some chemical reactions. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

This thesis investigates the possibility of constructing theories of composite particles of zero mass. Consideration is given primarily to the transformation properties of state vectors and operators used for the description of mass-less elementary particles under Lorentz transformation of the coordinate system. A method originally used by Wigner is developed more explicitly. The transformation properties of bilinear combinations of state functions and of operators are considered in some detail. It is found that the one example of a composite particle theory extant in the literature has incorrect transformation properties. No example of a correctly transforming theory is given. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

This thesis consists of two independent parts, both of which are applications of the quantum mechanical methods developed recently by R. P. Feynman. Part I is concerned with the non-relativistic theory, and applies Feynman’s formalism to the simple problem of the scattering of a particle by a potential field. The method and results are compared with those of the familiar Born-approximation. The two procedures are shown to be equivalent and to be valid under the same conditions. Feynman’s formulae are used to calculate the first and second order terms of the scattered particle wave function, with an arbitrary scattering potential. Part II uses the relativistic Feynman theory, and treats the scattering of positrons by electrons, and of two electrons. The calculation checks the work of H.J.Bhabha and C. Møller, who have obtained the same results by other methods. The differential cross-sections for the two scattering processes are calculated to first order, and an estimate is made of the feasibility of an experiment to determine whether the exchange effect described by Bhabha actually occurs in positron-electron scattering. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

The absolute cross section of the reaction D(p,ɣ)³He has been measured in the energy range from 400 Kev to 1100 Kev in the laboratory system. A target of deuterated polyethylene was used to measure the relative yield of the reaction over this range, and the results were normalized to an absolute measurement made with a deuterium gas target. The reaction is of interest because it enables some information to be obtained about the forces binding three nucleons together. It also has some significance in a number of astrophysical processes. In order to determine the cross section, the intrinsic efficiency of a 5 inch by 4 inch sodium iodide crystal scintillation counter was measured by simultaneous alpha particle and gamma ray counting on the 340 Kev resonance of the reaction ¹⁹F(p,[symbol omitted]ɣ)¹⁶0. The intrinsic efficiency of the detector was found to be .679 ± .03 for the 6.14 Mev gamma rays from this reaction, with the particular geometry used. The absolute cross section for the reaction D(p ɣ)³He was found by the gas target measurement to be 2.33 ± .07 microbarns for an incident proton energy of 643 kev. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

Fouling by a petroleum gas oil and a dilute suspension of sand in water was studied as a function of mass flow rate and wall temperature. The experiments were carried out by circulating the liquid through a single tube maintained at constant heat flux by electrical heating. The change in fouling resistance and pressure drop with time was measured. The fouling resistance of the water and of the oil at low heat fluxes grows to an asymptotic value. At higher heat fluxes the oil fouling resistance increased almost linearly with time after an induction period. The asymptotic fouling resistance of both the oil and the water decreased with increasing mass flow rate. At constant clean tube wall temperature the initial fouling rate of the oil decreased with increasing mass flow rate. The initial fouling rate of the water increased with increasing mass flow rate up to a critical mass flow rate, and then decreased with further increases in mass flow rate. At constant mass flow rate, the initial fouling rate of the oil depended exponentially on the clean tube wall temperature. An activation energy of 29 Kcal/mole was calculated for the oil fouling process by fitting the initial fouling rate data to an Arrhenius type of equation. The pressure drop increase showed the same general trends with mass flow rate and tube wall temperature as did the fouling resistance. Fouling resistances for heated Kraft cooking liquor, calculated from pulp mill operating data and from a single fouling experiment, appeared to follow similar trends to those, followed in common by the gas oil and the water. The experimental results of this study were compared to the mathematical model of Kern and Seaton. While the shape of most fouling curves was in agreement with that predicted generally by this model, dependence of the initial fouling rate and of the asymptotic fouling resistance of the gas oil on the mass flow rate were both in disagreement with the detailed predictions of the model. For low mass flow rates of the water, however, even the detailed predictions were borne out. It was, moreover, possible to remove part of the sand deposit by increasing the velocity of the water, in accord with the postulated removal mechanism of Kern and Seaton, but the coke-like deposit from the gas oil could not be similarly removed by increasing the oil velocity. Mathematical models are developed in which the deposition term is written as the product of a material flux to the wall region and a sticking probability, after Parkins, and the removal term depends on the shear stress, after Kern and Seaton. Specific cases are considered where deposition is controlled by transfer to the surface, adhesion at the surface, and a combination of both steps.. Where deposition is controlled partly by transfer and partly by adhesion, the model predicts mass flow rate and temperature dependence of the initial fouling rate in agreement with the experimental results found for the oil. The observed asymptotic fouling resistance of the oil, however, depended less strongly on the reciprocal of the mass flow rate than is predicted by the model. Where transfer alone controls the deposition process, the extended model reduces to a form similar to that of Kern and Seaton. / Applied Science, Faculty of / Chemical and Biological Engineering, Department of / Graduate

In this thesis, a detailed study is made of the phenomenon of Octet Enhancement in hadronic interactions. After a survey of the experimental consequences of Octet Enhancement is made in Chapter II, a review and discussion of the various theories of Octet Enhancement is given in Chapter III. In Chapter IV, a general group theorectical discussion, based on an extension of Glashow's Method (S. L. Glashovr, 1963) of spontaneous symmetry breaking is presented. A general theorem in connection with spontaneous symmetry breaking is stated and proved. The theorem lends itself to a number of interesting applications. Among these is a demonstration that if a unitary triplet exists in nature which is non-trivially coupled to the rest of the hadrons, then Octet Enhancement follows without recourse to any detailed dynamical assumption. In particular, the triplet need not be quarks in the sense of fundamental building blocks of all matter. It is also demonstrated group theoretically that ϕ-ω mixing can in principle occur as a particular form of spontaneous symmetry breaking, in exactly the same way that a spontaneous mass splitting can occur. Assuming Octet Dominance in the symmetry breaking of a degenerate nonet of vector mesons, it follows quite generally that the formulae [formulae omitted] must hold. Here again, no dynamical detail is required. In Chapter V, a bootstrap model consisting of an octet of vector mesons is constructed with which it is demonstrated step by step how Octet Enhancement follows from the intricate working of two dynamical principles — (a) the bootstrap hypothesis and (b) that the mesons participating in the bootstrap must be physical particles and not ghost states. In Chapter VI, the model is extended to study ϕ-ω mixing. A phenomenon which can be interpreted as a "sponteneous" ϕ-ω mixing is found to in fact occur. Furthermore, formulae (i) and (ii) also emerge from this model. The only extra assumption besides (a) and (b) that we have to make here is the mere "existence" of a unitary singlet vector meson whose "bare" mass (the mass of the particle before it is embroiled in the bootstrap) is equal to average mass of the octet. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

Wave-particle interaction in the ionosphere is studied theoretically for wave frequencies around the lower hybrid resonance (LHR) frequency. Expressions are derived by two methods for the growth rate of whistler-mode waves propagating in a magneto-active plasma penetrated by a tenuous beam of nonthermal particles. The first method employs the electrostatic dispersion equation; the second uses the full-wave dispersion equation which reduces to the electrostatic one for large values of refractive index. The equilibrium distribution function for the plasma is Maxwellian, and that for the diffuse streaming particles is also Maxwellian, but is shifted by a streaming velocity parallel to the background magnetic field. The first method assumes that the temperatures are isotropic, while the second assumes that the distributions are characterized by the perpendicular and parallel temperatures, T[subscript: I] and T[subscript: II] . The growth-rate expressions are fairly general, but numerical calculations are performed for the case of a cold plasma consisting of electrons, H⁺ , He⁺ , and 0⁺ ions and a beam of nonthermal electrons. The growth-rate expression obtained using the electrostatic dispersion equation shows that waves propagating slightly off the direction perpendicular to the background magnetic field can grow due to the Landau instability process which is excited by high energy (∼ 10 keV) electrons streaming along the direction of the magnetic field of the earth. The growing wave thus triggered is shown to have a frequency band with a sharp lower cutoff at the LHR frequency and an upper limit at the electron cyclotron frequency or electron plasma frequency, whichever is lower. The previous growth-rate expression is generalized by making use of the full-wave dispersion equation. It is shown that there are two regions in propagation angle 6 where the Landau instability may occur. The "electrostatic" region lies just below the resonant angle and, separated by a region of damping, the "low-θ" region lies above θ = 0 . The growth-rate values calculated in the "electrostatic" region correspond to the values obtained in the previous calculation. Generally, the maximum growth rate is larger in the "electrostatic" than in the "low-θ" region. It is also seen that with increasing frequency the "electrostatic" maximum growth rate increases monotonically and the cyclotron instabilities become important at frequencies above about ten times the LHR frequency. The influence of the following parameters on the growth rate is also examined: temperature ratio T[subscript: II]/T[subscript: I], streaming velocity of the nonthermal particles, and the ratio of the kinetic energy in the streaming motion to the thermal energy of the streaming electrons. The theory presented is applied to LHR noise bands discovered by the Canadian Alouette I satellite. It is shown that many features are in good agreement. Other observations, such as auroral hiss, also have features which suggest that the theoretical work may be relevant to these types of ionospheric noise. / Science, Faculty of / Earth, Ocean and Atmospheric Sciences, Department of / Graduate