Descoloração e Mineralização de Corantes Reativos por Processo Fotocatalítico Utilizando ZnO e Radiação UV

As indústrias consomem volumes elevados de água e outras substâncias químicas na síntese dos seus produtos e geram grande quantidade de rejeitos. Entre os mais importantes poluentes encontrados nos efluentes dessas indústrias estão os corantes sintéticos que representam um problema, pois não são facilmente destruídos por tratamentos convencionais. A fotocatálise heterogênea tem sido considerada como uma alternativa efetiva no tratamento de efluentes contendo esses corantes. Neste trabalho, estudou-se a cinética de descoloração e o grau de mineralização dos corantes sintéticos reativos Yellow 145, Black 5, Red 4 e Blue 21 através da fotocatálise utilizando ZnO puro e impregnado com íons Fe2+ e Co2+. Testes preliminares foram realizados para otimizar a concentração dos corantes e a massa mínima de catalisador a ser utilizado nos experimentos fotocatalíticos. Além da fotocatálise, experimentos individuais de fotólise e adsorção também foram realizados, porém se mostraram poucos eficientes. Através da espectrofotometria UV-Vis, verificou-se o total descoramento individual dos corantes em aproximadamente 30 minutos de irradiação com ZnO. O grau de mineralização de cada corante foi determinado através de análise de carbono orgânico total (COT), atingindo-se cerca de 70 a 80% de mineralização após 240 minutos de tratamento fotocatalítico. Foram comparadas, ainda, as eficiências de cada fotocatalisador ZnO, Fe/ZnO e Co/ZnO na mineralização de uma solução contendo a mistura dos quatro corantes já mencionados após 240 minutos de reação. A eficiência na mineralização da mistura dos corantes seguiu a seguinte ordem: Co/ZnO (32%), ZnO (78%) e Fe/ZnO (87%). A reação de degradação fotocatalítica do corante Black 5 seguiu uma cinética de primeira ordem, enquanto que os corantes Yellow 145, Red 4 e Blue 21 seguiram uma cinética de ordem zero.

Wave interactions in periodic structures and periodic dielectric waveguides

This work is concerned with a general analysis of wave interactions in periodic structures and particularly periodic thin film dielectric waveguides.

The electromagnetic wave propagation in an asymmetric dielectric waveguide with a periodically perturbed surface is analyzed in terms of a Floquet mode solution. First order approximate analytical expressions for the space harmonics are obtained. The solution is used to analyze various applications: (1) phase matched second harmonic generation in periodically perturbed optical waveguides; (2) grating couplers and thin film filters; (3) Bragg reflection devices; (4) the calculation of the traveling wave interaction impedance for solid state and vacuum tube optical traveling wave amplifiers which utilize periodic dielectric waveguides. Some of these applications are of interest in the field of integrated optics.

A special emphasis is put on the analysis of traveling wave interaction between electrons and electromagnetic waves in various operation regimes. Interactions with a finite temperature electron beam at the collision-dominated, collisionless, and quantum regimes are analyzed in detail assuming a one-dimensional model and longitudinal coupling.

The analysis is used to examine the possibility of solid state traveling wave devices (amplifiers, modulators), and some monolithic structures of these devices are suggested, designed to operate at the submillimeter-far infrared frequency regime. The estimates of attainable traveling wave interaction gain are quite low (on the order of a few inverse centimeters). However, the possibility of attaining net gain with different materials, structures and operation condition is not ruled out.

The developed model is used to discuss the possibility and the theoretical limitations of high frequency (optical) operation of vacuum electron beam tube; and the relation to other electron-electromagnetic wave interaction effects (Smith-Purcell and Cerenkov radiation and the free electron laser) are pointed out. Finally, the case where the periodic structure is the natural crystal lattice is briefly discussed. The longitudinal component of optical space harmonics in the crystal is calculated and found to be of the order of magnitude of the macroscopic wave, and some comments are made on the possibility of coherent bremsstrahlung and distributed feedback lasers in single crystals.

The modulated grating hologram

A phase and amplitude, off-axis hologram has been synthesized from three computer-generated transmission masks, using a multiple-exposure holographic recording method. Each of the masks controls one fixed-phase component of the complex hologram transmittance. The basic grating is generated optically, relieving the computer of the burden of drawing details the size of each fringe. The maximum information capacity of the computer plotting device can then be applied to the generation of the grating modulation function. By this method large digital holograms (25 mm by 25 mm) have been synthesized in dichromated gelatin. The recording method is applicable to virtually any holographic medium.

The modulated grating hologram was designed primarily for the application of spatial filtering, in which the requirement is a hologram with large dynamic range and large free spectral range. Choice of a low-noise, high-efficiency medium such as dichromated gelatin will allow exceptionally large dynamic range. Independence of the optically-generated carrier grating from the computer-generated modulation functions allows arbitrarily large free spectral range.

The performance of a holographic spatial filter will be limited ultimately by noise originating from imperfections in the holographic medium. The characteristics of this noise are analyzed, and in the case of a high diffraction efficiency hologram are shown to differ significantly from previous analyses. The dominant noise source in holograms of high diffraction efficiency will be scattering of the first order or imaging wave by deformations in the hologram surface or other effects of low spatial frequency. Experimental measurements in various low-noise holographic media verify these predictions.

Part I. Influence of membrane morphology on ion-exchange and charge propagation in composite polyelectrolyte electrode coatings. Part II. Dynamic surface tension measurements of polarization relaxation at mercury pool electrodes by the method of Wilhelmy.

Part I. Novel composite polyelectrolyte materials were developed that exhibit desirable charge propagation and ion-retention properties. The morphology of electrode coatings cast from these materials was shown to be more important for its electrochemical behavior than its chemical composition.

Part II. The Wilhelmy plate technique for measuring dynamic surface tension was extended to electrified liquid-liquid interphases. The dynamical response of the aqueous NaF-mercury electrified interphase was examined by concomitant measurement of surface tension, current, and applied electrostatic potential. Observations of the surface tension response to linear sweep voltammetry and to step function perturbations in the applied electrostatic potential (e.g., chronotensiometry) provided strong evidence that relaxation processes proceed for time-periods that are at least an order of magnitude longer than the time periods necessary to establish diffusion equilibrium. The dynamical response of the surface tension is analyzed within the context of non-equilibrium thermodynamics and a kinetic model that requires three simultaneous first order processes.

Wastewater Electrolysis Cell for Environmental Pollutants Degradation and Molecular Hydrogen Generation

This study proposes a wastewater electrolysis cell (WEC) for on-site treatment of human waste coupled with decentralized molecular H₂ production. The core of the WEC includes mixed metal oxides anodes functionalized with bismuth doped TiO₂ (BiO_x/TiO₂). The BiO_x/TiO₂ anode shows reliable electro-catalytic activity to oxidize Cl- to reactive chlorine species (RCS), which degrades environmental pollutants including chemical oxygen demand (COD), protein, NH4⁺, urea, and total coliforms. The WEC experiments for treatment of various kinds of synthetic and real wastewater demonstrate sufficient water quality of effluent for reuse for toilet flushing and environmental purposes. Cathodic reduction of water and proton on stainless steel cathodes produced molecular H2 with moderate levels of current and energy efficiency. This thesis presents a comprehensive environmental analysis together with kinetic models to provide an in-depth understanding of reaction pathways mediated by the RCS and the effects of key operating parameters. The latter part of this thesis is dedicated to bilayer hetero-junction anodes which show enhanced generation efficiency of RCS and long-term stability.

Chapter 2 describes the reaction pathway and kinetics of urea degradation mediated by electrochemically generated RCS. The urea oxidation involves chloramines and chlorinated urea as reaction intermediates, for which the mass/charge balance analysis reveals that N₂ and CO₂ are the primary products. Chapter 3 investigates direct-current and photovoltaic powered WEC for domestic wastewater treatment, while Chapter 4 demonstrates the feasibility of the WEC to treat model septic tank effluents. The results in Chapter 2 and 3 corroborate the active roles of chlorine radicals (Cl•/Cl₂^-•) based on iR-compensated anodic potential (thermodynamic basis) and enhanced pseudo-first-order rate constants (kinetic basis). The effects of operating parameters (anodic potential and [Cl^-] in Chapter 3; influent dilution and anaerobic pretreatment in Chapter 4) on the rate and current/energy efficiency of pollutants degradation and H₂ production are thoroughly discussed based on robust kinetic models. Chapter 5 reports the generation of RCS on Ir_0.7Ta_0.3O_y/Bi_xTi_1-xO_z hetero-junction anodes with enhanced rate, current efficiency, and long-term stability compared to the Ir_0.7Ta_0.3O_y anode. The effects of surficial Bi concentration are interrogated, focusing on relative distributions between surface-bound hydroxyl radical and higher oxide.

Enhanced Thermoelectric Performance at the Superionic Phase Transitions of Mixed Ion-Electron Conducting Materials

The quality of a thermoelectric material is judged by the size of its temperature de- pendent thermoeletric-figure-of-merit (zT ). Superionic materials, particularly Zn₄Sb₃ and Cu₂Se, are of current interest for the high zT and low thermal conductivity of their disordered, superionic phase. In this work it is reported that the super-ionic materials Ag₂Se, Cu₂Se and Cu_1.97Ag_0.03Se show enhanced zT in their ordered, normal ion-conducting phases. The zT of Ag₂Se is increased by 30% in its ordered phase as compared to its disordered phase, as measured just below and above its first order phase transition. The zT ’s of Cu₂Se and Cu_1.97Ag_0.03Se both increase by more than 100% over a 30 K temperatures range just below their super-ionic phase transitions. The peak zT of Cu₂Se is 0.7 at 406 K and of Cu_1.97Ag_0.03Se is 1.0 at 400 K. In all three materials these enhancements are due to anomalous increases in their Seebeck coefficients, beyond that predicted by carrier concentration measurements and band structure modeling. As the Seebeck coefficient is the entropy transported per carrier, this suggests that there is an additional quantity of entropy co-transported with charge carriers. Such co-transport has been previously observed via co-transport of vibrational entropy in bipolaron conductors and spin-state entropy in Na_xCo₂O₄. The correlation of the temperature profile of the increases in each material with the nature of their phase transitions indicates that the entropy is associated with the thermodynamcis of ion-ordering. This suggests a new mechanism by which high thermoelectric performance may be understood and engineered.

A small perturbation theory for cycloidal propellers

A hydromechanical theory is developed for cycloidal propellers for two limiting modes of operation wherein U » ΩR and U « ΩR, with U the rectilinear propeller speed (speed of advance) and ΩR the rotational blade speed. A first order theory is developed from the basic principles of the kinematics and dynamics of fluid motion and proceeds from the point of view of unsteady hydrofoil theory.

Explicit expressions for the instantaneous forces and moments produced by blade motions are presented. On the basis of these results an optimization procedure is carried out which minimizes the energy loss under the constraint of specified mean thrust. Under optimal conditions the propeller is found to possess high Froude efficiencies in both the high and low speed modes of propulsion. This efficiency is defined as the ratio of the average useful work obtained during one cycle of propeller operation to the average power input required to sustain the motion of the propeller during the cycle.

低密度台阶形闪耀光栅的制作

介绍了制作低密度闪耀光栅的过程,在制作时,对传统的制作过程进行了改进,有效提高了制作质量。以40μm闪耀光栅为例介绍了制作的过程,得到了良好的光栅表面形貌,并且闪耀级次的衍射效率达到了70%以上。相比传统的制作方法,效率提高了5%～10%。对比了理论上的衍射效率,分析了实验误差,发现把存在对准误差的光栅进行处理将会有效地提高其衍射效率,为进一步提高闪耀光栅的衍射效率提供了依据。

Continuous stochastic processes

A general review of stochastic processes is given in the introduction; definitions, properties and a rough classification are presented together with the position and scope of the author's work as it fits into the general scheme.

The first section presents a brief summary of the pertinent analytical properties of continuous stochastic processes and their probability-theoretic foundations which are used in the sequel.

The remaining two sections (II and III), comprising the body of the work, are the author's contribution to the theory. It turns out that a very inclusive class of continuous stochastic processes are characterized by a fundamental partial differential equation and its adjoint (the Fokker-Planck equations). The coefficients appearing in those equations assimilate, in a most concise way, all the salient properties of the process, freed from boundary value considerations. The writer’s work consists in characterizing the processes through these coefficients without recourse to solving the partial differential equations.

First, a class of coefficients leading to a unique, continuous process is presented, and several facts are proven to show why this class is restricted. Then, in terms of the coefficients, the unconditional statistics are deduced, these being the mean, variance and covariance. The most general class of coefficients leading to the Gaussian distribution is deduced, and a complete characterization of these processes is presented. By specializing the coefficients, all the known stochastic processes may be readily studied, and some examples of these are presented; viz. the Einstein process, Bachelier process, Ornstein-Uhlenbeck process, etc. The calculations are effectively reduced down to ordinary first order differential equations, and in addition to giving a comprehensive characterization, the derivations are materially simplified over the solution to the original partial differential equations.

In the last section the properties of the integral process are presented. After an expository section on the definition, meaning, and importance of the integral process, a particular example is carried through starting from basic definition. This illustrates the fundamental properties, and an inherent paradox. Next the basic coefficients of the integral process are studied in terms of the original coefficients, and the integral process is uniquely characterized. It is shown that the integral process, with a slight modification, is a continuous Markoff process.

The elementary statistics of the integral process are deduced: means, variances, and covariances, in terms of the original coefficients. It is shown that an integral process is never temporally homogeneous in a non-degenerate process.

Finally, in terms of the original class of admissible coefficients, the statistics of the integral process are explicitly presented, and the integral process of all known continuous processes are specified.

Kinetics and mechanisms of adsorption of Escherichia coli bacteriophage T_4 to activated carbon

A study was conducted on the adsorption of Escherichia coli bacteriophage T₄ to activated carbon. Preliminary adsorption experiments were also made with poliovirus Type III. The effectiveness of such adsorbents as diatomaceous earth, Ottawa sand, and coconut charcoal was also tested for virus adsorption.

The kinetics of adsorption were studied in an agitated solution containing virus and carbon. The mechanism of attachment and site characteristics were investigated by varying pH and ionic strength and using site-blocking reagents.

Plaque assay procedures were developed for bacteriophage T₄ on Escherichia coli cells and poliovirus Type III on monkey kidney cells. Factors influencing the efficiency of plaque formation were investigated.

The kinetics of bacteriophage T₄ adsorption to activated carbon can be described by a reversible second-order equation. The reaction order was first order with respect to both virus and carbon concentration. This kinetic representation, however, is probably incorrect at optimum adsorption conditions, which occurred at a pH of 7.0 and ionic strength of 0.08. At optimum conditions the adsorption rate was satisfactorily described by a diffusion-limited process. Interpretation of adsorption data by a development of the diffusion equation for Langmuir adsorption yielded a diffusion coefficient of 12 X 10^-8 cm²/sec for bacteriophage T₄. This diffusion coefficient is in excellent agreement with the accepted value of 8 X 10^-8 cm²/sec. A diffusion-limited theory may also represent adsorption at conditions other than the maximal. A clear conclusion on the limiting process cannot be made.

Adsorption of bacteriophage T₄ to activated carbon obeys the Langmuir isotherm and is thermodynamically reversible. Thus virus is not inactivated by adsorption. Adsorption is unimolecular with very inefficient use of the available carbon surface area. The virus is probably completely excluded from pores due to its size.

Adsorption is of a physical nature and independent of temperature. Attraction is due to electrostatic forces between the virus and carbon. Effects of pH and ionic strength indicated that carboxyl groups, amino groups, and the virus's tail fibers are involved in the attachment of virus to carbon. The active sites on activated carbon for adsorption of bacteriophage T₄ are carboxyl groups. Adsorption can be completely blocked by esterifying these groups.

I. The rate and mechanism of the vapor-phase reaction between water and parts-per-million concentrations of nitrogen dioxide. II. The rate and mechanism of the air oxidation of parts-per-million concentrations of nitric oxide in the presence of water vapor.

Part I

A study of the thermal reaction of water vapor and parts-per-million concentrations of nitrogen dioxide was carried out at ambient temperature and at atmospheric pressure. Nitric oxide and nitric acid vapor were the principal products. The initial rate of disappearance of nitrogen dioxide was first order with respect to water vapor and second order with respect to nitrogen dioxide. An initial third-order rate constant of 5.5 (± 0.29) x 10⁴ liter² mole^-2 sec^-1 was found at 25˚C. The rate of reaction decreased with increasing temperature. In the temperature range of 25˚C to 50˚C, an activation energy of -978 (± 20) calories was found.

The reaction did not go to completion. From measurements as the reaction approached equilibrium, the free energy of nitric acid vapor was calculated. This value was -18.58 (± 0.04) kilocalories at 25˚C.

The initial rate of reaction was unaffected by the presence of oxygen and was retarded by the presence of nitric oxide. There were no appreciable effects due to the surface of the reactor. Nitric oxide and nitrogen dioxide were monitored by gas chromatography during the reaction.

Part II

The air oxidation of nitric oxide, and the oxidation of nitric oxide in the presence of water vapor, were studied in a glass reactor at ambient temperatures and at atmospheric pressure. The concentration of nitric oxide was less than 100 parts-per-million. The concentration of nitrogen dioxide was monitored by gas chromatography during the reaction.

For the dry oxidation, the third-order rate constant was 1.46 (± 0.03) x 10⁴ liter² mole^-2 sec^-1 at 25˚C. The activation energy, obtained from measurements between 25˚C and 50˚C, was -1.197 (±0.02) kilocalories.

The presence of water vapor during the oxidation caused the formation of nitrous acid vapor when nitric oxide, nitrogen dioxide and water vapor combined. By measuring the difference between the concentrations of nitrogen dioxide during the wet and dry oxidations, the rate of formation of nitrous acid vapor was found. The third-order rate constant for the formation of nitrous acid vapor was equal to 1.5 (± 0.5) x 10⁵ liter² mole^-2 sec^-1 at 40˚C. The reaction rate did not change measurably when the temperature was increased to 50˚C. The formation of nitric acid vapor was prevented by keeping the concentration of nitrogen dioxide low.

Surface effects were appreciable for the wet tests. Below 35˚C, the rate of appearance of nitrogen dioxide increased with increasing surface. Above 40˚C, the effect of surface was small.

Part I: The abortive infection of bacteriophage øx174 at low temperatures. Part II: The early stages in the process of infection by bacteriophage øx174

Part I

The infection of E. coli by ΦX174 at 15°C is abortive; the cells are killed by the infection but neither mature phage nor SS (single-stranded) DNA are synthesized. Parental RF (replicative form) is formed and subsequently replicated at 15°C. The RF made at 15°C shows normal infectivity and full competence to act as precursor to progeny SS DNA after an increase in temperature to 37°C. The investigations suggest that all of the proteins required for SS DNA synthesis and phage maturation are present in the abortive infection at 15°C.

Three possible causes are suggested for the abortive infection at 15°C: (a) A virus-coded protein whose role is essential to the infection is made at 15°C and assumes its native conformation, but its rate of activity is too low at this temperature to sustain the infection process. (b) Virus maturation may involve the formation of a DNA-protein complex and conformational changes which have an energy threshold infrequently reached at 15°C. (c) A host-coded protein present in uninfected cells, and whose activity is essential to the infection at all temperatures, but not to the host at 15°C, is inactive at 15°C. An hypothesis of this type is offered which proposes that the temperature-limiting factor in SS DNA synthesis in vivo may reflect a temperature-dependent property of the host DNA polymerase.

Part II

Three distinct stages are demonstrated in the process whereby ΦX174 invades its host: (1) Attachment: The phage attach to the cell in a manner that does not irreversibly alter the phage particle and which exhibits "single-hit" kinetics. The total charge on the phage particle is demonstrated to be important in determining the rate at which stable attachment is effected. The proteins specified by ΦX cistrons II, III and VII play roles, which may be indirect, in the attachment reaction. (2) Eclipse: 'The attached phage undergo a conformational change. Some of the altered phage particles spontaneously detach from the cell (in a non-infective form) while the remainder are more tightly bound to the cell. The altered phage particles detached (spontaneously or chemically) from such complexes have at least 40% of their DNA extruded from the phage coat. It is proposed that this particle is, or derives from, a direct intermediate in the penetration of the viral DNA.

The kinetics for the eclipse of attached phage particles are first-order with respect to phage concentration and biphasic; about 85% of the phage eclipse at one rate (k = 0.86 min^-1) and the remainder do so at a distinctly lesser rate (k = 0.21 min^-1).

The eclipse event is very temperature-dependent and has the relatively high Arrhenius activation energy of 36.6 kcal/mole, indicating the cooperative nature of the process. The temperature threshold for eclipse is 17 to 18°C.

At present no specific ΦX cistron is identified as affecting the eclipse process. (3) DNA penetration: A fraction of the attached, eclipsed phage particles corresponding in number to the plaque-forming units complete DNA penetration. The penetrated DNA is found in the cell as RF, and the empty phage protein coat remains firmly attached to the exterior of the cell. This step is inhibited by prior irradiation of the phage with relatively high doses of UV light and is insensitive to the presence of KCN and NaN₃. Temporally excluded superinfecting phages do not achieve DNA penetration.

Both eclipsed phage particles and empty phage protein coats may be dissociated from infected cells; some of their properties are described.

I. A study of the dynamics of triplet excitons in molecular crystals. II. An investigation of delayed light emission from Chlorella pyrenoidosa

I. PREAMBLE AND SCOPE

Brief introductory remarks, together with a definition of the scope of the material discussed in the thesis, are given.

II. A STUDY OF THE DYNAMICS OF TRIPLET EXCITONS IN MOLECULAR CRYSTALS

Phosphorescence spectra of pure crystalline naphthalene at room temperature and at 77˚ K are presented. The lifetime of the lowest triplet ³B_1u state of the crystal is determined from measurements of the time-dependence of the phosphorescence decay after termination of the excitation light. The fact that this lifetime is considerably shorter in the pure crystal at room temperature than in isotopic mixed crystals at 4.2˚ K is discussed, with special importance being attached to the mobility of triplet excitons in the pure crystal.

Excitation spectra of the delayed fluorescence and phosphorescence from crystalline naphthalene and anthracene are also presented. The equation governing the time- and spatial-dependence of the triplet exciton concentration in the crystal is discussed, along with several approximate equations obtained from the general equation under certain simplifying assumptions. The influence of triplet exciton diffusion on the observed excitation spectra and the possibility of using the latter to investigate the former is also considered. Calculations of the delayed fluorescence and phosphorescence excitation spectra of crystalline naphthalene are described.

A search for absorption of additional light quanta by triplet excitons in naphthalene and anthracene crystals failed to produce any evidence for the phenomenon. This apparent absence of triplet-triplet absorption in pure crystals is attributed to a low steady-state triplet concentration, due to processes like triplet-triplet annihilation, resulting in an absorption too weak to be detected with the apparatus used in the experiments. A comparison of triplet-triplet absorption by naphthalene in a glass at 77˚ K with that by naphthalene-h₈ in naphthalene-d₈ at 4.2˚ K is given. A broad absorption in the isotopic mixed crystal triplet-triplet spectrum has been tentatively interpreted in terms of coupling between the guest ³B_1u state and the conduction band and charge-transfer states of the host crystal.

III. AN INVESTIGATION OF DELAYED LIGHT EMISSION FROM Chlorella Pyrenoidosa

An apparatus capable of measuring emission lifetimes in the range 5 X 10^-9 sec to 6 X 10^-3 sec is described in detail. A cw argon ion laser beam, interrupted periodically by means of an electro-optic shutter, serves as the excitation source. Rapid sampling techniques coupled with signal averaging and digital data acquisition comprise the sensitive detection and readout portion of the apparatus. The capabilities of the equipment are adequately demonstrated by the results of a determination of the fluorescence lifetime of 5, 6, 11, 12-tetraphenyl-naphthacene in benzene solution at room temperature. Details of numerical methods used in the final data reduction are also described.

The results of preliminary measurements of delayed light emission from Chlorella Pyrenoidosa in the range 10^-3 sec to 1 sec are presented. Effects on the emission of an inhibitor and of variations in the excitation light intensity have been investigated. Kinetic analysis of the emission decay curves obtained under these various experimental conditions indicate that in the millisecond-to-second time interval the decay is adequately described by the sum of two first-order decay processes. The values of the time constants of these processes appear to be sensitive both to added inhibitor and to excitation light intensity.

Equilibration of a liquid droplet-vapor-gas mixture downstream of a shock wave

The equations of motion for the flow of a mixture of liquid droplets, their vapor, and an inert gas through a normal shock wave are derived. A set of equations is obtained which is solved numerically for the equilibrium conditions far downstream of the shock. The equations describing the process of reaching equilibrium are also obtained. This is a set of first-order nonlinear differential equations and must also be solved numerically. The detailed equilibration process is obtained for several cases and the results are discussed.

Particle fluid mechanics in shear flows, acoustic waves, and shock waves

Three different categories of flow problems of a fluid containing small particles are being considered here. They are: (i) a fluid containing small, non-reacting particles (Parts I and II); (ii) a fluid containing reacting particles (Parts III and IV); and (iii) a fluid containing particles of two distinct sizes with collisions between two groups of particles (Part V).

Part I

A numerical solution is obtained for a fluid containing small particles flowing over an infinite disc rotating at a constant angular velocity. It is a boundary layer type flow, and the boundary layer thickness for the mixture is estimated. For large Reynolds number, the solution suggests the boundary layer approximation of a fluid-particle mixture by assuming W = W_p. The error introduced is consistent with the Prandtl’s boundary layer approximation. Outside the boundary layer, the flow field has to satisfy the “inviscid equation” in which the viscous stress terms are absent while the drag force between the particle cloud and the fluid is still important. Increase of particle concentration reduces the boundary layer thickness and the amount of mixture being transported outwardly is reduced. A new parameter, β = 1/Ω τ_v, is introduced which is also proportional to μ. The secondary flow of the particle cloud depends very much on β. For small values of β, the particle cloud velocity attains its maximum value on the surface of the disc, and for infinitely large values of β, both the radial and axial particle velocity components vanish on the surface of the disc.

Part II

The “inviscid” equation for a gas-particle mixture is linearized to describe the flow over a wavy wall. Corresponding to the Prandtl-Glauert equation for pure gas, a fourth order partial differential equation in terms of the velocity potential ϕ is obtained for the mixture. The solution is obtained for the flow over a periodic wavy wall. For equilibrium flows where λ_v and λ_T approach zero and frozen flows in which λ_v and λ_T become infinitely large, the flow problem is basically similar to that obtained by Ackeret for a pure gas. For finite values of λ_v and λ_T, all quantities except v are not in phase with the wavy wall. Thus the drag coefficient C_D is present even in the subsonic case, and similarly, all quantities decay exponentially for supersonic flows. The phase shift and the attenuation factor increase for increasing particle concentration.

Part III

Using the boundary layer approximation, the initial development of the combustion zone between the laminar mixing of two parallel streams of oxidizing agent and small, solid, combustible particles suspended in an inert gas is investigated. For the special case when the two streams are moving at the same speed, a Green’s function exists for the differential equations describing first order gas temperature and oxidizer concentration. Solutions in terms of error functions and exponential integrals are obtained. Reactions occur within a relatively thin region of the order of λ_D. Thus, it seems advantageous in the general study of two-dimensional laminar flame problems to introduce a chemical boundary layer of thickness λ_D within which reactions take place. Outside this chemical boundary layer, the flow field corresponds to the ordinary fluid dynamics without chemical reaction.

Part IV

The shock wave structure in a condensing medium of small liquid droplets suspended in a homogeneous gas-vapor mixture consists of the conventional compressive wave followed by a relaxation region in which the particle cloud and gas mixture attain momentum and thermal equilibrium. Immediately following the compressive wave, the partial pressure corresponding to the vapor concentration in the gas mixture is higher than the vapor pressure of the liquid droplets and condensation sets in. Farther downstream of the shock, evaporation appears when the particle temperature is raised by the hot surrounding gas mixture. The thickness of the condensation region depends very much on the latent heat. For relatively high latent heat, the condensation zone is small compared with Ʌ_D.

For solid particles suspended initially in an inert gas, the relaxation zone immediately following the compression wave consists of a region where the particle temperature is first being raised to its melting point. When the particles are totally melted as the particle temperature is further increased, evaporation of the particles also plays a role.

The equilibrium condition downstream of the shock can be calculated and is independent of the model of the particle-gas mixture interaction.

Part V

For a gas containing particles of two distinct sizes and satisfying certain conditions, momentum transfer due to collisions between the two groups of particles can be taken into consideration using the classical elastic spherical ball model. Both in the relatively simple problem of normal shock wave and the perturbation solutions for the nozzle flow, the transfer of momentum due to collisions which decreases the velocity difference between the two groups of particles is clearly demonstrated. The difference in temperature as compared with the collisionless case is quite negligible.