bluuebunny/crossref_metadata_2025 huggingface dataset:
Fluid flow through woven screens
Authors: Armour James C. , Cannon Joseph N.
Published: June 2004

A packed bed model has been adopted to develop a general correlation applicable to the flow of Newtonian fluids through all types of woven metal screens. Both of the main theoretical approaches to studying pressure drop in packed systems have been used by visualizing the screen as a collection of submerged objects with surface area to unit volume ratioafor laminar flow, and as a bundle of tubes of diameter D for turbulent flow. In the usual manner viscous and inertial energy losses are added to give an expression for the total pressure loss. Rearrangement of the general equation to the form of a friction factor yields a unique definition of the Reynolds number for screensNRe= ρu/μa2D. Procedures are described for collection of pressure drop‐velocity data for the flow of nitrogen and helium through plain square, full twill, fourdrinier, plain dutch, and twilled dutch weaves. The data are used to derive a viscous resistance coefficient α = 8.61 and an inertial resistance coefficient β = 0.52. The validity of the correlation equation is tested by using additional data from the literature. The correlation successfully predicts pressure drop for a Reynolds number range of 0.1 to 1,000, void fractions from 0.35 to 0.76, screen pore diameters from 5 to 550 μ, mesh sizes from 30 to 2,400 wires/in., and surface area to unit volume ratios from 1,200 to 29,000 ft.−1.
Density and pressure fluctuations in gas fluidized beds
Authors: Winter Olaf
Published: June 2004

A Bench‐scale size fluidization system was constructed for the purpose of conducting experiments to determine density and pressure fluctuations in gas fluidized beds. Density fluctuations and bubble sizes were measured with a photocell device and β‐ray absorption. Pressure fluctuations were determined with a conductivity cell. The frequency distributions of the density and pressure fluctuations and bubble sizes were determined as functions of several variables. They could be described by dimensionless coefficients and X2‐distributions with different degrees of freedom. Such variables as distance from the gas distribution plate, bed height, particle size, gas flow rate, and internal screens were considered.
Similarity type of solutions of the turbulent boundary layer equations for momentum and energy part I: An analysis of some existing solutions
Authors: Telles A. S. , Dukler A. E.
Published: June 2004

The law of the wall, the law of the wake, and the velocity defect law have been proposed as similarity types of solutions of the turbulent boundary layer momentum equation. Spalding proposed an approximation of the same type as the solution of the energy equation. This study shows these laws to be derivable from a small‐perturbation type of solution of the general boundary layer equations for turbulent flow. The limiting conditions where each can be expected to be valid are clearly demonstrated. In particular, the law of the wall is shown to be the zeroth‐order solution of the momentum equations when the solution is expressed in the form of a small‐perturbation expansion. The first‐order perturbation is shown to generate a relationship similar to Coles' law of the wake. Likewise, Spalding's approximation is shown to be the zeroth‐order small‐perturbation type of solution of the energy equation.
Mass transfer to falling films: Part I. Application of the surface‐stretch model to uniform wave motion
Authors: Howard D. W. , Lightfoot E. N.
Published: June 2004

A method is developed for predicting rates of gas absorption into laminar rippling films in terms of the surface velocities. The description is an extension of the surface‐stretch model of mass transfer (1) and is therefore useful for cases of high Peclet number. The description can be used with any of the presently known hydrodynamic models of rippling films and with any future models which may be developed, provided they satisfy two relatively nonrestrictive conditions: (1) the ripples are of a two dimensional nature, being of constant thickness in the direction normal to their direction of propagation, and having no velocity components in this transverse direction; and (2) the ripples propagate at constant celerity and with constant shape. It can be used for both traveling and standing waves and can be extended to describe the effects of high net‐mass transfer rates and combined diffusion and chemical reaction.
Thermodynamic equilibrium in the vapor phase esterification of Acetic acid with ethanol
Authors: Hawes Russell W. , Kabel Robert L.
Published: June 2004

A study of vapor‐phase equilibrium in the reaction system acetic acid‐ethanol–ethyl acetate‐water has been made including an evaluation of past investigations, a calculation of equilibrium constants from thermal data, and new experimental determinations utilizing gas chromatography in a novel method. It was found that the magnitude of the thermodynamic equilibrium constant and its true variation with temperature are appreciably different than previously indicated. This is due to the failure of earlier workers to adequately account for competing reactions, primarily the dehydration of ethanol to ethyl ether. Equilibrium constants were obtained at 100, 120.8, and 170°C. for the ethanol dehydration reaction. Equilibrium positions of the esterification reaction have been determined accurately at the same three temperatures, however the corresponding values of the thermodynamic equilibrium constant remain imperfectly specified because of uncertainty concerning the acetic acid association equilibrium.
Heat transfer coefficients and circulation rates for thermosiphon reboilers
Authors: Beaver P. R. , Hughmark G. A.
Published: June 2004

Heat transfer coefficients and circulating data were obtained for a single tube thermosiphon reboiler operated under vacuum and at atmospheric pressure. The results are compared with existing correlations. an analysis is presented for local heat transfer coefficients in the single phase and two‐phase regions.
Adsorption rate constants from chromatography
Authors: Schneider P. , Smith J. M.
Published: June 2004

A new method for determining adsorption equilibrium constants, rate constants, and intraparticle diffusivities is described and applied for the adsorption of ethane, propane, and n‐butane on silica gel. The method rests upon recently developed theory for relating the moments of the effluent concentration wave from a bed of adsorbent particles to the rate constants associated with the various steps in the overall adsorption process. It is necessary to operate at concentrations of adsorbable gas such that the adsorption isotherm is linear. However, it is possible to take into account effects of longitudinal dispersion and diffusion to the particle surface as well as the intraparticle processes of diffusion and adsorption on the pore surface.

The method gave reasonable values for intraparticle diffusivities and adsorption rate constants. Intraparticle diffusion was a major resistance for all particle sizes studied and for the largest size (R = 0.50 mm.) this step controlled the overall rate.

From the constants determined chromatographically it is possible to predict breakthrough curves for the adsorption of these hydrocarbons on silica gel. The predicted curves agree well with experimentally established breakthrough curves.
Continuous‐phase mass‐transfer coefficients for liquid extraction in agitated vessels
Authors: Schindler Harvey D. , Treybal Robert E.
Published: June 2004

Area‐free continuous‐phase mass‐transfer coefficients for continuous flow of ethyl acetate (dispersed) and water (continuous) were measured in a 9.5 in. diameter baffled vessel, agitated with 3 and 5 in. diameter flat‐blade turbines, and with the 3 in. turbine in the absence of baffles. Specific interfacial area was determined by a light‐transmission technique which permitted a vertical traverse of the vessel.

The specific area is greatest, and mean drop diameter smallest, near the impeller. The mean area is lower than that predicted from existing correlations for batch operation in the absence of mass transfer. Continuous‐phase mass‐transfer coefficients increase with increased impeller Reynolds number and dispersed‐phase holdup, and are about 2.5 times larger in the unbaffled vessel at the same impeller power. The coefficients are generally larger than those predicted by existing correlations based on suspended solids, and it is suggested that this and the effect of holdup is the result of drop coalescence and redispersion, which causes a renewal of the continuous phase surrounding each drop. Rough estimates of the minimum coalescence frequency in the baffled vessel and application of the renewal concept to the data appear to confirm this view. Lack of information on circulation rates prevents immediate test of the data from the unbaffled vessel.
Sinusoidal and pulse response of a plate distillation column by reflux upset
Authors: Marino Pasquale A. , Perna Angelo J. , Stutzman Leroy F.
Published: June 2004

A study was made to evaluate pulses as a forcing function on a 24‐plate distillation column. Pulses of two shapes, rectangular and displaced cosines, and of different widths were used as inputs to the reflux return line from the condenser to the column. The effect of the disturbance was a change in the liquid return rate which correspond to the shape and size of the pulse. The output responses of the system were temperatures measured at different times and at different plates in the column.

Bode diagrams were plotted from the experimentally determined data. From these plots, it was determined that the system could be approximated by linear first‐order equatons. The time constants for the linear system were determined both by direct sinusoidal forcing and by pulse forcing. Pulse data were considered acceptable when the values of the time constant and the phase angle determined by the pulse compared favorably with those determined by steady state sinusoidal forcing.
Chromatographic study of surface diffusion
Authors: Schneider Petr , Smith J. M.
Published: June 2004

A new method, based upon chromatography, was used to measure surface diffusion coefficients for ethane, propane, and n‐butane on silica gel. The diffusivities correspond to very low surface coverages (fraction of a monolayer of the order of 10−4) and hence should represent limiting values. A survey of available surface diffusion information, all at higher coverages, indicated that the results reported here are at the lower end of the range of diffusivities. The activation energy and heat of adsorption, for example, for n‐butane, were 4.4 and −7.8 k cal./mole, respectively.

Surface diffusion was a significant fraction of the total intraparticle mass transport, in part because in the small pores in silica gel gas phase diffusion was solely by the Knudsen mechanism. For propane, surface migration was 73% of the total transport at 50°C. and 61.5% at 125°C.
Condensation from superheated gas‐vapor mixtures
Authors: Stern Frederick , Votta Ferdinand
Published: June 2004

Superheated mixtures of vapor and noncondensable gas were cooled and condensed in down‐flow inside a single tube vertical condenser, 0.995 in. I.D. and 3.5 ft. long. The systems studied were air‐water, carbon dioxide‐water and helium‐water. A bulk stream mixing probe was developed which enabled the measurement of point values of the stream temperature and partial pressure at various positions within the condenser. The Reynolds number range of the investigation was 5,700 to 34,000.

A theoretical solution of the problem, using Bras' design method, was solved rigorously on a digital computer. Results indicated excellent agreement between the theoretical and experimental cooling paths and the required transfer area. The inclusion of the Ackerman correction factor (for the sensible heat carried by the diffusing vapor) into the calculation gave significantly better agreement for all cases tested.
Dispersion in developing velocity fields
Authors: Gill William N. , Ananthakrishnan V. , Nunge Richard J.
Published: June 2004

Convective diffusion in laminar flows which develop from rest and in the velocity entrance region of tubes, is studied. Criteria for the validity of the simple dispersion model are established by comparison of analytical results with numerical experiments.

It is found that the extent of dispersion is less in developing velocity fields than in those which are fully developed. This occurs because dispersion is enhanced by differences in the velocity of the fluid particles on a plane perpendicular to the main direction of flow. Such differences are greatest when the flow is fully developed.
Transient diffusion from a well‐stirred reservoir to a body of arbitrary shape
Authors: Ma Yi Hua , Evans Lawrence B.
Published: June 2004

A theoretical study was made of transient diffusion to a body immersed in a finite volume of well‐stirred fluid. The major contribution of this work was the development of a technique for solving the problem for a three‐dimensional body of arbitrary shape. The solutions are in a form that is useful for determining diffusion coefficients insolids by means of the constant‐volume experimental technique.

The partial differential equation coupled with the ordinary differential equation describing the diffusion process is transformed into a single integral equation in terms of the solute concentration in the reservoir. A numerical technique is then presented for solving the integral equation. Numerical solutions were computed for the three geometries that possess analytical solutions: the infinite slab, the infinite cylinder, and the sphere. By properly choosing the step‐size numerical results were easily obtained that agreed with the exact solution to four decimal places.

New solutions were computed for two three‐dimensional geometries: the finite cylinder and the rectangular prism. A range of shape factors and ratios of the volume of the reservoir to that of the solid body were employed for each geometry. It was shown that by selecting the ratio of volume to external surface area as the characteristic length of each shape object, the solutions for all shapes were brought close together and were identical during the initial part of the transient.
Graphical calculation of multiple steady states and effectiveness factors for porous catalysts
Authors: Stewart Warren E. , Villadsen John V.
Published: June 2004

Simple graphical methods are given for predicting the effectiveness factors of single reactions in particles of various shapes. A collocation procedure is used for small particles, and the known asymptotic solution is used for large particles. Multiple steady states and variable fluid properties can be handled directly. Examples are given for several nonlinear reaction rate laws.
The effect of pressure on the permeation of gases and vapors through polyethylene. Usefulness of the corresponding states principle
Authors: Stern S. A. , Mullhaupt J. T. , Gareis P. J.
Published: June 2004

The permeation of carbon dioxide through polyethylene membranes has been studied at pressures up to 54.4 atm. and at temperatures above and below the critical temperature of the gas (31.0°C.). The permeability coefficient is independent of pressure at the highest experimental temperature (61.0°C.), but becomes increasingly pressure‐dependent as the temperature is lowered. The principle of corresponding states can be used to correlate the solubility of both gases and vapors in polyethylene over a wide range of temperatures. This principle can also be invoked to obtain an upper limit for the penetrant pressure above which the permeability coefficient becomes pressure‐dependent. The effect of pressure on the permeability, solubility, and diffusivity of gases and vapors in polyethylene is discussed in some detail.
Axial dispersion in turbulent flow through standard 90 degree elbows
Authors: Cassell Robert E. , Perona Joseph J.
Published: June 2004

Axial dispersion was studied experimentally for turbulent flow through a 1 1/4‐in. piping system containing 90 deg. elbows. The Reynolds number range was 15,400 to 96,555. The imperfect pulse tracer technique was used with the axial dispersion numbers being obtained from the difference in variances of concentration‐time curves observed at two points in the system.

Elbows interconnected by short lengths of pipe with each succeeding one reversed so as to cause a change in the direction of flow, increased axial dispersion by 35 to 61% over that expected for straight pipe, while the same elbows turned so as to form a helix decreased the dispersion substantially; however, the amount of axial dispersion was still 8 to 22% greater than that observed for straight pipe.

The equivalent lengths of the elbows depend upon both their arrangement and the Reynolds number. Closely placed, helically arranged elbows required equivalent lengths of from 2.9 to 5.1 diam., while a reversed arrangement required 6.9 to 11.6 diam. Elbows separated by a developing length and randomly arranged yielded an equivalent length range of 3.6 to 10.6 diam. The geometical l/d ratio of the elbows used was 2.05.
Diffusion and solution of gases into thermally softened or molten polymers: Part II. Relation of diffusivities and solubilities with temperature pressure and structural characteristics
Authors: Durrill Preston L. , Griskey Richard G.
Published: June 2004

Solubilities and diffusivities of various gases (helium, nitrogen, carbon dioxide, argon, neon, krypton, and monochlorodifluoromethane) in molten or thermally softened polymers (polyethylene, polypropylene, polyisobutylene, polystyrene, and polymethylmethacrylate) have been correlated with structural characteristics, temperature, and pressure. Temperature dependence of both Henry's Law constants and diffusivities were of the Arrhenius equation form. No appreciable effect of pressure was found for either Henry's Law constants or diffusivities up to 300 atm. Earlier correlations for Henry's Law constants in solid polymer systems were found to be inapplicable for molten and thermally softened polymers. New correlations were developed individually for the latter systems. The correlating factor used was the gas Lennard‐Jones force constant. Existing correlations for diffusivities were also found not to apply to molten and thermally softened systems. New correlations were again developed on an individual polymer basis. These related diffusivity to gas Lennard‐Jones collision diameter or molecular diameter. Generalized correlations were also developed that held for a number of polymers. These were for both Henry's Law constants and diffusivities.
Maximum temperature rise in gas‐solid reactions
Authors: Luss Dan , Amundson Neal R.
Published: June 2004

A shell progressive kinetic model is used to determine the temperature rise in a spherical pellet for a gas‐solid diffusion controlled reaction. The effects of heat and mass transfer resistances in the gas film as well as inside the pellet are investigated. The predicted temperature rise may be severe enough to cause sintering to catalyst pellets in which reactions such as combustion of coke occur.
Vaporization at the base of bubbles of different shape during nucleate boiling of water
Authors: Hospeti N. B. , Mesler R. B.
Published: June 2004

Differently shaped bubbles were observed growing during nucleate boiling of water at atomspheric pressure. The surface temperature beneath the bubbles was measured simultaneously with a fast response surface thermocouple. The evaporation from the base necessary to account for the observed cooling was calculated. A comparison of the ratio of vapor volume formed at the base to the total volume of the bubble shows a dependency on bubble shape. The ratio is smallest for spherical bubbles, largest for hemispherical and intermediate for oblate bubbles.
Internal flow mechanism in filter cakes
Authors: Shirato Mompei , Sambuichi Masao , Kato Hiroo , Aragaki Tsutomu
Published: June 2004

The definition of filtration resistance is modified by considering relative solid‐liquid velocity.

The internal flow mechanism in a filter cake is reexamined in view of the movement of solids during compression. Under conditions of short filtrations involving highly concentrated slurries, the velocity of solids is shown to be comparable to the velocity of the liquid. A differential equation is proposed for the flow through compressible cakes in which the pressure gradient is assumed proportional to the difference in average velocities of the liquid and solid rather than to the average velocity of the liquid alone.

An improved definition of the average filtration resistance is developed on the basis of the new flow equation.
Rotational stability in viscoelastic liquids: Theory
Authors: Ginn R. F. , Denn M. M.
Published: June 2004

The onset of secondary motions between rotating concentric cylinders is related to the viscometric normal stress functions for a class of viscoelastic liquids which includes dilute polymer solutions. Both increased and decreased stability relative to a corresponding Newtonian liquid are possible for a given material, depending upon the particular relation between the viscometric functions and the geometric constants of the equipment. This predicted behavior is in agreement with experimental observations.
Rotational stability and measurement of normal stress functions in dilute polymer solutions
Authors: Denn M. M. , Roisman J. J.
Published: June 2004

The onset of rotational flow instability was determined experimentally for dilute solutions of six polymers. In general, the onset of secondary motions occurred later than for a Newtonian liquid of equal apparent viscosity, although, depending upon geometric ratios, some instabilities occurred earlier than in the Newtonian liquid. The stability theory of Ginn and Denn was used to calculate viscometric normal stress functions for ten solutions, with excellent agreement obtained with rheogoniometric measurements of the primary normal stress measurements in all but three cases. Torque measurements of the laminar secondary motion following instability showed some frictional drags significantly less than those observed in Newtonian liquids, a phenomenon analogous to the turbulent drag reduction observed previously in dilute polymer solutions.
Cyclic steady state diffusion
Authors: Simmons P. J. , Spinner I. H.
Published: June 2004

Analytic equations describing cyclic steady state diffusion in which the diffusivity depends on the direction of transfer, as well as on the system, have been obtained.

By imposing the cyclic steady state constraint, of periodically repetitive concentration profiles, simultaneous solution of separate Fick's diffusion equations for the on‐off segments of the cycle results in the desired equatins. The method of solution can be extended to more complex diffusion problems, such as coupled diffusion processes. Shallow bed experiments have been performed on particle‐diffusion controlled, cyclic steady state ion exchange. Agreement between the predicted and experimental transfer was obtained. Variables and parameters affecting cyclic steady state diffusion are discussed.
A drop dispersal model for rinsing
Authors: Tallmadge John A. , Li Sik U.
Published: June 2004

A new theory for convection‐free rinsing of flat plates was developed to include the drop dispersal mechanism as well as the previously considered diffusion mechanism. Cases where carryover is unequal to dragout were also included in the model. Based on film distribution data, the model offers better agreement with rinse data. The effect of drain time on film distribution and bottom drop volume was also investigated.
A phenomenological interpretation and correlation of drag reduction
Authors: Astarita Gianni , Greco Guido , Nicodemo Luigi
Published: June 2004

Drag reduction data for five concentrations of a water‐soluble polymer and three tube diameters are presented. The data are correlated by a single curve relating two dimensionless parameters; these have been obtained from a phenomenological analysis of the mechanism of drag reduction.
Packed distillation columns and absorbers at steady state operation
Authors: Rubac R. E. , McDaniel Ronald , Holland C. D.
Published: June 2004

In this paper the concept of a mass transfer section is applied to problems involving packed distillation columns and packed absorbers. When this concept is employed, the resulting equations required to describe packed distillation columns and packed absorbers are identical in form to those required to describe distillation columns and absorbers with plates. Data from the results of two field tests are presented and analyzed.
Thermal and material transport in nonisothermal packed beds
Authors: Schertz William W. , Bischoff Kenneth B.
Published: June 2004

The turbulent transport of mass, energy, and momentum was studied in a 4 in. diameter cylindrical column packed with 0.3 in. diameter stoneware spheres. Helium was used as a tracer material, with air as the mainstream fluid. The concentration of tracer present, the temperature, and the velocity of the gas were measured at several axial and radial increments. These data were analyzed numerically to obtain the radial component of the effective thermal conductivity and the radial component of the mass‐dispersion coefficient as functions of radial position. Experimental conditions covered isothermal determinations at room temperature and nonisothermal determinations in which a temperature gradient was established in the radial direction. Significant differences were found between the isothermal and strongly nonisothermal results, primarily for the velocity profiles and thermal conductivities. Correlations were developed for the local values of the parameters.
Foaming and frothing related to system physical properties in a small perforated plate distillation column
Authors: Lowry R. P. , Van Winkle Matthew
Published: June 2004

Experimental froth heights occurring on a perforated distillation tray were correlated with the determining system physical properties under distillation conditions. A photographic technique was used to measure accurately the foam and froth heights, produced in the 4 in. square test section of a laboratory distillation column, for several points in the composition range of five binary systems. Plate design parameters and operating vapor and liquid rates were held constant throughout the experimental study.

The froth height results from this investigation (11), as well as those from studies (17) of a 6 in. distillation column, show a linear relation with the expression, UA2 ρv/(ρL — ρV), the frothing factor, for the ranges of the physical properties investigated.

The foam height results of this study indicate that the mass transfer surface tension gradient, the heat transfer gradient, and the absolute value of surface tension all contribute to foam formation and stability. Because of the complex relation between the surface tension gradient and the frothing factor in relation to the degree of foaming, as well as the effects of other influencing variables, a unique correlation of the foam height data resulting from mass transture of the effect for several of the data points.

This investigation was conducted to obtain experimental data which could provide a basis for correlation of the foam and froth heights occuring on an operating perforated distillation tray with system physical properties.
Transport of heat and mass between liquids and spherical particles in an agitated tank
Authors: Brian P. L. T. , Hales H. B. , Sherwood T. K.
Published: June 2004

Data are reported for heat transfer from water to melting ice spheres and for mass transfer in the case of dissolving spheres of pivalic acid suspended in water agitated in a stirred vessel. The transport coefficients are found to depend on agitator power input but not on agitator design, in agreement with the Kolmogoroff theory. These experimental results are used with others in the literature to develop a correlation involving Nusselt and Prandtl or Schmidt numbers together with a dimensionless group involving agitation power. The correlation is essentially independent of solid‐liquid density ratio in the range 0.8 to 1.25, and in this range the gravity group also appears to be unimportant.
Converging flows of viscoelastic materials
Authors: Metzner A. B. , Uebler E. A. , Fong C. F. Chan Man
Published: June 2004

The kinematics of converging velocity fields such as those found in flows from a large duct or reservoir into a small tube are especially simple in the case of viscoelastic materials as they may be approximated by means of a diagonal deformation rate tensor. This result is shown to be valid in the present study in which aqueous polymeric solutions were utilized and is inferred as having been valid under the experimental conditions employed by Bagley in studies of molten polymers. It is suggested that asymptotic approximations based upon the diagonality of the deformation rate tensor may be of general use in analysis of flows of viscoelastic materials, that is, they could represent, potentially, simplifying approximations comparable in utility to the boundary layer approximations employed commonly in the analysis of flows of Newtonian fluids.

An interesting prediction of the present analysis is that for flows from a large duct into a small one a plot of isotropic pressure vs. axial position exhibits a minimum near the inlet to the smaller duct. Experimental results are presented in partial support of this unusual behavior. The analysis also suggests that an orfice jet thrust technique for measurement of normal stresses, closely related to recent independent studies by Middleman and by Fabula, may be an indirect but especially simple and sensitive tool for measurement of material properties.
Flow properties of suspensions with high solids concentration
Authors: Gay E. C. , Nelson P. A. , Armstrong W. P.
Published: June 2004

Equations were developed for evaluating the laminar flow behavior of high‐solids suspensions from the physical properties of the liquid and solid components. A technique was developed for calculating suspension flow rates as a function of pressure drop. The technique is applicable to the design of pipe lines. Flow measurements were made in pipe‐line viscometers of a unique design that minimized entrance and exit effects. Experimental flow data were obtained for suspensions consisting of nickel, alumina, copper, or glass solids in sodium, xylene, or glycerine vehicles with solids concentrations of 28 to 55 vol. %. The basis for the correlation of the data was an analytical investigation of the flow behavior that considered the particle‐particle interaction that takes place in a settled suspension. The correlation equations fit all systems investigated. They take into account the effects of liquid viscosity, liquid and solid densities, particle size, size distribution, particle surface area, volume fraction of solids in the suspension, and volume fraction of solids at maximum settled conditions.
The kinetics of condensation polymerization
Authors: Secor R. M.
Published: June 2004

The final stages of condensation polymerization are characterized by a rapid rise in molecular weight, as the condensation product is formed and diffuses out of the polymer. The process occurring is one of desorption accompanied by a chemical reaction. The penetration theory equations for a generalized condensation polymerization reaction have been solved and some solutions are presented. The penetration theory solution, obtained by finite‐difference computations, is compared with an analytical solution for the special case of no diffusional resistance.
Single‐phase flow through porous media
Authors: Slattery John C.
Published: June 2004

The local volume average of the equation of motion is taken for an incompressible fluid flowing through a porous structure under conditions such that inertial effects may be neglected. The result has two terms beyond a pressure gradient: g, the force per unit volume which a flowing fluid exerts on a porous structure, and the divergence of the local volume‐averaged extra stress tensor (viscous portion of the stress tensor).

Constitutive equations for g are examined with the aid of the principle of material indifference. When g is assumed to be a function of the velocity of the fluid relative to the solid as well as various scalars, the usual results for a nonoriented (isotropic) porous structure are obtained. When g is assumed to be a function of the local porosity gradient as well, we derive a new expression for g applicable to oriented (anisotropic) porous structures.

For a Newtonian fluid with a constant viscosity, the divergence of the local volume‐averaged extra stress tensor is proportional to the Laplacian of the averaged velocity vector. Boundary conditions for the averaged velocity vector are discussed. Three problems are solved for the flow of an incompressible Newtonian fluid in a nonoriented permeable medium. These solutions, as well as an order‐of‐magnitude analysis, suggest that we may often neglect both the Laplacian of average velocity and the boundary conditions for the tangential components of averaged velocity at an impermeable wall.

Two specific constitutive equations for g are proposed for the flow of incompressible Noll simple fluids in nonoriented porous structures. Flow through a porous medium bounded by an impermeable cylindrical surface is solved for these two constitutive equations, and the results are compared with previously available experimental data.
An equation of state for methane in the gas and liquid phases
Authors: Vennix A. J. , Kobayashi Riki
Published: June 2004

An equation of state was developed which represented experimental methane P‐V‐T data over the temperature range of 130 to 625° K. for pressures to 10,000 lb./sq. in. obs. with densities to 0.36 g./cc. For 598 experimental points the mean square percent deviation in the predicted pressures was 0.07% with only 10 points having deviations above 0.2%. The low density limit of the equation predicted second virial coefficients within 1 cc./mole of the accepted values for temperatures above 200° K.

The equation was developed by first analyzing isochoric data from the saturation point to the high temperature or pressure limit. An expression was then obtained, reflecting qualitative behavior of the isochores, that reproduced experimental data along each isochore with an average pressure error of 0.02% and a maximum error of 0.08%. This expression had the form P = A + BT + C exp [E (T — T0)] + D exp (k—F/T) where k and T0 were normalizing constants and A through F were functions of density. From the density dependence of these parameters a single expression was obtained which fit the entire range of experimental data.
On the interdependence of temporary and permanent deactivation in a reactor‐regenerator system
Authors: Gwyn J. E. , Colthart J. D.
Published: June 2004

No Abstracts.
Correlation of liquid slug velocity and frequency in horizontal cocurrent gas‐liquid slug flow
Authors: Gregory G. A. , Scott D. S.
Published: June 2004

No Abstracts.
Free convection melting of ice spheres
Authors: Vanier C. R. , Tien Chi
Published: June 2004

Experimental results have been obtained for heat transfer to melting ice spheres by measuring the rate of change of apparent weight. It is found that the traditional correlation format of Nusselt number against Rayleigh number is satisfactory only for bulk temperatures above 7°C. Average Nusselt numbers obtained from the sphere experiments are closely related to previous theoretical work with vertical flat plates.
The effect of surface active agents on interphase mass transfer
Authors: Burnett J. C. , Himmelblau D. M.
Published: June 2004

The effect of various soluble and insoluble surface active agents on the absorption of ammonia into a static aqueous system was studied. Saturated straight‐chain hydrocarbons with four to twenty‐two carbon atoms and polar end groups were selected as the surface active agents to be studied. Alcohol, amine, and amide end groups were investigated. Most of the insoluble surface active agents, which were studied as films, were found to decrease the ammonia absorption rate. There was a definite correlation between the amount of mass transfer reduction and the hydrocarbon chain length, while the effect of the various end groups appeared to depend on the chain length. Surface mass transfer coefficients were computed for each surface active agent that retarded mass transfer. Most of the soluble surface active agents were found to increase the ammonia absorption rates. For all cases of enhanced mass transfer, movements in the interface could be observed. It was concluded that the interfacial movements were caused by the Marangoni effect. In general, as the chain length of the surface active agent decreased, the mass transfer enhancement increased. A mathematical model based on a surface renewal theory was fitted to the experimental data.
Distillation decoupling
Authors: Luyben William L.
Published: June 2004

This paper presents a quantitative study of two types of decoupling elements to achieve non‐interacting feedback control of overhead and bottoms compositions in binary distillation. Ideal decoupling, where the closed loop response of each loop is the same as it would be if the other loop were on manual control, and simplified decoupling, where two interaction compensators are used to isolate each loop, are investigated.

The decoupling elements themselves are physically realizable in both cases, but unstable loops develop with ideal decoupling in higher purity columns because of increased positive feedback. Simplified decoupling gave effective, stable, noninteracting loops for all the cases studied.

The decoupling elements are designed in the frequency domain from a linear model of the column, and their effectiveness is tested by digital simulation of the nonlinear column model.
Effect of molecular weight distribution on the shear dependence of viscosity in polymer systems
Authors: Graessley William W. , Segal Leon
Published: June 2004

The viscosity of concentrated solutions of polystyrene were measured in steady shearing flow with a Weissenberg rheogoniometer. The polymers ranged in weight average molecular weight M̄w from 97,000 to 3,370,000 and in distribution breadth M̄w/M̄n from 1.05 to 3.1. The solvent was n‐butylbenzene, and the solutions ranged in concentration from 0.20 to 0.55 g./cc. These data were supplemented by measurements on bulk polystyrenes and polyethylenes with distribution breadths as high as M̄w/M̄n = 20. Master curves of reduced viscosity vs. reduced shear rate were calculated theoretically for each molecular weight distribution. The experimental viscosity data superimposed satisfactorily on these curves and furnished the viscosity at zero shear rate τ0 and an experimental time constant τ0 for each solution. The time constant paralleled closely the Rouse relaxation time τR in all systems. Residual variations in the ratio τ0/τR with molecular weight and concentration correlated uniquely with the product cM̄w. These results indicate that the viscosity behavior of a polymer can be predicted with reasonable accuracy from data on its molecular weight distribution.
Radial migration of spherical particles in couette systems
Authors: Halow J. S. , Wills G. B.
Published: June 2004

Several studies have been made in Couette systems of the primary motion (angular translation and rotation) of spheres suspended in viscous liquids. Radial migration trajectories, however, have been unreported for single spheres.

In this study, a prediction of radial migration is developed and compared with experimental measurements. The predicted trajectories were found to agree well with the measured ones.

Ultimately, radially migrating spheres reached an equilibrium position located approximately midway between the cylinder walls. The model developed predicted an equilibrium position just slightly inside the midpoint, while measured equilibrium positions fell between the midpoint and 0.4, the annular thickness from the inner cylinder walls. The differences in equilibrium positions are attributed to the approximate nature of the model.
Temperature profiles for polymer melts in tube flow
Authors: Collins Edward A. , Filisko Frank E.
Published: June 2004

The present state of the theory of nonisothermal tube flow is inadequate to predict the behavior of polymer melts. In addition, relatively few experimental measurements on radial temperature profiles of polymer melts in the tube flow have been reported. For non‐Newtonian systems, the separation of viscous losses due to frictional heat generation and those due to the effect of shear rate is a formidable problem which has hampered progress. This paper will describe a method of measuring shear induced heating and present experimental data on radial temperature profiles in tube flow. A novel method of estimating the velocity profile is also described.
Light intensity profiles in a perfectly mixed photoreactor
Authors: Jacobm Solomon M. , Dranoff Joshua S.
Published: June 2004

The light intensity distribution in a perfectly mixed photoreactor has been studied experimentally and analytically. Experimental measurements of intensities within the reactor were made with a specially designed light probe. These data were then used to test the validity of a model which treats the ultraviolet lamp as a linear source radiating in all directions. It was found that this model, which seems appropriate and allows reasonable computations, is somewhat in error owing to the neglect of the finite size of the lamp and the existence of reflection and refraction effects within the reactor. An empirical correction function was determined for use with the model which then yields predictions in close agreement with experimental data when the reactor is filled with a light absorbing liquid.
Analytical and experimental studies of facilitated transport
Authors: Ward W. J.
Published: June 2004

Facilitated transport is a process in which permeation through a liquid film is chemically augmented. Because of the scientific and engineering interest in this phenomenon, the purpose of this work was to carry out a detailed mathematical and experimental investigation of facilitated transport. The differential equations describing facilitated transport are presented, and a generally applicable numerical solution recently developed by G. M. Roe for this type of boundary value problem is summarized. The experimental investigation consisted of measuring the steady state rate of transport of nitric oxide through thin films of ferrous chloride solution and of determining independently the values of the system parameters of which the nitric oxide flux was a function. The experimental results were accurately predicted by using the model developed by Roe. This is the first demonstration of a general quantitative understanding of facilitated transport.
Thermodynamic properties of the system N2O4⇌2NO2⇌2NO + O2
Authors: Seshadri D. N. , Viswanath D. S. , Kuloor N. R.
Published: June 2004

Thermodynamic properties of the chemically reactive system N2O4⇌ 2NO2⇌ 2NO + O2have been evaluated over a pressure range of 0.005 to 200.0 atm. and a temperature range of 200° to 900°K. by making use of Lennard‐Jones potential. In these calculations, the dissociation of nitrogen tetroxide to nitrogen dioxide, nitric oxide and oxygen, and the effect of pressure on the equilibrium constants for the system of reactions N2O4⇌ 2NO2and 2NO2⇌ 2NO + O2have been taken into account.
A statistical model of a porous medium with nonuniform pores
Authors: Haring R. E. , Greenkorn R. A.
Published: June 2004

A random network model of a porous medium with nonuniform pores has been constructed. Nonuniformity is achieved by assigning two‐parameter distributions to pore radius and pore length. Statistical derivations result in expressions for bulk model properties which are consistent with known empirical behavior of porous media such as capillary pressure, hydraulic permeability, and longitudinal and transverse dispersion. A series of experiments is suggested whereby the parameters of porous media structure may be determined from observed macroscopic behavior by using the expressions developed in this paper.
Laminar‐turbulent transitional flow phenomena in isosceles triangular cross‐section ducts
Authors: Hanks Richard W. , Cope Richard C.
Published: June 2004

A theoretical analysis of the laminar‐turbulent transition phenomenon is presented for the case of steady, isothermal, fully developed flow of Newtonian fluids in straight ducts of constant isosceles triangular cross section. As a result of this analysis, the simultaneous existence of macroscopically large stable regions of laminar and turbulent flow are predicted to occur during the transition phenomenon. The existence of this special type of flow field, which has not been previously predicted theoretically, is shown to be a consequence of the presence of an asymmetric shear stress distribution. The results of an experimental study are also presented. These data verify the predictions made by the theoretical analysis.
Initiation of thermal convection in finite right circular cylinders
Authors: Catton Ivan , Edwards D. K.
Published: June 2004

Linear perturbation analyses are extended to determine the lowest Rayleigh number at which convection initiates in a vertical cylinder heated on the bottom and cooled on the top. The critical Rayleigh number for the first mode of convection in a right circular cylinder with a perfectly conducting wall is shown to be three times larger than that in such a cell with a perfectly adiabatic side wall. An adjusted wave number is shown to make the results of Pellew and Southwell applicable to the adiabatic wall in a manner similar to that used by Pnueli and Ostrach for the perfectly conducting side wall. The results are compared with experiment and are in very good agreement.
The absorption of carbon dioxide by weak base ion exchange resins
Authors: Weber Oscar W. , Miller Irving F. , Gregor Harry P.
Published: June 2004

A study of the feasibility of using ion exchange resin systems for carbon dioxide absorption from gas streams was completed with the conclusion that such a system could compete very successfully with atmospheric control systems now in use. A detailed study of such a system based on polyethylenimine showed that this material is superior to any of the commercially available weak base resins tested. The kinetic data obtained correlated very well when a model was postulated that was based on diffusive transfer through a gas film, a water film, and the resin particle in series, with diffusion with the resin particle as the rate determining step.
Film formation in two‐phase annular flow
Authors: Anderson R. J. , Russell T. W. F.
Published: June 2004

The liquid film in annular two‐phase flow is maintained by droplet movement to and from the gas core and by wave action. This work examines droplet movement and its effect on the liquid film. Film formation and movement both axially and circumferentially were investigated by using transient techniques.
Continuous filter cake washing performance
Authors: Kuo M. T. , Barrett E. C.
Published: June 2004

A previous report (1) has presented the derivation of new filter cake washing equations. This report presents the procedure for their application and contains an example of application to a specific batch washing system. It also presents the adaption of the equations to permit their use in predicting the performance of a continuous rotary‐drum filter.
Mass transfer in two‐phase flow in horizontal pipelines
Authors: Jepsen John C.
Published: June 2004

The objective of the present study was to obtain data on the rate of liquid‐phase controlled mass transfer in two‐phase gas‐liquid flow in horizontal pipes. Studies were made on the effect of the mean gas and liquid flow rate, pipe diameter, and pipe orientation on k𝓁a, the mean liquid‐phase film mass transfer coefficient. Experimental studies were made on 1 and 4 in. I.D. horizontal pipelines; on 4 in. I.D. 180 deg. vertical short radius bend (H/D = 2); and on 3/16, 5/16, and 7/16 in I.D. tubes wound in 4‐in. diameter spirals (upflow). A general correlation is presented for k𝓁a as a function of the two‐phase frictional energy dissipation, liquid‐phase physical properties, and pipe diameter.