bluuebunny/crossref_metadata_2025 huggingface dataset:
Continuous foam fractionation: The effect of operating variables on separation
Authors: Grieves R. B. , Wood R. K.
Published: June 2004

Continuous foam fractionation has a great deal of promise as a chemical engineering separation technique; however more information is needed concerning the effect of operating variables upon the separation which may be obtained. An experimental investigation is presented of the influence of temperature, of liquid residence time, and of the position of feed introduction upon the foam fractionation of the ethylhexadecyldimethylammonium bromide‐water system. The study involves three series of experiments and ninety foam separation runs. For a given air rate and feed stream concentration and rate, the drain stream concentration and rate increase linearly with temperature and the foam concentration and enrichment ratio are increasing functions of temperature. Equations derived from a multiple linear regression analysis enable the calculation of the drain stream concentration and rate from the feed concentration, air rate, and temperature.

Based upon experiments involving the variation in liquid residence time by two methods, changes in solution height have no influence upon the separation, indicating the rapid achievement of equilibrium. Changes in feed rate and air rate show that the volume of air employed per unit volume of feed treated is a prime variable affecting the separation.

Positioning the feed inlet at the solution‐foam interface, compared with feeding into the solution, provides a significant increase in drain rate and decrease in drain concentration. Moving the feeder higher into the column of foam results in a continued decrease in drain concentration, but in the passage of the drain rate and foam concentration through maximum values at a height corresponding to approximately the midpoint of the column of foam.
Solution of the linearized equations of multicomponent mass transfer: II. Matrix methods
Authors: Toor H. L.
Published: June 2004

Solutions to the equations of multicomponent mass transfer may be written as matrix generalizations of the solution to the equivalent binary mass transfer equation when intial and boundary concentrations are constant, there are no homogeneous reactions, and all physical properties including the diffusion coefficient matrix are concentration independent.

The analogue of the binary mass transfer coefficient is a multicomponent mass transfer coefficient matrix which depends only upon the mass transfer coefficients of the equivalent binary system and the diffusion coefficient matrix of the multicomponent system.

When interphase transfer takes place, the inverse multicomponent mass transfer coefficient matrices of each phase are additive. Their sum yields an overall resistance to mass transfer which is the inverse of the overall multicomponent mass transfer coefficient matrix.
Effects of reduced gravity on nucleate boiling bubble dynamics in saturated water
Authors: Siegel R. , Keshock E. G.
Published: June 2004

A study was made of nucleate boiling bubble dynamics in saturated distilled water for various reduced gravity fields. The nucleation occurred on a very smooth horizontal nickel surface at low heat fluxes. Since because of the smooth surface finish only a few nucleation sites were active, it was possible to photograph individual bubbles that were not interfered with by adjacent bubble columns. Data were taken at seven different gravity fields in the range from 1.4 to 100% of earth gravity by placing the apparatus on a counterwieghted falling platform. Measurements were made of bubble departure diameters and frequencies, growth rates, contact angles, base circle diameters, and rise velocities. Comparisons were made to determine whether the measured gravity dependence of these quantities was in agreement with that predicted by correlations in the literature.
Turbulent disruption of flocs in small particle size suspensions
Authors: Thomas David G.
Published: June 2004

In the absence of turbulent fluctuations the main effect of a velocity gradient on the floc properties is a rearrangement of particles within the floc producing a more dense floc structure. When the suspension is sufficiently dilute that floc‐floc collisions are negligible, the limits on the floc diameter are (1 + α)5/3 < (Df/Dp) ⩽ (1 + α)2, where α is the ratio of the volume of fluid immobilized in the floc structure to volume of solids in the floc structure as determined from hindred‐settling measurements. These results set an upper limit on the floc size.

Under turbulent flow conditions the principle mechanism leading to floc rupture is pressure differences on opposite sides of the floc which cause bulgy deformation and rupture. The breakup of the floc is resisted by the yield stress τy and is promoted by an increase in the energy dissipation per unit mass of fluid ϵ. Because the energy dissipation per unit mass is at a maximum near the pipe wall, the floc size is at a minimum in this same region.

By application of the concepts of local isotropy, the floc size is found to be proportional to (τy9/ϵ5)1/2once the turbulent intensity is sufficient to overcome the yield stress. In the wall region the floc diameter is proportional to (du/dr)3 (τy9/ϵ8)1/2.
Numerical and experimental study of damped oscillating manometers: II. Non‐Newtonian fluids
Authors: Biery John C.
Published: June 2004

To test the importance of visco‐elastic properties of non‐Newtonian fluids in an oscillatory system of low frequency the dynamic characteristics of a series of non‐Newtonian fluids were studied in oscillating manometers. The manometer fluid behavior was simulated on a digital computer by numerically integrating the axial component of the equation of motion. In the simulation cone and plate steady state rheological data were represented mathematically with the Sisko rheological model. Good agreement between simulation and experimental data was obtained. This agreement implies that steady state rheological models can be utilized in the description of unsteady state non‐Newtonian systems where the characteristic period of the system is many times greater than the relaxation and retardation times of the fluid. When this characteristic period approaches these times, then rheological models which incorporate viscoelastic terms explicitly probably should be used.
An experimental study of surface cooling by bubbles during nucleate boiling of water
Authors: Rogers Thomas F. , Mesler Russell B.
Published: June 2004

By using a special surface thermocouple Moore and Mesler have measured large temperature fluctuations during nucleate boiling of water on chromel P surface. They found that the temperature dropped 20° to 30°F. in about 2 msec. but required 10 to 20 msec. to recover. They have postulated that the surface was cooled during initial bubble growth by evaporation of a microlayer into the bubble. To test this hypothesis a technique was developed to photograph a bubble growing from an artificial site as the surface temperature was measured.

Temperature fluctuations were recorded on an oscilloscope which automatically triggered the bubble photographs by means of a time delay unit and flash tube. Photographs of bubbles were taken at 1 μsec. exposure time and ranged from about 10 μsec. after the start of the temperature drop to about 1 msec. before the start of another cycle. The photographs show that the surface cools during bubble growth and recovers during bubble departure.
Mass transfer in a packed, pulsed column
Authors: Krasuk J. H. , Smith J. M.
Published: June 2004

Equations in terms of a pulse Reynolds number and dimensionless pulse velocity are presented for mass transfer coefficients in pulsed flow in a packed bed. Mass transfer from the wall and from the particles is considered. The development, applicable up to a particle Reynolds number of 40, is based upon a previous study of pulsed laminar flow in an empty tube.

The experimental measurements consisted of rates of dissolution of β‐naphthol from the wall and from the particles within the bed. From these data time‐average mass transfer coefficients kp were computed. The improvement in kp increased with frequency and decreased with average flow rate, although the increase was always less than in an empty tube at equivalent conditions.

Steady flow measurements indicated that the coefficient for mass transfer from the tube wall was influenced by the degree of settling of the bed. This effect could be related to the change in porosity accompanying the settling process. A new empirical correlation is proposed to account for the effect of porosity changes.
The study of gas‐solid equilibrium at high pressures by gas‐chromatography: Part I. Ethane, propane, and n‐butane at essentially infinite dilutions in the methane‐silica gel system
Authors: Gilmer H. B. , Kobayashi Riki
Published: June 2004

The measurement of vapor‐solid distribution coefficients or K values of a solute distributed between a gas phase and an adsorbed phase at essentially infinite dilutions has been investigated. Gas‐solid chromatography is the technique employed in which the solute of interest is eluted through a tube packed with a solid adsorbent by a flowing gas phase which may or may not be appreciably adsorbed. The data taken for the eluted solute samples were then related to the K value and isobaric heat of adsorption for the solutes in the vapor‐solid system.

A previous mathematical solution describing the chromatographic process is extended to include the case of an appreciably adsorbed pure component elution gas. This theory allows the calculation of solute K values and heats of adsorption for a solute at essentially infinite dilution in the vapor‐solid system. It is necessary to have adsorption data for the elution gas covering the range of interest. For this reason the necessary elution gas adsorption isotherms were determined gravimetrically for the temperature and pressure range of the study.

For comparison purposes a single ethylene adsorption isotherm at 25°C. was obtained along with retention volume data for methane, ethane, and propane at essentially infinite dilution in the ethylene‐silica gel system at 25°C. Agreement of the data of this study and the literature was thought to be sufficiently good to warrant further use of the technique.

Methane adsorption isotherms on silica gel were gravimetrically measured at −40°, −20°, 0°, 20°, and 40°C. from 100 to 2,000 lb./sq.in.abs. Retention volume data over the same pressure and temperature ranges were taken for ethane, propane, and n‐butane at essentially infinite dilution in the methane‐silica gel system.
Droplet growth in binary liquid systems
Authors: Ayen Richard J. , Westwater J. W.
Published: June 2004

Experimental measurements of the growth of liquid drops suspended in three different, supersaturated, binary liquid mixtures were made with cinephotomicrography. Diameters up to 5μ were reached in from 5 to 500 sec. Results for acetone drops and for isoamyl alcohol drops growing in glycerol solutions agree within 20 and 40% of the theoretical expression of Scriven with mass diffusivities estimated from the Wilke‐Chang correlation. For glycerol drops in acetone, free convection was evident, and the experimental growth rates were lower than predicted by a factor of 5. Scriven's equation seems to be substantiated. Therefore, drop‐growth measurements is a new method for obtaining liquid‐liquid diffusivities, limited however to systems with negligible free convection.
Optimization of multistage cyclic and braching systems by serial procedures
Authors: Aris Rutherford , Nemhauser George L. , Wilde Douglass J.
Published: June 2004

The calculus of variations, dynamic programing, and Pontryagin's maximum principle all are methods for optimzing serial decision processes, the kind associated with multistage operations having no recycle or bypass. Addition of recycle to a serial process makes it cyclic, and branching structures can be built up by connecting serial ones. The concept of cut state makes possible the decomposition of cyclic and branched systems into serial ones solvable by serial procedures. Under favorable circumstances cut states can be directed to their optimum values by efficient optimum seeking methods, which is not possible for ordinary state variables. These method are worthwhile only for loops having at least three stages, and the treatment of converging branches is more complicated than for diverging ones. Visualization of the various system structures is aided by functional diagrams. Definitions and nomenclature are developed for continued research on optimization of macrosystems by serial techniques.
Oscillations of drops falling in a liquid field
Authors: Schroeder R. R. , Kintner R. C.
Published: June 2004

Frequencies and amplitudes of oscillations for nineteen pure systems were measured photographically. The period of oscillation was longer than that predicted by Lamb. The discrepancy was not due to wall effects, viscosity, or velocity of fall but to amplitude of oscillation. Modification of previous expressions included an amplitude function which could be experimental or empirical. Oscillations began near the peak velocity, and a vortex trail was necessary for them to take place. Oblate‐prolate oscillations did not cause drop breakup, as all systems ceased to oscillate and wobbled randomly below maximum drop size. Oscillations do not decay with time.
Adsorption of ethyl alcohol on silica gel
Authors: Masamune Shinobu , Smith J. M.
Published: June 2004

This work utilizes the developments of the foregoing paper (10) to analyze adsorption data, in the form of breakthrough curves, for ethyl alcohol on silica gel at 90° to 155°C. It was found that for the smallest particle size, and in the lower part of the temperature range, the overall rate was determined by the surface adsorption process. At other conditions intraparticle diffusion was also a significant resistance in the overall process. The theoretical breakthrough curves agreed well with the experimental ones, so that the surface rate constant and diffusivity could be calculated.

Analysis of the diffusivity results showed that surface migration on the pore walls was the predominant contribution rather than gas‐phase diffusion in the pore volume.
Kinetics of the heterogeneous decomposition of iron pentacarbonyl
Authors: Carlton Herbert E. , Oxley Joseph H.
Published: June 2004

The decomposition of iron pentacarbonyl at pressures between one and 400 Torr was studied from 120° to 300°C. Up to about 200°C. the rate was primarily limited by surface kinetics of adsorbed carbonyl. Gas phase diffusional resistances were controlling at higher temperatures. In the kinetically controlled region the deposition rate was correlated by a Langmuir type of equation. Corrections for diffusion resistances in the kinetic region and kinetic resistances in the diffusion region were found to be appreciable.
Hydrates at high pressures: Part III. Methane‐argon‐water, argon‐nitrogen‐water system
Authors: Saito Shozaburo , Kobayashi Riki
Published: June 2004

The experimental procedure for determining the initial hydrate formation conditions along the univariant gas‐water rich liquid‐hydrate locus through the measurement of equilibrium pressures and temperatures alone in a constant volume system has been successfully applied to several binary gas mixtures with water to pressures as high as 15,000 lb./sq. in.

The general hydrate theory of van der Waals and Platteeuw, after appropriate modifications, was found valid for the accurate prediction of the initial hydrate formation conditions for selected mixtures of argon‐methane and argon‐nitrogen.

The calculated methane‐argon compositions in the hydrate phase are presented as a function of the methane‐argon composition in the gas phase on a water‐free basis but were not verified experimentally.
Stability criteria for miscible displacement of fluids from a porous medium
Authors: Schowalter W. R.
Published: June 2004

Stability criteria are formulated for displacement of a fluid from an infinite porous medium by a second more dense fluid miscible with the fluid being displaced. Pure displacing fluid is separated from pure displaced fluid by a region of constant thickness in which the two fluids interpenetrate. The steady displacement process takes place at a constant velocity in the direction of gravity. It is shown that appreciable differences in pure‐component densities, viscosity variation within the zone of interpenetration, and the displacement velocity can have a major effect on the stability criteria of such a flow.
Solution of problems involving conventional and complex distillation columns at unsteady state operation
Authors: Waggoner R. C. , Holland C. D.
Published: June 2004

The θ method of convergence has been applied to conventional and complex columns at unsteady state operation. A different holdup for each stage may be specified in terms of molal, mass, or volumetric units. Plate efficiencies were used, and the K values and enthalpies were taken to be polynomials in temperature.
The effect of shape and density on the free settling of particles at high Reynolds numbers
Authors: Christiansen E. B. , Barker Dee H.
Published: June 2004

Terminal velocity drag coefficients CD were determined for cylinders, prisms, disks, and spheres in air and water at NRe from 1,000 to 300,000, the regime where particles rotate and/or oscillate. These and other similar data show that CD is a function of particle and fluid densities ρp and ρf, as well as shape and NRe.

By considering CD a function of particle moment of inertia and the rotational moment generated by circulation (or alternatively the field force and the lift), one can deduce that \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm C}_{\rm D} = {\rm f}\left({\frac{{\rho {\rm p}}}{{\rho {\rm p}}}\,{\rm or}\,\frac{{\rho {\rm p} - \rho {\rm f}}}{{\rho {\rm f}}},\hbox{a length ratio, N}_{{\rm RE}}} \right) $\end{document}. This relationship correlates the data for ρp = 1.2 to 8.3 and ρf = 0.1 to 1.3 g./cc. to within ± 10%.
Particle flow patterns in a fluidized bed
Authors: Marsheck R. M. , Gomezplata Albert
Published: June 2004

A modified thermistor anemometer probe was used to measure solid particle flow patterns in a 9.5‐in. diameter fluidized bed. The probe was calibrated and found to measure the direction and mass velocity of the silica‐alumina cracking catalyst used. Flow patterns were determined at heights of 6.5, 12.5, 18.5, and 24.5 in. above the support plate with superficial air velocity from 0.25 to 1.00 ft./sec. and bed depths of 14 to 30 in.

Radial flow patterns were found not to be symmetrical about the axis of the bed but were similar at angles of 60 deg. This indicated that there were six similar particle flow pattern sections around the column axis.

The percentage of the cross‐sectional area of the fluidized bed through which the particle flow is upward was found to be approximately 60%. There was no definite dependence of this area on any of the variables studied.

The catalyst bulk circulation rate, defined as the average mass velocity of the particles at a given cross section in a fluidized bed without regard to the direction of flow, was determined for each fluidization condition and correlated as a function of the superficial air velocity and the ratio of the distance above the support plate to the height of the fluidized bed.
Study of nitrogen and neon pool boiling on a short vertical pipe
Authors: Lapin Abraham , Wenzel L. A. , Totten H. C.
Published: June 2004

An experimental study in the behavior of nitrogen and neon pool boiling was performed. The test section consisted of a vertical pipe 3 in. O.D. × 7½ in. long. The variables studied are: heat input, submergence, and surface finish. Several copper heaters were tested, in addition to nickel and cadmium plated heaters. The results were correlated for nitrogen by an equation which gave an average deviation of ± 16% for all the heaters except the cadmium plated heater. The paper describes the experimental equipment and technique, summarizes the data, and compares them to literature values and equations.
Generalized thermodynamic properties of real gases: Part I. Generalized PVT behavior of real gases
Authors: Viswanath D. S. , Su Gouq‐Jen
Published: June 2004

The object of this paper, first in the series dealing with the generalized thermodynamic properties of real gases, is to present generalized compressibility charts in the reduced temperature range of 1.0 to 15.0 and a reduced pressure range of 0 to 40.0. A detailed summary of deviations of the present charts with PVT values of different gases is presented. A summary of the comparison of the present charts with the existing charts is also given.
Analysis of phase‐boundary motion in diffusion‐controlled processes: Part III. Penetration of metal ions into cellulose xanthate fibers and growth of sulfuric acid droplets in humid air
Authors: Griffin J. R. , Coughanowr D. R.
Published: June 2004

In Part I (1) three general methods of solving moving‐boundary problems were developed, and in Part II (2) the three methods were applied to the problem of evaporation from a flat surface into a gas of infinite depth. In this final paper, more challenging problems in cylindrical and spherical coordiates are considered, and new solutions to these are presented.
Effect of the equilibrium relationship on the dynamic characteristics of distillation column sections
Authors: Mohr C. Michael
Published: June 2004

The dependence of the dynamic characteristics of distillation column sections on the shape of the equilibrium relationship and the number of plates comprising the section is discussed. Dynamic characteristics, valid near the steady state operating condition, were obtained for simple column sections separating binary mixtures by a straightforward calculation with a digital computer. Sections with concave downward equilibria respond significantly more slowly than comparable sections with linear equilibria. Sections with concave upward equilibria respond faster. This behavior is explained in terms of the internal recycle within the section. The rate of propagation of a disturbance from end to end in the section is only weakly influenced by the shape of the equilibrium relationship.
Foam fractionation of colloid‐surfactant systems
Authors: Grieves R. B. , Bhattacharyya Dibakar
Published: June 2004

The presence of colloidal particulates has a significant effect upon the foam fractionation of aqueous solutions of surface‐active agents. An experimental investigation is presented of the foam fractionation‐flotation of the stannic oxide‐cetyltrimethylammonium bromide (CTAB) and stannic oxide‐alkyl benzene sulfonate (ABS) systems. The average diameter of the stannic oxide particles was 180Å, and particle concentrations were determined by turbidmetry. For stannic oxide‐CTAB a froth flotation mechanism controls, and upon foaming feed sols of fixed concentration, fractional residuals of particulates and surfactant are approximately equal. Maximum enrichment ratios are obtained at maximum aeration time, minimum air rate, and maximum foam height. Increasing the feed concentration of particulates increases the collapsed foam volume, while the CTAB concentration in the residual sol first decreases and then becomes virtually constant. For stannic oxide‐ABS sols, no particulates are removed preferentially in the foam. A foam fractionation mechanism controls, and compared with ABS solutions the addition of stannic oxide decreases the foam volume and residual ABS concentration, producing a pronounced increase in the enrichment ratio.
Effect of packing on the catalytic isomerization of cyclopropane in fixed and fluidized beds
Authors: Ishii Tadao , Osberg G. L.
Published: June 2004

An experimental study with fixed and fluidized beds in the isomerization of cyclopropane on a silica alumina catalyst is reported for a temperature range of 150° to 250°C. and of 5 to 150 W/F (g‐catalyst, hr./g.‐mole). The effects of various cylindrical screen packing, 0.2‐, 0.4‐, and 1.0‐in. diameter, and 1.0‐in. diameter pall ring, on final conversion were determined. Reactor scale effects were also considered with reactors of 0.9‐, 1.8‐, and 6.0‐in. diameter and bed heights 1.8 to 11.0 in.

Overall conversions were higher in a fluidized bed with packing than in a normal fluidized bed but were less than in a fixed bed, though approaching it in some cases. Rate data from the fixed bed closely followed first‐order kinetics. When the same catalyst was tested in a normal fluidized bed, the rate was dependent on linear gas velocity and catalyst bed height. With packing present in the fluidized bed, this dependency was much less, but packing size and shape had some effect.

Several previously proposed reactor models were considered for correlating the data.
On stress‐relaxing solids: Part III. Simple harmonic deformation
Authors: Vela Saul , Kalb J. W. , Fredrickson A. G.
Published: June 2004

The viscoelasticity of a number of polymer solutions was studied by subjecting the solutions to simple harmonic displacements in a pipe. Both water‐based and organic‐based solutions were used. Results were analyzed in terms of a modification of the operator equation of linear viscoelasticity. A three‐constant model used earlier was found to correlate most of the data. Further experiments to verify the model are suggested.
The prediction of the viscosity of multicomponent, nonpolar gaseous mixtures at atmospheric pressure
Authors: Strunk Mailand R. , Fehsenfeld Gary D.
Published: June 2004

The method for predicting the viscosity of binary nonpolar gaseous mixtures from pure component Lennard‐Jones force parameters and composition has been extended to multicomponent mixtures. The 136 mixtures examined contained from three to seven components from sixteen different gases in the temperature range from 5° to 1,014°C. The predicted gaseous viscosities should fall between −0.3 and −6.7° of the actual viscosities 95% of the time. With a slight modification of the constant in the viscosity expression, the viscosity can be predicted to within ±3.2% of the experimental viscosity 95% of the time for mixtures containing three or more components.
Stagnation in a fluid interface: Properties of the stagnant film
Authors: Merson R. L. , Quinn J. A.
Published: June 2004

The mechanism whereby surface‐active agents cause stagnation in a fluid interface has been extensively studied for water flowing in a horizontal channel. Known surface‐active contaminants exhibiting varied surface behavior were added to the water. Distinctly different phenomena were observed with compressible and incompressible films.
Films of non‐Newtonian fluids adhering to flat plates
Authors: Gutfinger Chaim , Tallmadge John A.
Published: June 2004

This paper presents a study of flux, film thickness, and velocity profiles in the drainage and withdrawal processes of non‐Newtonian fluids on flat plates. The flow equations for the drainage from a vertical plate are solved for a three‐constant or Ellis model fluid. The solution is compared with that of the Newtonian fluid.

The withdrawal case is solved for the power law fluid. The solution consists of matching of the equation of capillary statics in the liquid bath to the flow equation in the entrained film. Experimental data of coating of an endless belt with a film of a non‐Newtonian fluid are presented and discussed in view of the theory developed.
Bounded and patched solutions for boundary value problems
Authors: Churchill Stuart W.
Published: June 2004

The technique of bounding, that is of constructing general solutions for all ranges of the variables and parameters from solutions for a few limiting and special cases, is outlined and illustrated for problems in conduction and convection. The technique of patching, that is of constructing approximate solutions for multiphase media by the combination of pseudo solutions for the different regions, is also outlined and illustrated for problems in conduction and freezing. The shortcomings and possible inaccuracies of these two techniques are indicated as well.
Significance of pressure gradients in porous materials: Part I. Diffusion and flow in fine capillaries
Authors: Wakao Noriaki , Otani Seiya , Smith J. M.
Published: June 2004

Equations are derived for the effect of a total pressure gradient on flow and diffusion of a binary gas system in a fine capillary. The results apply over the pressure and pore radius regimes from Knudsen flow to Poiseuille flow.

Application of the equations to a pure component leads to an expression for the permeability which predicts the observed minimum flow in the slip‐flow region. This expression agrees well with Knudsen's data for carbon dioxide and for new measurements for nitrogen in a glass capillary (radius = 0.01244 cm.).
The stability of nonlinear systems in the region of linear dominance
Authors: Gura I. A. , Perlmutter D. D.
Published: June 2004

A technique has been developed for finding quantitative regions of asymptotic stability for nonlinear systems by using a known proof of the theorem which substantiates the linearization. In a sense, the method defines a region in which the first‐order approximation is dominant from the point of view of stability. While the computations necessary can be somewhat involved, the procedure is essentially identical in all situations, and once established, can easily be used for a vast class of autonomous systems. The practical problems of both reversible and irreversible chemical reactions occuring in a continuous flow stirred vessel have been analyzed. Stability regions were obtained which are sufficiently extensive to be practical from the process viewpoint.
Local rates of mass transfer from spheres in ordered arrays
Authors: Rhodes John M. , Peebles Fred N.
Published: June 2004

The local mass transfer rates from a sphere in a regular packing array have been determined by measuring the local radius change of a slightly soluble 1.500‐in. diameter benzoic acid test sphere after having been immersed in a water stream. Results in the form of typical local Sherwood number profiles are reported for single spheres over a particle Reynolds number range of 166 to 1,560, and for spheres in simple cubic packing and rhombohedral packing over particle Reynolds number ranges of 488 to 2,409 and 1,680 to 3,410, respectively. All runs were made at room temperature. An idealized flow pattern around spheres in simple cubic packing is presented.
Forced convection mass transfer: Part I. Effect of turbulence level on mass transfer through boundary layers with a small favorable pressure gradient
Authors: Thomas David G.
Published: June 2004

The effect of free stream turbulence level on forced convection through laminar and turbulent boundary layers on a flat was studied in a wind tunnel with a small but nonzero favorable pressure gradient by means of the naphthalene sublimation technique.

With the small favorable pressure gradient used in this study, the rate of forced convection through laminar boundary layers agreed with Polhausen's theoretical equation for turbulence levels less than 2.8% but increased in a regular fashion for turbulence levels greater than 2.8% and was almost tripled at a free stream turbulence level of 11%. There was no evidence of an interaction between pressure gradient and turbulence level which would produce disproportionate effects on the rate of forced convection through laminar boundary layers. Substantially no effect of turbulence level on forced convection through turbulent boundary layers was observed for turbulence levels up to 7%.
Unsteady state gas‐liquid slug flow through vertical pipe
Authors: Street James R. , Tek M. Rasin
Published: June 2004

Macroscopic mass and momentum balances have been used to predict the unsteady behavior of gas‐liquid slug flow through vertical pipe. Equations have been developed to predict the time‐dependent pressure drop along the pipe as well as the time‐averaged pressure drop. The results of the analysis indicate that the gas bubble lengths and frequencies of generation must be known before the pressure drop can be predicted as a function of time. In this work the bubble generation was specified in two ways: by experimental measurement of the bubble lengths and frequencies of generation from an optical technique developed for this purpose, and by assuming a periodic generation of gas bubbles of uniform length. The comparisons between predicted and measured pressure drops (both time dependent and time averaged) are satisfactory and appear to support the theoretical model. An extension of the results obtained in light of the published information on solid‐gas and immiscible liquid‐liquid systems in slug flow permits the introduction of generalized concepts of slug flow behavior in two‐phase systems.
The self‐diffusivity of substances in the gaseous and liquid states
Authors: Mathur G. P. , Thodos George
Published: June 2004

Relationships applicable for the prediction of self‐diffusivities of gases and liquids have been developed from available experimental values and an application of dimensional analysis. Separate relationships were found to apply for gases at normal pressures and for gases at elevated pressures. For the liquid state a different dependence on the conditions of temperature and pressure was observed and was taken into account to develop the relationship for this state of aggregation.
Effectiveness factors in a nonisothermal reaction system
Authors: Cunningham R. A. , Carberry J. J. , Smith J. M.
Published: June 2004

Hydrogenation rates of ethylene on a copper‐magnesium oxide catalyst were measured for fine catalyst particles and ½ in. spherical pellets from 60° to 160°C. Experimental effectiveness factors for this exothermic reaction system ranged from 0.2 to 25, depending upon the temperature and density of the catalyst pellets. The activation energy for the particles was 11,800 cal./g. mole (above 120°C.), while E for the pellets decreased to zero at high temperatures. Reasons for this behavior are discussed.

The effective thermal conductivity of the catalyst pellets was measured as a function of density and the effective diffusivity was estimated from pore size and pore volume measurements. In principle this information and the rate data for the particles are sufficient to predict effectiveness factors for the pellets. However available prediction methods are based upon first or second order rate equations which do not fit the ethylene hydrogenation reaction.
Thermal conductivity measurements for nitrogen in the dense gaseous state
Authors: Misic Dragoslav , Thodos George
Published: June 2004

A coaxial cylindrical type of cell was designed and constructed for the measurement of the thermal conductivity of gases at high pressures and moderate temperatures. This cell was used to establish the thermal conductivity of nitrogen for pressures up to 4,625 lb./sq.in.abs. and for temperatures of 22.2° and 50.5°C. The resulting thermal conductivity values were found to be in agreement with values reported in the literature for nitrogen at these elevated pressures. These experimental measurements indicate that the cell developed for this investigation is capable of producing reliable thermal conductivities for gases at high pressures.
Heat transfer in a round tube with sinusoidal wall heat flux distribution
Authors: Hsu Chia‐Jung
Published: June 2004

Sufficiently accurate values of first twenty eigenvalues, eigenfunctionsRn(1), and the coefficients for series expansion, as well as asymptotic expressions for these quantities, have been obtained for heat (or mass) transfer to fully developed laminar flow inside a round tube with uniform wall heat (or mass) flux. The first ten eigenfunctions are shown graphically for the radius range 0 ≤r/ro≤ 1.

These quantities are used to calculate the Nusselt numbers for sinusoidal wall heat flux distribution and are compared with the corresponding slug flow Nusselt numbers.
Freezing front motion and heat transfer outside an infinite, isothermal cylinder
Authors: Tien L. C. , Churchill S. W.
Published: June 2004

A numerical method is developed for calculation of the temperature field in a material that freezes outside an isothermal cylinder. Numerical values are presented for the freezing front location and for the rate of heat transfer to the cylinder. The computed values are compared with the analytical solutions for the limiting cases of zero latent hear, negligible heat capacity, and freezing adjacent to a flat plate. The results have many applications, including the freezing of wet soil outside underground pipes or storage tanks for cryogenic fluids.
Ion flotation of dichromate with a cationic surfactant
Authors: Grieves Robert B. , Wilson Thomas E. , Shih Kenneth Y.
Published: June 2004

An experimental investigation is presented of the flotation of dichromate ion from aqueous solution with a cationic surfactant, ethylheaxadecyldimethylammonium (EHDA) bromide. Dichromate forms a colloidal complex with EHDA ion in a molar ratio of approximately 1 : 2. Excess surfactant causes the formation of a stable foam to which the complex is adsorbed, providing the separation of dichromate from aqueous solution. Batch flotation studies were conducted utilizing approximately 2‐liter solutions containing from 10 to 200 mg. of dichromate ion (4.8 to 96.3 mg. of hevavalent chromium), with masses of EHDA‐Br ranging from 400 to 800 mg. The effects of mass of surfactant added, dichromate concentration, pH, and possible interfering anions were determined. A comparison is made with pure surfactant solutions, and the mechanism of the process is discussed.

Most efficient operation is achieved with a molar feed ration of EHDA ion to dichromate ion from 2.1 to 3.0, and removal ratios ranging from 80 to 95% are obtained. Reduction of the residual dichromate below 10% of the feed concentration requires additional surfactant and produces excessive foam, which could be overcome by modifications in operating conditions.
Mass transfer at high mass fluxes: Part I. Evaporation at the stagnation point of a cylinder
Authors: Mendelson Harvey , Yerazunis Stephen
Published: June 2004

An experimental method for measuring mass transfer rates at high mass fluxes is developed for the case of evaporation at the stagnation point of a cylinder. Evaporation of carbon tetrachloride at the stagnation point was measured and determined to be consistent with theoretical predictions. It was observed that water exhibits a significant interfacial resistance to evaporation at high transfer rates. Evaporation coefficients based on the discrepancy between experimental determinations and theoretical expectations were found to be a strong function of temperature and to be consistent with the majority of reported measurements made at lower temperatures. The experimental method should be useful for application to other configurations and flow conditions for studying mass transfer at high mass fluxes.
An eddy viscosity model for friction in gas—solids flow
Authors: Julian F. M. , Dukler A. E.
Published: June 2004

The equations normally used to predict velocity distribution and eddy viscosity in single‐phase flow systems can be adapted to fit gas‐solids flow systems by including a term to account for the quantity of solid matter carried by the gas stream. This solids loading is expressed as pounds of solid per pound of gas. These modified equations can then be used to calculate the pressure drop of a solids‐laden gas stream flowing in a pipe by means of a two‐phase friction factor. Comparison of this approach with available pressure drop data is used to check its validity and to evaluate the constants in the equations.
Phase equilibria for strongly nonideal liquid mixtures at low temperatures
Authors: Eckert C. A. , Prausnitz J. M.
Published: June 2004

Investigation of the nonideal behavior of mixtures of simple molecules is an important step toward improved understanding of the theory of solutions. This work describes an equilibrium apparatus suitable for the measurement of vapor‐liquid and vapor‐liquid‐liquid equilibria of simple fluid mixtures at cryogenic temperatures. Vapor‐liquid data are reported for the argonethane and nitrogen‐carbon tetrafluoride systems. Contrary to expectations, limited liquid‐phase miscibility was not observed for either of these mixtures. These results and those for other nonideal mixtures of simple molecules are compared with predictions of upper critical solution temperatures by the theory of regular solutions. Usefulness of this theory is impaired by its neglect of the order‐disorder phenomenon and, more seriously, by the geometric‐mean assumption for the intermolecular forces between dissimilar molecules.
Interaction model for critical temperatures of multicomponent mixtures of methane‐free aliphatic hydrocarbons
Authors: Ekiner Okan , Thodos George
Published: June 2004

A mathematical treatment based on an interaction model has yielded an expression capable of establishing the critical temperatures of multicomponent aliphatic hydrocarbon mixtures. This model postulates an infinite‐series expansion for the difference between the actual critical temperature and its corresponding pseudocritical value. For methane‐free aliphatic hydrocarbon mixtures, this infinite series has been truncated beyond the third‐order interactions. Explicit relationships are given for the second‐order interaction coefficientsAijandBijas a function of the binary‐system parameter τijand the third‐order interaction coefficient βijkas a function of χijk, the ternary‐system parameter.

This interaction model has been applied to one hundred‐sixteen different compositions of binary, ternary, quaternary, and quinary aliphatic hydrocarbon systems to produce an overall average deviation of 0.35%. Owing to the different interaction behavior of methane, systems containing methane have not been included in this study.
Mathematical models for mass transfer accompanied by reversible chemical reaction
Authors: Huang Chen‐Jung , Kuo Chiang‐Hai
Published: June 2004

Based on the film‐penetration theory, the film theory, and the surface renewal theory, theoretical equations are obtained for the rate of interphase mass transfer accompanied by a first‐order reversible reaction. The film‐penetration theory is again found to be the more general concept and the other two theories are merely the limiting cases of the film‐penetration theory. The rate equation based on the film‐penetration theory can also be reduced to those obtained by other investigators on the basis of simpler postulations.

Contrary to the previous findings in other chemical mass transfer systems, it is found that the predicted effects of chemical reaction on the overall mass transfer rate are indeed sensitive to the theory or the model adopted in postulating the mechanism. One exception to this is when the diffusivities of the reactant and the product are nearly equal. For this special case, the three theories predict practically the same effects of a reversible reaction.

An approximate rate equation is proposed for mass transfer with a high order reversible reaction. When the forward reaction is very rapid, the reaction rate constants become insignificant variables and the mass transfer rate is a simple function of the diffusivity ratio, the concentration ratio, and the order of reaction.
Falling cylinder viscometer for non‐Newtonian fluids
Authors: Ashare Edward , Bird R. Byron , Lescarboura Jaime A.
Published: June 2004

It is shown how previous analyses of the falling cylinder viscometer for Newtonian fluids can be extended to non‐Newtonian fluids. Specific relations are given for the velocity of descent for several simple non‐Newtonian viscosity functions. A differentiation procedure is presented whereby the non‐Newtonian viscosity for a fluid can be deduced from velocity of fall measurements. In the course of the development, some useful approximate expressions for axial non‐Newtonian flow in annuli are developed. Finally, a comparison of the Ellis and power law models is made by an analysis of the axial annular flow data of Frederickson and of McEachern.
Confined wakes: A numerical solution of the Navier‐Stokes equations
Authors: Paris Jean , Whitaker Stephen
Published: June 2004

A numerical solution of the two‐dimensional Navier‐Stokes equations is presented for the confined wake formed by the merging of two‐plane Poiseuille flow streams. The system of finite‐difference equations for the stream function and vorticity is solved by the Peaceman‐Rachford elimination method for Reynolds numbers of 1, 50, 387, and 647. While the stability of the numerical method is not a problem for this range of Reynolds numbers, the number of points in the finite‐difference network (and hence the computation time) does become burdensome.

At high Reynolds numbers, the primary boundary‐layer simplification is imposed to yield a set of parabolic equations for the vorticity and stream function. These equations are solved by a straightforward “marching” technique, thus providing a solution with a minimum of computational effort. The “boundary‐layer equations” presented in this paper are not subject to the order to obtain the Prandtl boundary‐layer equations. The method outlined here represents an approximate solution for high Reynolds numbers, which gives surprisingly good agreement with the complete solution.
Nonlinear least squares analysis of catalytic rate models
Authors: Kittrell J. R. , Hunter W. G. , Watson C. C.
Published: June 2004

Conventional data generation and analysis procedures used to select a descriptive Hougen‐Watson reaction rate model have been reviewed and some statistical objections to these conventional procedures have been presented. In an attempt to assess the practical importance of these objections, a recently published example was analyzed with both conventional techniques and nonlinear least squares procedures, which more closely conform to theoretical weighting requirements. Comparisons were made between the results of the conventional linear least squares analysis of isothermal data and those of nonlinear least squares analyses of both isothermal and nonisothermal data. It was found that the nonlinear least squares procedures were useful for a rational selection of an acceptable model and estimation of its parameters.

General observations were made concerning good regions for further experimentation if a discrimination among rival models is desired. Additional well‐designed experiments were found to be necessary to allow a reduction of the confidence region of the parameters of the Hougen‐Watson models to an acceptable size.
Chemical reaction in the turbulent wake of a cylinder
Authors: Saidel G. M. , Hoelscher H. E.
Published: June 2004

A rapid, irreversible, second‐order chemical reaction in the turbulent wake of a cylinder was studied. A hypothesis relating the correlation of the fluctuating concentrations directly to the mean concentrations of the reacting species was found applicable, at least, when tested for a pseudo first‐order reaction system.

Experimentally, the mean concentration profiles of a colored reactant were obtained with and without reaction by time‐exposure photographs. Since the reactant changed from colored to colorless during reaction, the rate of reaction could be determined directly from the rate of color disappearance.

Both the reaction rate and the turbulent intensity divided by the half‐width of the wake were found to be inversely proportional to the distance from the source for x/d values from 35 to 180. This indicates a direct relationship between them. Consequently, the concentration correlation function also may be related directly to the turbulent intensity divided by the wake half‐width.

In addition, it is shown that the rate of reaction is faster in the center of the wake than it is toward the edges.