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In slurry transport, the critical velocity is defined as the minimum velocity demarcating flows in which the solids form a bed at the bottom of the pipe (bed load flows) from fully suspended flow. An analysis based on balancing the energy required to suspend the particles with that derived from dissipation of an appropriate fraction of the turbulent eddies is used to develop a correlation for prediction of the critical velocity. Comparison of the results with available experimental critical velocity data, relating to a rather wide variety of slurry systems, confirms that the present correlation does a superior job of prediction than all previously proposed critical velocity correlations.

A theoretical analysis of a dispersed flow biological reactor is presented in which Monod growth kinetics are used to describe the substrate utilization rate and the bacterial growth rate. Different bacterial and substrate dispersion coefficients are taken into account. Approximate perturbation solutions are established for two limiting situations, when the inverse Peclet number ϵ is very small and when it is very large. In the former case the perturbation analysis is singular. These perturbation solutions are compared with the solutions of the numerically integrated equations over a range of parameters corresponding to actual activated sludge systems. The application to the activated sludge system is discussed. On presente une analyse theorique d'un reacteur biologique a debit disperse et dans lequel on emploie la cinetique de croissance de Monod pour decrire le taux d'utilisation du substrat et celui de la croissance bacterienne. On considere differents coefficients de dispersion des bacteries et du substrat. On a etabli des solutions approximatives des perturbations dans le cas de deux situations limitatives, a savoir lorsque le nombre inverse de Peclet(ϵ) est tres petit et lorsqu'il est tres considerable; dans le premier cas, l'analyse des perturbationes est singuliere. On compare les solutions des perturbations avec celles d'equations integrees numeriquement, et ce, pour une echelle de parametres qui correspond a des systemes reels de boue activee. On discute l'application des resultats au systeme de boue activee.

A multiphase model for the flow of dense, noncolloidal, settling slurries through horizontal pipelines, and an associated Galerkin-finite element numerical scheme to carry out computer simulations based on the model, were developed. The principal elements of the model are: equations for estimation of the velocity distributions for each component; and those for the concentration distributions. In the former, which are derived from the local volume-averaged, time-smoothed conservation of mass and momentum equations, the total stress is comprised of components to account for interparticle and particle-boundary as well as viscous and turbulent interactions. The governing equations for the concentration distributions are derived similarly from the convective diffusion equation, with the eddy diffusivity modified to account for the presence of the solid particles. Numerical simulations and detailed comparisons with experiment for the flow of gypsum, coal, crushed glass, sand and gravel, covering particle sizes from 38.3 μm to 13,000 μm, and pipe diameters from 4 cm to 49.5 cm, were carried out. The agreement between model prediction and experiment is excellent.

Although multicomponent, liquid phase adsorption is often encountered in industrial application, most of the studies concerning fixed-bed sorption processes have been dealt primarily with systems containing one adsorbable species. The present work provides a numerical solution to the fixed-bed, multicomponent adsorption problem, taking into account both separately or in combination the effect of liquid and/or solid phase mass transfer resistance and of variation of the assumed governing adsorption isotherm. Numerical solutions of several example problems are presented and compared with results based on equilibrium theory and a simplified method developed by Cooney and co-workers previously (1972).

Pressure drop correlations for flow of slurries in pipelines were developed for each of the following four flow regimes: flow with a stationary bed, saltation flow, heterogeneous flow, and homogeneous flow. A total number of 2 848 data points, comprised of 1 912 collected from the published literature together with 936 taken using our own test pipelines and relating to ranges of the pertinent variables extensive enough to span all four flow regimes were used as the basis of these correlations. Also, these data were used in developing an associated quantitative regime delineation scheme. The correlations provide an improved predictive capability over previously available procedures and are also broader in scope. The delineation procedure developed here permits straightforward classification of the data according to the flow regime prevailing, and it is moreover inclusive of all the data and is self-consistent.

The temperature field resulting from the frictional heating of a fluid confined in the region between a cone and a plate, which are in relative steady rotation, is calculated for prescribed thermal boundary conditions. The convective heat-transfer problem pertaining to the three dimensional velocity field, characteristic of this geometry, is solved as an asymptotic expansion for small Reynolds number and small cone angle. Together with adaptations of previously published results for plane Couette flow of fluids with temperature-dependent transport properties, these solutions provide quantitative measures of the effects of conduction, convection, frictional heating, as well as the temperature sensitivity of the fluid transport properties.

A detailed examination of the critical velocity in pipeline flow of non-colloidal slurries was carried out. Published critical velocity correlations were collected and were recast into a standard form so that they could be compared with each other, and they were also tested against a broad collection of experimental critical velocity data. Altogether, a total collection of 864 experimental critical velocity data, representing a broad variety of solid materials and pertaining to wide ranges of the variables involved, were used in these tests. This rather substantial body of experimental data was also used as the basis for developing a set of improved critical velocity correlations, which were established by fitting the data to various forms of the standard equation. Among the principal results of this work are the following: The dependence of the critical velocity on pipe diameter is very nearly equal to D 1 2 , while its dependence on particle size, for slurries of non-colloidal particles, is very nearly equal to d0. The analytical result due to Oroskar and Turian indicates that υc depends on pipe diameter as D0.6, and on particle size as d0, while the best empirical fits to the data suggest that the dependence on pipe diameter is approximately D0.5, and that on particle size is at most d0.06. In addition, both the newly established empirical correlations and the analytical correlation due to Oroskar and Turian predict a maximum in the υc vs. C curve, the maximum occurring at solids volume concentration of 0.25 to 0.30. The comparisons with experimental data further established that the analytical result by Oroskar and Turian, and the empirical correlations developed in this work, do a superior overall job of predicting the data than other published correlations.

A simulation procedure for predicting the dynamic behavior of a deep bed filter over the entire practicable range of filter operation is developed. The method is based on synthesizing available quantitative results relating to filtration, and to porous media flows, within an overall framework which views the process to consist of two principal stages dominated by appropriate limiting deposition modes. Evaluation of the results through comparison with available data indicates, to the extent the nature of these types of data permits, that the method is surprisingly effective and even capable of predicting on satisfactorily quantitative basis some intricate details of observed filter behavior.

The use of tracer dispersion measurements in conjunction with associated pressure drop data, as an indirect diagnostic technique for the determination of particle deposit morphology in deep-bed filters, was investigated. The dispersion measurements consisted of the injection of an electrolyte tracer pulse at the inlet and the monitoring of the tracer peak as it traveled down the bed, while the pressure drop data consisted of the axial pressure gradient histories as deposition took place. These data are interpreted using dispersion and pressure drop theories established on the basis of assumed models of deposit morphology. The validity of this technique was confirmed experimentally.

The efficacy of sinus surgery continues to be an issue of debate among otolaryngologists. In an attempt to address this controversy, a case-series study design was used to assess the perceived efficacy of sinus surgery in terms of the alleviation of sinus symptoms and overall health benefit. Self-administered questionnaires were mailed to 142 individuals who had sinus surgery performed between January 1984, and December 1985. After one follow-up attempt, 114 questionnaires were completed and returned (80% response). Overall, a high percentage of cases reported postoperative improvement in breathing difficulties (90%), nasal congestion (88%), headache/facial pain (85%), recurrent sinus infections (83%), and postnasal drip (80%). In addition, 88% of cases reported the surgery to be of some overall health benefit. These results suggest that sinus surgery, as perceived by surgically treated individuals, may be effective in the management of chronic sinus disease.

A model is developed for predicting the sedimentation velocity in suspensions of multisized nonflocculating solids, in which the retarding effect of the smaller particles on the setting velocities of the larger ones is taken into account. Tests of the model, and comparisons with other models, demonstrate that it provides improved prediction of data on suspensions comprising both discrete particle size mixtures and continuous size distributions, and that it is applicable to continuous countercurrent solid-liquid operations.

A procedure for the application of the so-called h-transformation in solving fixed-bed multicomponent adsorption problems is developed. In order to apply this procedure, it is necessary to select an appropriate value for the transition-motion factor ξ, and the criteria for making this selection are established in this work.

The hydrodynamic drag force in a uniform flow field acting on a spherical body with small particles attached to its surface was determined experimentally. The experimental data are used to substantiate the approximate force expressions derived from available theories for several types of collector-particle geometries. Procedures for applying these results to the prediction of the pressure drop across a filter bed with various degrees of particle deposition are also developed.

Resistance coefficients for flow of suspensions of well defined glass beads of narrow size fractions in 1-inch and 2-inch straight pipes, in standard 45°, 90° and 180° bends, in 90° smooth bends of various curvature radii, and also in gate and globe valves were measured. The measurements were made for two sizes of fine glass beads, -325 mesh and -200-325 mesh, covering wide ranges of turbulent Reynolds number and solids concentrations from 0 to 50 weight percent. These friction loss data were analyzed with regard to the effects of Reynolds number and suspended solids concentration, and the calculated resistance coefficients were compared with those estimated from available design procedures recommended for turbulent single-phase Newtonian flow. Within the range of particle sizes examined in this work no particle size effects could be discerned. The effects of Reynolds number and suspended solids concentration on the friction loss measurement were calculated.

Formal approximate solutions, for small ϵi, for the system where G is a general function of the N-dependent variables fi, are obtained by the method of matched asymptotic expansions. Uniformly valid approximations are composed for the region 0 ⩽ x ⩽ 1 by synthesizing expansions pertaining to three separate regions; near x = 0, near x = 1, and the intermediate region in between. Restrictions on the approximations are developed, and these can be used to evaluate the effects of the magnitudes of the λi, of the behavior of G, and of possible disparities in the values of the various parameters ϵi. The results obtained are of considerable practical value because they are readily applicable to actual situations, as demonstrated by a number of specific examples, and because it is possible to evaluate how good the approximation is in each individual case.

The plane Couette flow of a frictionally heated temperature dependent Ellis fluid is solved. The critical stress, above which steady-state temperature and velocity fields under prescribed boundary conditions cannot be established, is determined as a function of the Ellis number El and the parameter α.

The terminal velocities of spheres falling in aqueous solutions of hydroxyethyl cellulose and polyethylene oxide were determined with ruby and steel spheres. For each sphere the terminal velocity was obtained in seven cylinder sizes covering a range of sphere-to-cylinder diameter ratio from 0.0067 to 0.18. The data were used in an extrapolation to correct for the cylindrical wall effect. Several alternative extrapolation procedures for estimating the zero shear viscosity were attempted and the results were compared. An empirical correlation for the drag coefficient was developed in terms of the Ellis parameters of the fluids, and the Faxen wall correction for Newtonian flow. the correlation gives the drag coefficient within 4% for all cases in which the quantity ηvt/Dτ1/2 is less than 0.3.

The temperature rise resulting from viscous dissipation in the fluid in a cone-and-plate viscometer is derived approximately using a variational method. In the derivation it is not necessary to make reference to any specific rheological model. It is concluded that for one commercially available instrument the maximum temperature rise is about 3°C. Hence viscous heating effects can lead to observable errors when a cone-and-plate instrument is operating at high speeds; such effects have been observed experimentally.

A numerical method for the solution of the problem of steady state, incompressible Newtonian flow through periodically constricted tubes is developed. All terms of the Navier-Stokes equation are retained, including the nonlinear inertia terms. Sample calculations for a uniform periodically constricted tube, the geometry of which is connected with the modeling of a packed bed of sand are given, including streamlines, axial and radial velocity profiles, pressure profiles, and the dimensionless pressure drop versus Reynolds number relation. The effect of some geometric characteristics of periodically constricted tubes on their friction factor is investigated numerically, and comparison of some existing experimental data with calculated ones is made.

Analytical solutions are given for the velocity and temperature profiles in a Newtonian fluid between two infinite parallel planes, one of which is moving fast enough that viscous dissipation heating effects are important. The temperature dependence of the viscosity and the thermal conductivity are taken into account. In one set of solutions both plates are maintained at the same temperature, and in another set of solutions there is zero heat flux through the moving plate. These results are then applied to the cone-and-plate viscometer, to show how the torque vs. angular speed curves deviate from linear behaviour because of the temperature dependence of the transport properties. The analytical expressions are compared with experimental flow curves, which seem to indicate that the viscous heating effects are slightly larger than the theoretical expressions would predict.

A new model for porous media comprised of monosized, or nearly monosized grains, is developed. In applying this model to a packed bed, the bed is assumed to consist of a series of statistically identical unit bed elements each of which in turn consists of a number of unit cells connected in parallel. Each unit cell resembles a piece of constricted tube with dimensions which are random variables. The problem of flow through each unit cell is reduced, subject to reasonable assumptions, to the determination of the flow in an infinitely long periodically constricted tube. The solution of this flow problem is given in a companion publication. This model, together with the solution of the flow through it, can be used for the modeling of processes which take place in the void space of a bed. As a preliminary test, theoretical friction factor values, based on the proposed model, were compared with experimental ones for two different beds and found to be in good agreement even in the region of high Reynolds numbers where the nonlinear inertia terms are significant.

Batch adsorption experiments using a well-mixed system of secondary effluent domestic waste water and granular activated carbon were performed, and the rate of decay of organic contaminants associated with bacterial action was determined. These results were used to establish that a Freundlich type adsorption isotherm characterized the system and that the decay of organic solutes by bacteria could be represented by a modified first order rate expression. Comparison of the experimental concentration histories, expressed in terms of the total organic carbon content of the liquid phase, with theoretical results for two assumed mass transfer models (internal diffusion and pore diffusion) permitted evaluation of diffusion coefficients for the system. For internal diffusion the coefficients ranged between 1.6 x 10\U-9\N sq cm per sec and 2.6 x 10\U-8\N sq cm per sec, while for pore diffusion the range was from 3.4 x 10\U-9\N sq cm per sec to 1.6 x 10\U-7\N sq cm per sec.