bluuebunny/crossref_metadata_2025 huggingface dataset:
Performance predictions for a cocurrent spray dryer
Authors: Baltas Leon , Gauvin W. H.
Published: June 2004

A step‐by‐step prediction procedure has been developed to predict the evaporation of a sodium nitrate spray consisting of small drops moving at terminal velocity through the drying air. The procedure accounts both for the existence of radial gradients as well as radial mixing in the dryer and is selfsustaining except for values of the local air velocity.

Because the procedure can be applied only to the free‐fall zone, at some distance below the nozzle, a method was developed for the indirect determination of the amount of water remaining in the partly evaporated droplets at the beginning of the free‐fall zone. This procedure was then applied to experimental data on drop size distributions obtained at the beginning of this zone. Owing to uncertainties concerning the salt concentration in the drops, a number of assumptions had to be made and the procedure was only partially successful in describing the spray evaporation, although it did compute the radial spray transfer. It was possible, however, to indicate by means of a model drop distribution the general validity of the procedure.
Transport characteristics of a cocurrent spray dryer
Authors: Baltas Leon , Gauvin W. H.
Published: June 2004

The design of an experimental cocurrent spray dryer and its method of operation are described. The rationale for the development of some new measurement techniques and modifications to existing ones is discussed. These techniques were used to obtain profiles at several dryer levels of the air velocity, air humidity, and spray mass velocity for the case of a 30% sodium nitrate solution sprayed into 100°C. air. Somewhat less detailed measurements of the spray moisture and radial turbulent diffusivity were also made.

The humidity and spray moisture measurements gave very nearly identical results for the progress of the evaporation along the length of the dryer. The axial injection of the spray was found to result in steep gradients for the air velocity, air humidity, and salt mass velocity but these were found to decay under the influence of turbulent mixing which is also generated by the spray injection.
Optimal design of jacketed tubular reactor with taylor diffusion
Authors: Leung Vincent P. , Chang Kun S.
Published: June 2004

No Abstracts.
A numerical solution for the single‐screw extrusion of a polymer melt
Authors: Dyer David F.
Published: June 2004

A general numerical‐analysis procedure is presented for the screw extrusion of a non‐Newtonian material. The full Navier‐Stokes energy and continuity equations are used in the numerical procedure. The flow is taken as steady and incompressible, and the viscosity is written according to the Ostwald‐de Waele model in which the viscosity is assumed to be inversely proportional to the square root of the second invariant of the rate of deformation tensor and exponentially dependent on the temperature.

The procedure allows the prediction of vorticity, stream‐function, swirl velocity, internal energy, and viscosity over any cross section of a groove containing plastic. Calculations for the mass extrusion rate and power consumption (shear rate) for the screw extruder are also given. Typical cases are considered for which all the quantities listed above are determined. The results compare favorably with other theoretical work.
Static pressure and velocity profiles in swirling incompressible tube flow
Authors: King M. K. , Rothfus R. R. , Kermode R. I.
Published: June 2004

The phenomenon of reversing axial flow in swirling incompressible flow through a tube has been investigated experimentally. The study was carried out in a 2 in. I.D. test section of plexiglass tubing 10 ft. long. The swirl was introduced by injection of the total fluid stream through two symmetric tangential inlets perpendicular to the tube. Measurements have been made with specially constructed stagnation and static pressure probes.

Velocity and pressure profiles obtained for tests conducted at four Reynold's Numbers in one fixed geometrical configuration are presented and discussed in general terms. Swirl decay rate is characterized in a plot of weighted tangential velocity/inlet velocity ratio versus distance along the test section from the inlets. A model presented by a previous investigator to explain the flow reversal phenomenon is discussed in the light of present work. Finally the data is used in an order of magnitude analysis to reduce the turbulent Navier‐Stokes equation describing the flow to simpler (though still indeterminate) form.
Scale‐up criteria for stirred tank reactors
Authors: Evangelista J. J. , Katz Stanley , Shinnar Reuel
Published: June 2004

A method is derived for the design of stirred tank reactors for homogeneous reactions. A simple mixing model proposed previously by Curl (4) is used to compute the effects of finite mixing time on complex chemical reactions. It is also shown how the parameters of the model can be obtained by tracer experiments, or estimated theoretically by the assumption of isotropic turbulence. It is shown that in many practical cases the assumption of ideal mixing is a good approximation. However, the effects of imperfect mixing are more likely to be felt in a large reactor than in a pilot plant. Some quantitative examples are discussed. Methods are derived to compute the average outlet concentration for complex systems such as autothermic reactions, polymerization, crystallization, etc.
Combined forced and free convective diffusion in vertical semipermeable parallel plate ducts
Authors: Ramanadhan Krishnan , Gill William N.
Published: June 2004

The effect of natural convection on polarization and flow patterns in liquid phase convective diffusion in a vertical duct with semipermeable membrane walls has been investigated theoretically. It is found that at low flow rates, gravitational fields can play a significant role in distorting the velocity profiles and thereby they affect the transition from laminar to turbulent flow. Natural convection also significantly affects mass transfer rates and therefore the extent of polarization at low flow rates. Results are presented for both momentum and mass transfer in upward and downward flows for different wall Peclet numbers. The hydrodynamic stability of the system also has been investigated and critical values of the buoyancy parameters are reported. Also, these results enable one to estimate when natural convection may create errors in membrane testing systems.

The analysis and results are of practical interest in reverse osmosis and other membrane separation processes. The more productive the system, the more likely it will be that buoyancy effects are important.
Simultaneous flow and temperature correction in the equilibrium stage problem
Authors: Tierney John W. , Yanosik John L.
Published: June 2004

Iterative methods for the solution of the steady state equilibrium stage problem are studied. Equations are first developed for calculating the effect of a change in temperature or flow rate on all energy balances, and then it is shown that these equations can be used in the multiple variable form of the Newton‐Raphson correction process to correct either the temperatures or the flow rates when only energy balance errors are used. Similar equations for material balance errors which have been developed previously are then combined with the energy balance equations to provide a method for simultaneous correction of the temperatures and the flow rates. Because first‐order interactions between flow rates and temperatures are included the method is applicable to a wide range of equilibrium stage problems. Sample problems are presented, and it is shown that quadratic convergence is obtained for the simultaneous correction process.
Area‐free mass transfer coefficients for liquid extraction in a continuously worked mixer
Authors: Keey R. B. , Glen J. B.
Published: June 2004

No Abstracts.
On integration of the coexistence equation for binary vapor‐liquid equilibrium
Authors: Van Ness H. C.
Published: June 2004

Numerical integration of the coexistence equation for isothermal P‐x data can be carried out by standard techniques. Two questions are considered with respect to this procedure: (a) Do continuous, analytic P‐x relations exist which fail to provide thermodynamically acceptable results? (b) Does it matter from what point one starts the numerical integration? It is the purpose of this paper to demonstrate in each case that the answer is affirmative.
Fixed bed adsorption drying
Authors: Chi C. W. , Wasan D. T.
Published: June 2004

In this paper, mathematical models for a single adsorbate component present in a gas phase have been developed for isothermal and adiabatic dynamic adsorption‐desorption processes with special emphasis on adsorption drying by supported hygroscopic salts. The proposed generalized models are applicable to both an unsupported absorbent bed and a fixed bed of adsorbents impregnated on a supporter which may have nonlinear equilibrium relationships. The partial differential equations governing the dynamic adsorption‐desorption processes and the nonlinear equilibrium relations were solved numerically on the digital computer.

An experimental study was conducted to measure the adsorption and desorption rates of water vapor by lithium chloride impregnated on a solid supporter, Torvex.

The proposed adiabatic adsorption‐desorption model has been verified for unsupported adsorbent beds in the cases of water vapor adsorption from air by silica gel and of methane adsorption from a helium‐methane mixture by activated carbon. The validity of the generalized adiabatic model for supported adsorbent beds with nonlinear equilibrium relationships was established by a direct comparison of experimental data obtained in this study with the predicted values.
Numerical evaluation of temperature profiles and interface position in filaments undergoing solidification
Authors: Morrison Milton E.
Published: June 2004

A numerical method has been described for the solution of the general equations which depict solidification in the cylindrical coordinate system. The method has been outlined for cooling and solidification of a moving filament of molten polymer. The solution is given in terms of six dimensionless variables: αl/αs,kl/ks,hR/kR,L/[Cps(To−Tc)],To/Tc, and σϵpR(To−Tc)3/kR. Plots are shown for the solution of the heat transfer equations and associated boundary conditions for several values of the dimensionless variables. The method describes the process of cooling and freezing liquids when convective and/or radiative energy losses are considered. The form of the theoretical equation compares very favorably with experimental data.
Evaporation rates of volatile liquids in a laminar flow system: Part I. Pure liquids
Authors: Clark Michael W. , King C. Judson
Published: June 2004

Normal pentane and isopentane were evaporated into nitrogen in laminar, concurrent flow in a rectangular channel. Composition profiles within the gas phase were measured, and the evaporation rates were compared with theoretical predictions with satisfactory agreement. The interfacial mole fraction of the evaporating species in the gas phase ranged as high as 0.74. A solution is reported for the Leveque problem under high flux conditions.
Mass transfer in a nonuniform impinging jet: Part II. Boundary layer flow‐mass transfer
Authors: Scholtz M. T. , Trass Olev
Published: June 2004

Exact solutions of the boundary layer equations were used to calculate the local mass transfer coefficients for an impinging jet with a parabolic velocity distribution. Boundary conditions were obtained from an inviscid flow solution and also from experimental pressure distributions. Experimental data for the air/naphthalene system were in good agreement with theoretical results. Mass transfer from the impingement surface was independent of nozzle height in the range 0.5 to 12 nozzle radii. For lower nozzle heights the effect of the constriction of flow between the nozzle and the surface led to increased transfer rates near the nozzle wall; data followed the predicted behavior.
Vapor‐liquid equilibria and dielectric constants for the helium‐carbon dioxide system
Authors: Burfield Diana W. , Richardson H. P. , Guereca R. A.
Published: June 2004

Phase equilibria data are presented for the helium‐carbon dioxide system at 253°, 273°, and 293°K. and pressures to 139 atm. Equilibrium is established under flow followed by nonflow conditions, and liquid and vapor samples are isolated without disturbing equilibrium. Liquid‐and vapor‐phase compositions are monitored with miniaturized capacitors, and compressibility factors are computed from resulting dielectric constants. The data are internally consistent and compare favorably with available literature values.
Thermocapillary flow around hemispherical bubble
Authors: Larkin Bert K.
Published: June 2004

A hemispherical bubble, attached to a plate, is surrounded by an initially quiescent and isothermal liquid. By suddenly heating the plate, a thermal gradient over the bubble surface results. Because surface tension is temperature dependent, tangential stresses arise at the bubble surface. The liquid is viscous, and motion in the liquid phase begins. Such motion is an example of thermocapillary flow. This problem, besides being of interest from a fundamental point of view, is of possible concern in the design of space vehicles capable of storing cryogenic fluids for long periods of time in a weightless condition.

Solutions to the problem are developed by numerical treatment of the governing equations. Flow and temperature fields, which depend upon the Prandtl and Marangoni numbers, were obtained for Prandtl numbers 1 and 5 and Marangoni numbers from 0 to 100,000.

Results show that liquid is pulled toward the intersection of the bubble and the plate, then flows around the bubble surface, and leaves the bubble as a jet. The extent of the jet increases with increasing Marangoni number and decreases with increasing Prandtl number.

Thermocapillary flow increases heat transfer (Nusselt number) over that obtained from conduction, but the increase is modest. The Nusselt number increases with the Marangoni number and is insensitive to the Prandtl number. At a Marangoni number of 40,000, the local Nusselt number was increased by a factor of 2. In order for thermocapillary flow to become a dominant heat transfer mechanism, the Marangoni number must exceed 100,000.
Correlation and prediction of vapor‐liquid equilibria with the redlich‐kwong equation of state
Authors: Zudkevitch David , Joffe Joseph
Published: June 2004

A modified Redlich‐Kwong equation has been applied to the calculation of phase equilibria in multicomponent systems. The two parameters of the Redlich‐Kwong equation are treated as temperature functions. They are obtained for each pure component from experimental vapor pressures and liquid densities with the help of a generalized fugacity coefficient correlation for saturated vapors. The need to submit coefficients for pure components is thus eliminated. At least one experimental vapor‐liquid equilibrium point is required to establish an interaction constant for each binary system. Applications have been made to binary and multicomponent systems containing hydrocarbons, hydrogen, carbon dioxide, and hydrogen sulfide.
Bubble coalescence in fluidized beds
Authors: Lin S. P.
Published: June 2004

The two‐dimensional motion of two circular bubbles moving in train up through a fluidized bed is considered. By using continuum equations of motion for this two‐phase flow situation, neutral coalescence curves are obtained which indicate, for given bubble radii and distance apart, whether or not the bubbles will coalesce. The conclusions are in agreement with the available experimental results.
An experimental study of oscillating reactors
Authors: Baccaro G. P. , Gaitonde N. Y. , Douglas J. M.
Published: June 2004

The hydrolysis of acetyl chloride was studied in a laboratory reactor designed to act as a chemical oscillator. The observed oscillating outputs are in fairly good agreement with the numerical solutions of the stirred tank reactor equations and the approximate analytical solutions published previously.
Entrance region flow of the Bingham fluid in a circular pipe
Authors: Chen S. S. , Fan L. T. , Hwang C. L.
Published: June 2004

The laminar, isothermal entrance region flow of the Bingham fluid in a circular pipe is studied at first by using the momentum integral method and the boundary‐layer equation for the Bingham fluid. In addition to the velocity boundary layer, the existence of the shear stress boundary layer is considered. The solution is valid only near the entry because of limitation of the boundary‐layer model. The Campbell‐Slattery method originally devised for the Newtonian fluid is also used to analyze the Bingham entrance region flow. The results are compared with those obtained through the use of the momentum integral method and those obtained through the use of the variational method by other investigators. While the results obtained in this work appear to be generally reasonable and valid, the results by the other investigators have been found to be somewhat erroneous.
Viscosity of nonpolar gaseous mixtures at normal pressures
Authors: Yoonm Poong , Thodos George
Published: June 2004

The relationship between μ*ξ and TR for nonpolar gases at normal pressures is used to predict the viscosity for their mixtures. For such mixtures, pseudocritical temperatures are used to obtain TR. To establish ξm for a mixture, a binary interaction model has been applied that utilizes composition and the ξ values of the pure components.

Viscosities have been calculated for twenty binary systems which include helium and hydrogen. These calculated values produce an average deviation of 1.97% for 148 compositions. This method was also applied to the helium‐neon‐argon ternary system at 100°C. to obtain for four mixtures examined an average deviation of 2.2%.
Kinetics of the Hopcalite‐catalyzed oxidation of carbon monoxide
Authors: Brittan Michael I. , Bliss Harding , Walker Charles A.
Published: June 2004

The oxidation of carbon monoxide with Hopcalite catalyst was studied in an isothermal recycling reactor with special attention paid to the changes of gas phase compositions with time.

Conversion‐time data exhibit significant departures from first‐order behavior often ascribed to this reaction. In early stages the reaction rate declines more rapidly than would a first‐order reaction; later the reverse is true. A mechanism, based on careful analyses of the literature and of our observations, is proposed. A kinetic model based on this mechanism is shown to reproduce the data of any run satisfactorily, but there is a considerable variation in values of the constants from run to run.
Separation of gaseous mixtures by permeation through polyethylene film
Authors: Reilly J. W. , Henley E. J. , Staffin H. K.
Published: June 2004

The permeation of polyethylene film by carbon dioxide, ethane, and propane at elevated pressures was investigated. In addition, the separation of mixtues of ethane and propane by permeation was studied.

Both hydrocarbon vapors' permeation exhibited pressure dependence, with propane showing the greatest variation over the same range.

In the case of the mixture separation study, the achieved degree of separation was lower than would be predicted on the basis of the pure component permeation constants. Moreover, the total flow of vapor through the film was greater than would be expected on the basis of the individual gas flows. This was attributed to an anomalous diffusion phenomenon of ethane in the presence of dissolved propane due to a plasticization of the polymer network.
Transient creeping flow around spheres
Authors: Sy Francisco , Taunton J. W. , Lightfoot E. N.
Published: June 2004

An explicit description is given for the gravitationally induced motion of an initially stationary gas bubble under creeping flow conditions. Analysis has shown that such a solution is good for all values of the Weber number as long as the quadratic terms in velocity are negligible in the Navier‐Stokes equation. It was also determined that the description of transient flow around a sphere from potential flow theory agrees with the short‐time limit of the creeping flow equations as applied to a gas bubble and solid sphere.

The necessary steps to obtain a solution for the more general case of a spherical drop with appreciable density and viscosity is presented. Also, numerical comparison of the motion of a gas bubble and a weightless solid sphere shows that the times required to reach a given fraction of terminal velocity are nearly the same.
A model for the thixotropy of suspensions
Authors: Fredrickson A. G.
Published: June 2004

A model for the rheological behavior of thixotropic systems is presented. The model is intended for systems exhibiting no elastic or anisotropic effects. It is shown how the constants of the model can be determined by a systematic program of experimentation. It is also shown how the model can be tested and amended, if necessary, by the same program of experiments. The model is advanced for suspensions of rigid, solid particles in liquids; it is not expected to be valid for materials of polymeric constitution or for suspensions of elastic, deformable particles in liquids.
Statistical models for surface renewal in heat and mass transfer. Part IV: Wall to fluidized bed heat transfer coefficients
Authors: Koppel L. B. , Patel R. D. , Holmes J. T.
Published: June 2004

Heat transfer coefficients were measured for glass particles at the same wall surface of a fluidized bed for which glass particle residence times were measured in a previous study. The data compared well with theoretical predictions of the dependence of heat transfer coefficients on particle residence times. Heat transfer coefficients for metal particle systems, for which direct measurements of residence times were not available, were predicted with fair accuracy by estimating residence times from a dimensionless correlation proposed in a previous study. The ability of the particle surface renewal models to accurately predict heat transfer coefficients is strong evidence of their physical validity.
An eddy cell model of mass transfer into the surface of a turbulent liquid
Authors: Lamont John C. , Scott D. S.
Published: June 2004

Experimental gas absorption studies for bubbles transported in turbulent pipe flow of water strongly indicate that liquid phase controlled mass transfer is due to surface renewal by turbulent eddies. Predictions of transport behavior from the conditions of turbulent flow cannot be made in support of this mechanism because no satisfactory theory of turbulent transport near a gas‐liquid interface is available. This work considers a model of the hydrodynamic behavior near the surface which provides a link between the observed mass transfer behavior and the state of the turbulent field.

In this model, the very small scales of turbulent motion are considered to be controlling. These motions are idealized, and their flow and mass transfer behavior are solved analytically. The overall result for eddies of various sizes is related to the turbulent energy spectrum by using only the easily accessible parameter ϵ, the energy dissipation rate. This model gives quantitative agreement to within a factor of 2 for three widely different experimental situations including gas‐liquid and liquid‐solid interfaces. However, the predicted Reynolds number dependence is somewhat higher than the experimental result.

The model attempts to clearly define the basic physical process at the interface. Therefore, it indicates the direction for further experimentation needed to clarify the basic relationship between the mass transfer rates in the liquid phase and the hydrodynamic behavior of the turbulent liquid.
Heat transfer to cylinders in a confined jet at high temperature
Authors: Chevalier P. H. , Kubanek G. R. , Gauvin W. H.
Published: June 2004

Temperature and velocity measurements were carried out at the center of the test section of an 8‐in. I.D. cylindrical graphite chamber in a confined nitrogen jet issuing from a 40‐kw. D.C. plasma torch. The test section was located 10.5 in. below the torch nozzle, and temperatures and velocities up to 4,300°F. and 120 ft./sec. were obtained.

The overall rates of heat transfer by forced convection were measured to water cooled circular and square cylinders in two orientations. Results indicated that, owing to the high level of turbulence of the jet, turbulent boundary layers prevailed in the low range of Reynolds numbers investigated. Correlations are presented in terms of the Nusselt, Reynolds, and Prandtl numbers, with the physical properties of the gas evaluated at the bulk temperature.
Sucrose inversion by partially deactivated ion exchange resin beds
Authors: McGovern Terence J. , Dranoff Joshua S.
Published: June 2004

The inversion of sucrose by partially deactivated ion exchange resin catalysts has been studied in a fixed bed reactor under conditions where intraparticle diffusion of sucrose is slow. Results show that the reaction remains apparently first order for deactivated catalyst. Activity is directly related to hydrogen content of the resin and is also dependent on the nature of the ion used to poison the catalyst.
Motion of liquid drops in non‐Newtonian systems
Authors: Marrucci Giuseppe , Apuzzo Gennaro , Astarita Gianni
Published: June 2004

Predictive equations for terminal velocities of liquid drops in Newtonian and non‐Newtonian systems are reviewed. The wave theory analogy is extended to include liquid‐liquid systems. Experimental data obtained with seven different systems are presented. The agreement with predictive equations is satisfactory. Interface rigidity was observed in all the systems investigated.
The calculation of the critical locus curve of a binary hydrocarbon system
Authors: Hissong Douglas W. , Kay Webster B.
Published: June 2004

A method of calculating the critical properties of binary hydrocarbon systems is presented which is based upon the rigorous thermodynamic equations for the critical point of a binary mixture. By using these equations together with an equation of state, a completely analytical procedure was developed with the aid of a digital computer. The Redlich‐Kwong and the Dieterici equations of state were chosen for study. The Redlich‐Kwong equation was found superior for predicting critical pressures and temperatures by this method, although the Dieterici equation was better for critical volumes. The two interaction parameters arising from the equation of state were calculated from combining rules or from available experimental critical data on binary systems. To facilitate the latter approach, a mathematical optimization routine was used to find the best values of the interaction parameters for twenty‐one binary hydrocarbon systems for which critical data were experimentally determined. The optimum values of the interaction parameters were correlated as functions of the ratio of molecular weights of the components. These correlations enable one to predict quite precisely the critical properties of the binary systems from the pure component data alone.
Experimental and computational studies of the dynamics of a fixed bed chemical reactor
Authors: Sinai José , Foss A. S.
Published: June 2004

Experimental measurements of the temperature response of a fixed bed reactor to sinusoidal disturbances in the feed concentration, temperature, and flow rate show that a simple one‐dimensional mathematical model with distributed thermal capacitance satisfactorily describes the dynamic behavior of the reactor for modest excursions about an operating point. The reaction considered is a liquid‐phase exothermic reaction whose rate depends on the concentration of two reactants and the temperature.

A computational analysis reveals that the amplitude and phase of the traveling concentration and temperature waves are influenced in a complex manner by the interaction between the two waves. The interaction, which is treated here as interference between traveling waves, is made complex by the difference in the rates of propagation of the temperature and concentration waves and by the variation of their speeds throughout the bed.
Some mathematical characteristics of menisci and their use in determination of surface tension
Authors: Biery J. C.
Published: June 2004

By expressing the meniscus height and the sine of the angle between the horizontal and a tangent to the meniscus curve as simple exponential functions of radial position, a new calculational procedure for determining surface tensions from menisci has been developed. These simple functions, when combined with the Laplace‐Young equation, generated three useful equations for calculating surface tensions as a function of radial positions. The overall procedure by using the three equations and five smoothing methods was tested on both experimental and calculated menisci. The results from the procedure for the calculated menisci agreed within 1.5% with the original surface tensions used to generate the meniscus. The agreement of values generated with the method and the comparison method previously reported for experimental menisci was within ±8% in general and within ±2% for the best formed menisci.
Spray quenching
Authors: Laskowski Jan J. , Ranz William E.
Published: June 2004

A study was made of spray quenching by high velocity gas atomization. A mathematical model of both high and low temperature spray quenching was developed. Data were taken for proving and validity of the model.

Experiments were performed on a vertical downward flow of air‐water in a 1.0 in. diameter tube. Injection was by either of two modes. The first was a set of six peripheral liquid jets projecting water perpendicularly into the high velocity airstream. The second mode of liquid injection was by means of a 360° peripheral, annular slot, which laid down a continuous wall film at the point of injection. Air velocities of 430 and 200 ft./sec. and liquid injection rates of from 150 to 1,200 ml./min. were studied. The following physical quantities were measured: liquid fluxes, wall film flow rates, drop size distributions, and median drop size. An attempt was made to measure gas temperature in a dense spray by using two different types of temperature probes, but only liquid temperatures could be detected. A comparison of data with published data and correlations was made.

The best quenching conditions obtained were a liquid‐to‐gas mass ratio of 0.25, a Sauter mean drop diameter of 45 μ, and an indicated characteristic quench time of 10−3 sec.
Recoverable shear measurements in a parallel plate rheometerz
Authors: Fruh S. M. , Rodriguez Ferdinand
Published: June 2004

A parallel plate rheometer has been devised which permits measurements of shear stresses of 102 to 105 dynes/sq.cm. and shear rates of 10−5 to 1 sec.−1. A linear, air lubricated bearing is used to align the apparatus, and a linear variable differential transformer is used to sense changes in position. With a sample of polyisobutylene and with several samples of poly(dimethyl siloxane), it has been established that a Hookean range exists for each sample at low stresses. Hooke's law in shear states that the modulus is independent of stress, where the modulus is defined as the ratio of the shear stress in steady, creeping flow to the strain which can be recovered after the stress is removed. Other conclusions supported by the present work are that the Hookean range does not extend to stresses which are high enough to cause non‐Newtonian flow, that the modulus decreases with increasing molecular weight although not in direct proportion, and that a sample with a broad molecular weight distribution has a lower modulus than one with a narrow distribution.
Concentration fluctuations and chemical conversion associated with mixing in some turbulent flows
Authors: Torrest Robert S. , Ranz William E.
Published: June 2004

Microconductivity probes were used for the measurement of point values of mean concentrations and root‐mean‐square concentration fluctuations for mixing of salt solutions in turbulent shear flows. Mixing studies covered a range of flow conditions, with Reynolds numbers on the order of 104, and included ducted turbulent jets, dispersion in turbulent pipe flow, a plane mixing zone, and several multiple injection systems. The test sections all had characteristic dimensions of about 2 cm. The results for mixing experiments are compared with available previous work. Lack of resolution for root‐mean‐square concentration fluctuations in some previous work is indicated.

Reaction product concentrations for a rapid, second‐order, irreversible reaction in multiple injection systems, the plane jet, and the mixing zone were also obtained. The relation between conversion in reaction experiments and fluctuation level and decay in the equivalent mixing experiments is illustrated.
A modified Redlich‐Kwong equation for supercritical helium and hydrogen
Authors: Vogl Walter F. , Hall Kenneth R.
Published: June 2004

A modified Redlich‐Kwong equation of state is developed in which the two parameters are expressed as functions of temperature. The critical values for the two constants in the equation are completely determined by the values of the critical properties of the gas. The optimum values of the constants for each isotherm (Z vs. P) are found, followed by a curve‐fitting routine that obtains the constants as functions of temperature. The resulting equation of state predicts experimental helium compressibility data to within an average of 0.90% absolute error for data in the range 0 < pressure ⩽ 700 atm., 5.26°K. ⩽ temperature ⩽ 1,500°K. For hydrogen, the prediction is to within an average of 0.79% absolute error for temperatures from 34° to 600°K. and pressures up to 2,900 atm.
A modified Redlich‐Kwong equation of state
Authors: Gray Ralph D. , Rent Nancy H. , Zudkevitch David
Published: June 2004

A new modification of the Redlich‐Kwong equation of state is presented. The modification follows the procedure suggested by Redlich, Ackerman, et al., in which a deviation function (a function of temperature, pressure, and acentric factor) is added to the compressibility factor from the original equation to improve the agreement with data. The purpose of the present modification was to improve predictions of the Redlich‐Kwong equation in the saturated vapor region up to the critical point while retaining a relatively simple form to make analytical relations for derived properties possible. The equation for pressure correction to vapor enthalpy, derived from the compressibility factor by standard thermodynamic procedures, is also presented. Comparisons of predicted vapor compressibility factors and vapor enthalpy pressure corrections with literature data are given, demonstrating the advantages of the proposed modification when the saturated vapor region is of principal interest.
Drop‐size distributions produced by turbulen pipe flow of immiscible liquids
Authors: Collins S. B. , Knudsen J. G.
Published: June 2004

Drop‐size distributions in turbulently flowing dispersion of immiscible liquids were investigated. The observed drop‐size distributions were actually a composite of two superimposed distributions. One is the distribution produced by the injection nozzle and the other is that produced by breakup in the turbulent flow field. A mathematical model was developed which predicted both the shape of the observed distributions and kinetics of the droplet breakup process for the distribution produced by the turbulent flow field.

The flowing dispersion composed of water and insoluble organic phase was photographed at 27, 209, 421, and 576 pipe diameters below the mixing jet and at distances of 0.05, 0.1, and 0.4 diam. from the wall. Average flow rates varied from 14 to 20 ft./sec. in the 0.750‐in. I.D. tube. Three organic phases were studied at concentrations ranging from 0.6 to 10% by volume. Dispersed phase viscosity and interfacial tension varied from 1 to 18 cp. and 13 to 40 dynes/cm.

No distribution law with any theoretical basis could be found which correlated experimental distributions.

The stochastic model describing the breakup process postulates that each breakup event leads to two daughter drops with uniformly distributed volume ratios and a very small satellite droplet. An empirical correlation exists to predict only one of the three parameters of the model.
Iterative methods for solving problems in multicomponent distillation at the steady state
Authors: Billingsley D. S. , Boynton G. W.
Published: June 2004

The multicomponent distillation problem is formulated so that unknown compositions do not appear explicitly either in the equilibrium and material balance equations or in the heat balance equations. Use of this formulation in absolute iteration as well as Newton‐Raphson iteration is discussed. Other types of staged separation processes may be similarly expressed.
Convective diffusion of heat in composite media with heat sources and sinks
Authors: Baker B. S. , Gidaspow Dimitri , Wasan D. T.
Published: June 2004

Convective diffusion of heat is a problem which arises in many areas. Since most thermal transport situations involve more than one material insulation, supports, etc., the treatment of composite regions is of interest. In certain systems, namely, those involving chemical or nuclear reactions, heat generation may be either localized or distributed. In this paper a general analytical treatment of this problem is made by using a double Fourier series technique involving an extended orthogonality concept. This treatment is then applied to the solutions of heat transfer situations arising in electrochemical energy conversion systems. Experimental temperature profiles are presented which test the theory.
Kinetics of ozone decomposition and reaction with organics in water
Authors: Hewes C. G. , Davison R. R.
Published: June 2004

The decomposition of ozone in water is found to be second order at pH 2 and 4 with the rate insensitive to pH. At pH 6 the reaction order is 3/2 to 2 and at pH 8 it is first order. Above pH 6 the rate increases rapidly with pH. Ozonation can greatly reduce the organic matter in waste water. The reaction rate of ozone with organics in flocculated secondary sewage effluent is found to depend on the rate of ozone decomposition, which is independent of the subsequent reaction with the organics.
Peak‐time method for measuring thermal diffusivity of small solid specimens
Authors: Harmathy T. Z.
Published: June 2004

A simple test method is developed for determining the thermal diffusivity of solids and granular materials by measuring the time at which the peak on a temperature‐time record occurs. It allows the use of small easily prepared specimens and specimens of irregular shape (for example, stones). The tests can be performed at room temperature as well as at high temperatures, and can be repeated in short time intervals.
Second virial coefficients of polar fluids and mixtures
Authors: Halm Roland L. , Stiel Leonard I.
Published: June 2004

Relationships have been developed for the calculation of second virial coefficients of polar fluids from the critical constants, acentric factor w, and fourth parameter x of the substance. Coefficients for the expansion of the reduced second virial coefficient in w and x are presented for 0.64 ≤TR ≤ 0.94. Comparisons with available experimental data indicate that good results are obtained by the method of this study for most polar fluids. The second virial coefficient for water is found to exhibit anomalous behavior. Procedures have also been established for extending the relationships for pure fluids to the second virial coefficient of mixtures containing nonpolar or polar components.
Diffusion in sodium mordenite
Authors: Satterfield Charles N. , Margetts William G.
Published: June 2004

The rates of diffusion of CH4, nC4H10, iso‐C4H10, and C4F10 into well‐characterized single crystals of sodium mordenite were studied at 25°C to 100°C., using a rapidly responding constant‐volume system. The diffusion coefficients are of the order of 10−8 to 10−9 sq. cm/sec. and exhibit a maximum value with time, probably due to an initial temperature increase caused by the heat of sorption. The implications to catalysis of these and other studies of diffusion in zeolites are discussed.
Entry region mass transfer in turbulent pipe flow
Authors: Wasan D. T. , Jones W. O. , Von Behren G. L.
Published: June 2004

A general treatment is presented for mass transfer in turbulent pipe flow with special emphasis on the mass transfer entry region and the role of interfacial velocity on the rate of mass transfer. This study includes numerical solutions of the convective diffusion equation with an entering fully developed flow. Solutions for constant properties and a constant wall boundary condition are presented over a wide range of Reynolds numbers, Schmidt numbers, and aspect ratios.

An expression was developed for predicting the entry region mass transfer coefficient in both gaseous and liquid systems at ordinary fluxes with negligible interfacial velocities and at small aspect ratios. The proposed equation for a binary system is

Experimental concentration profiles have been reported on the vaporization of acetone into a turbulent air stream within a short cylindrical test section. Data are also reported on concentration measurements in an air‐carbon dioxide gaseous mixture with a large interfacial velocity at the inner surface of a porous pipe test section.

The numerical solutions of the diffusion convection equation have been compared with the experimental data in the mass transfer entry region, and a pronounced effect of the interfacial velocity on the mass transfer coefficient was found.
Phase equilibria in the methane‐ethane‐propane‐n‐pentane‐n‐hexane‐n‐decane system
Authors: Vairogs Juris , Klekers A. J. , Edmister W. C.
Published: June 2004

An experimental facility for vapor‐liquid equilibrium measurements at high pressures (100 to 15,000 lb./sq. in. abs.) and ordinary temperatures (100° to 300°F.) on multicomponent mixtures is described. The vapor‐liquid phase behavior of a six‐component hydrocarbon mixture, which simulated a natural gas and a condensate, was studied with this apparatus. Measurements were made at 150° and 250°F. and pressures ranging from 100 lb./sq. in. abs. to the single‐phase pressures for these systems and temperatures.
Transfer of surface‐active agents across a liquid‐liquid interface
Authors: England Dennis C. , Berg John C.
Published: June 2004

Analytical solutions are obtained for the transfer of an adsorbing solute across a liquid‐liquid interface taking into account the effects of molecular diffusion in both bulk phases, adsorptive accumulation at the interface, and energy barriers to adsorption and/or desorption. These solutions show that while adsorptive accumulation alone affects the transfer rate but little, the presence of an adsorption or desorption barrier can significantly affect the bulk concentration profiles and decrease the mass transfer rate. The presence of a desorption barrier is shown to cause the dynamic interfacial tension to pass through a minimum below the steady state value. For some systems it is conceivable that the interfacial tension minimum would be sufficiently low that a slight agitation would result in spontaneous emulsification.

Dynamic interfacial tension data for oil‐water systems with interface ages from 0.05 to 1.5 sec. are obtained using a laminar contracting liquid jet. The data indicate the presence of a small net desorption barrier to the transfer of normal and isobutyric acids from oil to water and large barriers to both the adsorption and desorption of 1,5 pentanediol.
Separation of nitrogen and methane via periodic adsorption
Authors: Turnock Philip H. , Kadlec Robert H.
Published: June 2004

The periodic process utilizes a rapid pressure swing cycle in an adsorbent bed to effect the separation of gas mixtures. During the first portion of a cycle the compressed gas mixture flows into the adsorbent‐filled column. Next, while the feed gas is restrained, an exhaust orifice is opened at the feed end of the column providing depressurization. The product stream is enriched in the component exhibiting the lowest coefficient of adsorption.

A mathematical model based upon the assumption of instantaneous equilibrium between the gas phase and the adsorbed gas was formulated and solved to simulate the periodic, adsorption process. The measured nitrogen content of the product gas stream was found to correlate with the ratio of the product gas rate to the feed gas rate.

At 24°C. the calculated pressure response, feed gas flow rate, and product gas composition correspond favorably with related experimental measurements for all values of the feed gas pressure, cycling frequency, and product gas flow rate within the ranges investigated.
Computation of near‐optimal control policies by trajectory approximation: Hyperbolic‐distributed parameter systems with space‐independent controls
Authors: Parkin Elliot S. , Zahradnik R. L.
Published: June 2004

Trajectory approximations have been used to compute near‐optimal control policies for a number of lumped‐parameter systems. In this paper the technique is generalized to distributed‐parameter systems. The essence of the method is the approximation of the state and adjoint variables of the problem by a linear combination of spatially dependent trial functions and time‐dependent mixing coefficients. Application of the method of weighted residuals to the spatial variations reduces the problem to one involving a system of ordinary differential equations for the mixing coefficients.

Results are presented of an application of the algorithm to the determination of nearoptimal control policies for a tubular plug‐flow heat exchanger with uniform wall flux forcing. The results compare favorably with the optimal solutions and indicate that the method could be of considerable value in implementing optimal control for a wide class of systems.
Vapor‐liquid and liquid‐liquid vapor phase behavior of the carbon monoxide‐propane and the carbon monoxide‐ethane systems
Authors: Trust D. B. , Kurata Fred
Published: June 2004

Low‐temperature vapor‐liquid phase data are reported for the carbon monoxide‐propane and the carbon monoxide‐ethane systems. The data for the carbon monoxide‐propane system are reported at eight temperatures ranging from −125°C to +50°C., with pressure up to 2,000 lb./sq. in. abs., those for the carbon monoxide‐ethane system are reported at four temperatures from −100°C to 0°C., with pressures ranging up to the critical locus. Liquid phase immiscibility was observed at low temperatures in both the carbon monoxide‐ethane and the carbon monoxide‐propane systems. The pressure‐temperature loci for these two systems in liquid‐liquid vapor equilibrium were determined.
Molecular thermodynamics of gases in mixed solvents
Authors: O'connell J. P.
Published: June 2004

The general thermodynamic relation between Henry's constant for a solute in a mixed solvent and Henry's constants for the solute in the pure solvents is discussed in terms of limiting activity coefficients. The inadequacy of several common excess free energy expressions is shown, and results are presented for a form of Kirkwood‐Buff solution theory based on pair distribution functions. Several unknown integrals in the theory are approximated by an empirical function of solvent composition and of solvent properties which generally predicts experimental data for gases in both simple and complex binary solvents with good accuracy. Prediction of fugacities of gaseous components in ternary and higher solvents and in nonideal solutions is considered.
Radiation‐induced polymerizations in continuous stirred‐tank reactors
Authors: Chen H. T. , Hill F. B.
Published: June 2004

A theoretical study of the performance characteristics of continuous stirred‐tank reactors when used to conduct radiation‐induced polymerizations is presented. The effects on conversion and molecular weight distribution of the interaction of radiation attenuation, chemical kinetics, and mixing are examined for initiation by ultraviolet light and by Co60 gamma radiation.