bluuebunny/crossref_metadata_2025 huggingface dataset:
Effects of mixing on chain reactions in isothermal photoreactors
Authors: Hill Frank B. , Felder Richard M.
Published: June 2004

An analytical study of the interaction of mixing, radiation attenuation, and chemical kinetics in isothermal photoreactors is presented. For a particular chain reaction mechanism in the presence of stationary state kinetics and low conversion, the conditions required for the existence of mixing effects are formally stated, and the direction of change of conversion and quantum yield resulting from the introduction of mixing is established. Calculated results are presented for monoenergetic, unidirectional sources. Factors considered include mode of chain termination, radiation attenuation law, photoreactor geometry, state of mixing, and reactor optical thickness. Chemical and mixing time scale considerations are discussed.
An application of adaptive control to a continuous stirred tank reactor
Authors: Crandall Edward D. , Stevens William F.
Published: June 2004

This paper reports on an investigation of the effect of adaptive control on a closed‐loop chemical plant. The plant controlled was a simple closed‐loop feedback system, the elements of which were a proportional controller and an elementary continuous stirred‐tank reactor. The reaction involved was an exothermic, single‐reactant decomposition, with the control criterion being the integral of the square of the deviation of the output composition from a value determined by a reference model. The adaptive control system incorporated an automatic identification scheme and a decision process, and operated in the presence of disturbances in cooling water temperature and/or catalyst activity.

The adaptive control system yielded excellent results. For all disturbances, the output of the adaptive controlled plant remained much closer to the reference model output than did the output of the simply controlled plant. Inclusion of an adaptive capability in a control system thus appears to be desirable and often feasible.
Experimental studies of three‐dimensional filtration on a circular leaf
Authors: Leonard J. I. , Brenner Howard
Published: June 2004

A previous study (3) revealed a discrepancy between the actual shape of a spheroidal filter cake formed on a laterally unconfined circular test leaf, and that predicted from theory. This discrepancy was tentatively attributed to either cake compressibility or filter cloth resistance that was neglected in the mathematical model and not controlled in the original experiments. More extensive and systematic experiments reported in the present paper, employing incompressible cakes and filter media of negligible resistance, display similar behavior. (Cake incompressibility and negligible septum resistance were quantitatively established by conventional one‐dimensional experiments.) It is speculated that the observed departure from theory may be due to the inapplicability of Darcy's law, especially in the early stages of cake formation.
On finite amplitude roll cell disturbances in a fluid layer subjected to heat and mass transfer
Authors: Sani R. L.
Published: June 2004

The system consists of a thin, transversely infinite horizontal fluid layer initially in mechanical but not thermostatic or speciestatic equilibrium. The top and bottom surfaces of the layer are assumed to be unconstrained, and the stability of the system to buoyancy driven finite amplitude roll cell disturbances is investigated. The system is capable of exhibiting both a subcritical stationary and oscillatory instability. The average vertical transport of heat and mass is computed and it is found that the convective transport associated with a stationary type of instability is much greater then that corresponding to an oscillatory instability.
Dimensional analysis in photochemical reactor design
Authors: Dolan William J. , Dimon Carl A. , Dranoff Joshua S.
Published: June 2004

The equations which describe the performance of a continuous tubular photochemical reator have been formulated and analyzed by dimensional analysis. Experimental data obtained in a study of the decomposition of hexachloroplatinic acid in water were correlated as suggested by the dimensional analysis, thus partially confirming the validity of the approach.
Diffusion through the liquid‐liquid interface: Part II. Interfacial resistance in three‐component systems
Authors: Ward W. J. , Quinn J. A.
Published: June 2004

In an investigation of the transfer of solute molecules across the liquid‐liquid interface, the transfer of acetic acid, benzoic acid, oleic acid, and cholesterol between benzene and water was measured. Experiments were carried out with a laminar jet apparatus wherein the organic phase was spread as a thin film on the surface of an aqueous jet. The results indicate that any interfacial resistance in these systems is negligibly small.
Stresses in a viscoelastic fluid in coverging and diverging flow
Authors: Adams E. B. , Whitehead J. C. , Bogue D. C.
Published: June 2004

Birefringent studies have been carried out on a viscoelastic fluid (polystyrene in Aroclor) flowing in straight, converging, and diverging channels, for the purpose of obtaining point‐by‐point stress data (the shear stress and the difference in normal stresses). A preliminary analysis in terms of the Coleman‐Noll second order theory for viscoelastic fluids shows good agreement.
Multicomponent vapor‐liquid equilibria at high pressures: Part I. Experimental study of the nitrogen—oxygen—carbon dioxide system at 0°C
Authors: Muirbrook N. K. , Prausnitz J. M.
Published: June 2004

A description is given of a dynamic vapor‐liquid equilibrium apparatus in which both phases are recirculated by vane pumps especially designed for high‐pressure service. Equilibrium phase compositions as well as vapor and liquid molar volumes up to the critical pressure are reported for the two binary systems nitrogen‐carbon dioxide and oxygen‐carbon dioxide and for the ternary.
The determination of eddy mass diffusivities for the air‐water system in a wetted‐wall column
Authors: Bunch David W. , Strunk Mailand R.
Published: June 2004

Eddy mass diffusivities as a function of radial position for different Reynolds numbers have been determined for air flowing countercurrently to water in a wetted‐wall column. The ratios of the eddy mass diffusivity to the eddy viscosity also were determined. The wetted‐wall column was constructed from Pyrex glass with an I.D. of 2.75 in. and a wetted section 39 in. in length. An approach section was constructed from the same material and of adequate length to insure full development of the velocity profile. The gas phase Reynolds numbers varied from 3,200 to 54,300. The liquid phase flow was laminar. The concentration and velocity profiles of the air stream were measured experimentally and bulk temperatures of all streams were obtained. A probe was developed to measure the concentration profiles. The probe consisted of platinum wires wrapped in a helix around a glass capillary tube on which a thin layer of lithium chloride in polyvinyl alcohol had been deposited. The resistance of the probe was a reliable indication of the water vapor concentration in the air stream. The probe was calibrated and used for all concentration measurements. Eddy mass diffusivities were evaluated from a solution of the steady state mass diffusion equation by means of a digital computer with experimental velocity and concentration profiles. Qualitatively, the eddy diffusivity profiles are similar to those which have been obtained for heat and momentum transfer. When these profiles are used with the diffusion expression, they are capable of accurate evaluation of the concentration profile. The ratio of the eddy mass diffusivity to the eddy viscosity was determined and was found to be less than 1.0 over most of the cross section, but the ratio increased to values greater than 1.0 near the center and near the walls of the column.
Axial dispersion of spheres fluidized with liquids
Authors: Kennedy S. C. , Bretton R. H.
Published: June 2004

Solids dispersion due to the simultaneous diffusion (random particle motion) and classification (segregation) of fluidized spheres has been investigated. The model developed permits calculation of the mean concentration of spheres of both sizes in a mixture of two sizes of fluidized spheres as a function of bed length. Fick's law has been applied to the diffusional phenomenon. A hypothesis has been advanced and confirmed which permits calculation [Equation (5)] of the classification velocity for each size of sphere in a fluidized mixture. Calculation of the classification velocities in a mixture of spheres is based on the relation of void fraction to superficial velocity for the individual sizes of spheres. To facilitate carrying out these calculations, a generalized equation has been developed for the relation of void fraction to superficial velocity in terms of the Galileo number (d3gΔρρƒ/μ2) and sphere‐to‐column diameter ratio. Measurement of the bead size gradients (change in bead size with bed length) at steady state fluidization was used to investigate dispersion. Closely sized glass beads of 0.1 and 0.2 cm. diameters were fluidized with liquids of 1 and 15 cps. at void fractions of 0.5 to 0.8 in 2.5 and 5.0 cm. columns. Lead beads of 0.12 cm. diameter were also used. Further, several experiments were conducted by a method which is analogous to that used in molecular diffusion cells.
The low temperature removal of small quantities of nitrogen or methane from hydrogen gas by physical adsorption on a synthetic zeolite
Authors: Kidnay Arthur J. , Hiza Michael J.
Published: June 2004

A flow system was used to measure the physical adsorption isotherms of two mixtures of nitrogen and hydrogen and two mixtures of methane and hydrogen on a synthetic zeolite. The measurements were made at liquid nitrogen temperature and at pressures of 4 to 85 atm. Static systems were used to measure the pure component isotherms of nitrogen, methane, and hydrogen at the same temperature and over the appropriate pressure ranges.

Although many different methods have been proposed for using pure component adsorption isotherms to predict the mixture isotherm, the only method giving quantitative agreement with the data of this study is the empirical “adsorption enhancement factor” (4).

In addition to the adsorption isotherms, the concentration‐time or breakthrough curves of the mixtures were measured at flow rates ranging from 40 to 300 lb./(hr.)(sq.ft.). The method proposed by Eagleton and Bliss (18) was used to correlate these curves.
Laminar converging flow of dilute polymer solutions in conical sections: Part I. Viscosity data, new viscosity model, tube flow solution
Authors: Sutterby J. L.
Published: June 2004

This investigation is reported in two parts. Necessary background information is introduced in Part I. The converging flow investigation proper is described in Part II (18).

In Part I, viscosity data are presented for polymer solutions used in the converging flow experiment. These data are fitted with a new three‐parameter viscosity model which fits the data better than previous three‐parameter models. (The viscosity model parameters are used in Part II to characterize rheological behavior of the polymer solutions in the converging flow experiment.) The corresponding relationship between flow rate and pressure drop for laminar flow in cylindrical tubes is derived. (In Part II this relationship is used in deriving an analogous relationship for slow non‐Newtonian flow in conical sections.)

The primary purpose of Part I is to provide background information for Part II. However, the new viscosity model and the tube flow relationship are of some interest in themselves. The new viscosity model should prove useful for describing viscosity data of a variety of polymer solutions and polymer melts. A simple procedure for fitting the model to viscosity data is described. The tube flow relationship can be used for predicting pressure losses once the viscosity model parameters have been determined. Conversely, it can be used for determining the viscosity model parameters from tube flow data.
Characterization and gain identification of time varying flow processes
Authors: Mellichamp D. A. , Coughanowr D. R. , Koppel L. B.
Published: June 2004

A method for continuously estimating the gain of a flow process by sinusoidal perturbation is presented. The resulting output perturbation is correlated with a second sinusoid to generate periodically an estimate of the process gain. A method of implementing such an identifier on a small analog computer is described.

The experimental testing of this identifier computer with both a real process (a pH regulating system) and with an analog computer simulation of the process is described. The results of identification tests with a nonstationary system are presented. From these results it is concluded that the identifier estimates the process gain satisfactorily, introducing a delay (equal to one‐half the period of identification) and making an effective sampling or clamping of the gain estimate (over each period of identification).
The influence of diffusivity on liquid phase mass transfer to the free interface in a stirred vessel
Authors: Kozinski Allen A. , King C. Judson
Published: June 2004

Liquid phase mass transfer coefficients were measured in a continuous flow, stirred vessel containing a gas and a liquid phase. Helium, hydrogen, oxygen, argon, and carbon dioxide were desorbed from distilled water into nitrogen at seven different levels of agitation. At low stirring speeds the system was stratified and mass transfer coefficients were proportional to diffusivity raised to a power between 0.5 and 0.6. At higher stirring speeds the interface was broken and corrections for desorption into the entrained bubbles indicated that the mass transfer coefficient at the main free interface was proportional to a higher power of diffusivity. The results are interpreted in the light of a general model considering eddy diffusion and surface renewal effects.
Mass transfer in a horizontal rotating cylinder with applications to the oxygenation of blood
Authors: Landino Enrique , McCreary J. G. , Thompson W. A. , Powers J. E.
Published: June 2004

The horizontal rotating cylinder blood oxygenator has been developed to minimize shear, eliminate bubbles, reduce holdup, and provide for rapid change of the controlled temperature of the blood.

To aid in the development of this apparatus a detailed mathematical model was formulated. A simplified model was also developed which yielded an analytical expression relating the amount of material transferred between the gas and liquid in the apparatus to operating variables. In developing these models an attempt was made to include a realistic mechanism for oxygen absorption in blood.

Preliminary experiments were carried out by absorbing carbon dioxide into distilled water in the horizontal rotating cylinder. These preliminary results were found to be in good agreement with previous theoretical predictions and calculations that indicated that the equipment should be adequate to act as a lung substitute for a dog. When it was employed in this manner during open‐heart surgery, insufficient oxygen was transferred to support the dog.

It is concluded that the most probable reason for failure of the horizontal cylinder to act satisfactorily as a blood oxygenator is poor mixing in the blood pool.
The time‐optimal control of discrete‐time linear systems with bounded controls
Authors: Lesser Herbert A. , Lapidus Leon
Published: June 2004

The discrete‐time, time‐optimal control of high‐order, linear systems with bounded controls is formulated as a problem in linear programming. The solution obtained requires a certain minimum number of controls to be on their bounds. Numerical results are obtained for a system with controls bounded on one and both sides and extensions indicated for state variable constraints. The method proves to be extremely fast and simple to solve on a high‐speed digital computer.
Formation of interfacial area at high rates of gas flow through submerged orifices
Authors: Abdel‐Aal H. K. , Stiles G. B. , Holland C. D.
Published: June 2004

Interfacial area was formed by passing air through orifices that were submerged horizontally beneath 4.5 ft. of each of four different liquids. The flow rates of the air ranged from 0.095 to 1.34 (st. cu. ft./min.), the diameters of the orifices ranged from 0.03125 to 0.1875 in., and the I.D. of the orifice holders ranged from 1 to 2.5 in.

The areas were measured with a photocell, a recorder, and an integrator. This combination gave the time average of the interfacial area that passed a selected plane of the column.

The interfacial area produced was correlated as a function of the physical properties of the fluids, the diameter and number of orifices per plate, and the gas flow rate.
Heat transfer to non‐Newtonian fluids in transitional and turbulent flow
Authors: Petersen A. W. , Christiansen E. B.
Published: June 2004

Turbulent and transitional flow heat transfer correlations for non‐Newtonian fluids are presented. By means of an extension of the Reichardt‐Metzner‐Friend correlation to nonisothermal flow, and a new definition of Prandtl number to account for deviations from Newtonian behavior, turbulent flow data are correlated to a standard deviation of 14.8%. By means of a normalizing procedure, data for the complex case of transitional flow heat transfer to non‐Newtonian fluids are correlated to a standard deviation of 17.7%. At the transition region boundaries, the correlation is consistent with laminar and turbulent flow correlations. A basic similarity in the Newtonian and non‐Newtonian heat transfer mechanisms is suggested.
Free and forced convection in conduits with asymmetric mass transfer
Authors: Gill William N. , Casal Eduardo Del , Zeh Dale W.
Published: June 2004

Approximate solutions for the thermal entrance region and a new exact solution for the fully developed region have been obtained for nonlinear fully developed conduit flows with unsymmetrical transverse flow. Entrance region solutions are obtained by a generalized version of Mercer's method. The effects on combined free and forced convection of asymmetric mass transfer, in the asymptotic region of fully developed thermal and hydrodynamic conditions, are studied and a new exact solution is given which applies to such problems.
A theory of withdrawal of cylinders from liquid baths
Authors: White David A. , Tallmadge John A.
Published: June 2004

A theory of the amount of liquid entrained by cylinders upon withdrawal from liquid baths is derived for a wide range of cylinder radii. The theory is based on matching curvatures for static and dynamic menisci. Predicted values are expressed as the effect of the dimensionless wire radius (Goucher number) and dimensionless withdrawal speed (capillary number) on the dimensionless flux.

The theory was verified experimentally for all wire radii by removing short cylinders from oily fluids and with other information. The fluids used included kerosene, mineral oil, motor oil, and glycerine, with viscosities from 2 to 500 centipoise; Goucher numbers ranged from 0.05 to 1.2. Deviations, which were noted at high capillary numbers where velocity gradients become appreciable, indicated that the theory is a plug flow or low speed theory. Also discussed are differences found with water and the conditions under which films coalesced into droplets.
Bubble shapes in nucleate boiling
Authors: Johnson M. A. , De La Peña Javier , Mesler R. B.
Published: June 2004

An attempt is made to explain the differently shaped bubbles observed growing on a surface during nucleate boiling of water. Some of the bubbles photographed were very close to the spherical shape, while others were close to the hemispherical. Also, a number of bubbles had intermediate shapes and were called oblate bubbles.

Measurements of bubble dimensions and growth rates obtained from high‐speed films were analyzed. By using a modified Rayleigh equation, the relative importance of the inertial and surface tension forces was computed. it appeared that the differences in shapes among bubbles can be explained on the basis of the relative importance of these forces.

It was found that for spherical bubbles inertial forces are small because of the slow growth rate and surface tension is clearly the dominant force. For hemispherical bubbles, however, the fast growth rate causes a very large inertial force which is greater than surface tension. For the oblate bubbles neither of the forces was found to be dominate and inertia as well as surface tension determines the shape.
Application of the Gibbs‐Konovalow equations to binary phase equilibria
Authors: Franzen H. F. , Gerstein B. C.
Published: June 2004

The Gibbs‐Konovalow relations are shown to provide a unified approach to the description of binary two‐phase equilibria. The relations are applied to a consideration of high order transitions (7) and are shown to easily lead to well‐known, but generally uncorrelated, hehavior of slopes of lines separating two single‐phase regions in binary systems. In particular, the conditions under which the slope of the temperature‐composition line is zero, constant, or undefined in the neighborhood of congruent and peritectic

The meanings of these terms will be amplified in the text

processes are derived.
The P‐V‐X behavior of the liquid system acetone‐carbon disulfide at elevated pressures
Authors: Winnick Jack , Powers J. E.
Published: June 2004

The change in volume on mixing for a system showing large positive deviations from ideality is examined at one temperature to pressures of 100,000 lb./sq.in. Original atmospheric pressure density data and compression measurements over the entire mole fraction range for this system, acetone–carbon disulfide, are reported at 0°C. These are correlated with the semiempirical Tait equation to yield change in volume on mixing as a function of mole fraction and pressure.

This volume change is found to decrease from the maximum of 1 cc./mole at atmospheric pressure to about 0.4 cc./mole at 100,000 lb./sq.in. The maximum also shifts during this pressure increase from 0.53 mole fraction acetone to 0.74.
Liquid‐liquid phase behavior of binary solutions at elevated pressures
Authors: Winnick Jack , Powers J. E.
Published: June 2004

Isothermal pressure elevation can sometimes cause liquid‐liquid phase separation of binary liquid mixtures. A quantitative thermodynamic analysis of this effect is made and applied to the system acetone–carbon disulfide at 0°C. with the use of available P‐V‐T‐X data and vapor pressure data at low pressure. Visual observations of the phase separations at pressures up to 80,000 lb./sq.in. were used to compare with the results of the thermodynamic analysis.
An equation of state for gas mixtures
Authors: Othmer Donald F. , Chen Hung Tsung
Published: June 2004

A pressure‐volume‐temperature equation for mixtures of two or more gases has been developed using the “reference substance” technique of comparing the properties of one substance with those of a standard under the same conditions.

The compressibility factor is a function of temperature and pressure, with the variation from one substance to another being determined by the forces of attraction and repulsion between molecules. Thus, if the Lennard‐Jones 6‐12 potential function is used to describe the molecular interaction, the change in the compressiblity function reflects the different force constants, which in turn are functions of the critical constants.

A mixture of gases is assumed to have the same thermodynamic properties as some hypothetical or pseudo gas which would have the same force constants existing between each pair of molecules in the mixture. The force constants of the pseudo gas may be evaluated from pseudo critical constants, which may be evaluated from the critical constants of individual components of the mixture.

With the resultant force constants, there can be calculated the ratio of the compressibility factors of the gas mixture to those of a pure gas, nitrogen, taken as a reference substance, all values taken at the same reduced temperature and pressure. The compressibility factor of the mixture may be calculated from this ratio and the compressibility factor of the reference substance; and the PVT relations are immediately determinable.

A comprehensive survey of the literature for PVT data of gas mixtures was made. More than 1,000 experimental values of PVT data for thirty‐four binary systems and four ternary systems have been studied. The proposed method showed an average deviation from experimental data, representing all published work, of 2.3%.
Computational studies of transients in packed tubular chemical reactors
Authors: Crider J. E. , Foss A. S.
Published: June 2004

Concentration and temperature transients in a packed‐bed tubular chemical reactor were calculated from mathematical models in order to detemine the effects upon the reactor dynamics of several phenomena. The phenomena studied are the thermal capacity of the packing, the resistance to heat flow between the packing and the fluid, the coupling of temperature and concentration through the rate of chemical reaction, axial fluid mixing, radial fluid mixing, and the loss of heat at the wall. Three mathematical models were used: a two‐dimensional finite‐stage model, a one‐dimensional finite‐stage model, and a one‐dimensional first‐order differential model. The chemical reaction considered in these models was an exothermic, homogeneous, liquid phase, second‐order reaction.

Machine calculations of transients following step changes in feed temperature or concentration showed that only the first three phenomena were important. It was also found that concentration transients in some cases initially moved in the direction leading away from the final steady state or overshot the final steady state. Further, a concentration node point was found to exist in the reactor under some circumstances. The one‐dimensional models considered were shown to be simple but quantitatively and conceptually useful.
The influence of axial dispersion on carbon dioxide absorption tower performance
Authors: Brittan Michael I. , Woodburn Edward T.
Published: June 2004

Carbon dioxide was absorbed from mixtures with nitrogen by countercurrent contact with water in an experimental packed tower. Radial and axial gas concentration profiles were determined from measurements made within the packing. Substantial gas phase channeling was observed. Characterizing the gas flow regime by both piston flow and axial diffusion models yielded mass transfer data and computed axial gas concentration profiles. Differences between the mass transfer results for the two models allowed the influence of axial dispersion to be assessed. Comparison of the piston flow and axially dispersed profiles with the experimental profiles enabled conclusions to be drawn regarding the applicability of the axial diffusion model and the accuracy of available dispersion parameter values.

The axial diffusion model appears to be a satisfactory representation of the process. The dispersion coefficients used were found to be too high, which emphasizes shortcomings in the transient response experiments yielding dispersion coefficients. The influence of dispersion on the performance was found to be only moderately adverse. The effect increases with increasing liquid rate, decreasing gas rate, and decreasing packing height. It is improbable that the effect is large enough to account for the difference between industrial scale performance and that predicted from available mass transfer correlations.
Viscosity and thermal conductivity of nitrogen—n‐heptane and nitrogen—n‐octane mixtures
Authors: Carmichael L. T. , Sage B. H.
Published: June 2004

Measurements of the thermal conductivity and viscosity ofn‐heptane andn‐octane in the gas phase were made at temperatures of 100° and 160°F. and at pressures below 1 atm. In addition, measurements of the viscosity and thermal conductivity of binary gas mixtures of nitrogen andn‐heptane were made at 160°F. at pressures below 1 atm.
Bubble growth by dissolution: Influence of contact angle
Authors: Buehl W. M. , Westwater J. W.
Published: June 2004

The rate of growth of bubbles forming on a wall from a liquid initially uniformly supersaturated with a dissolved gas was investigated. Attention was directed to the effect of the contact angle.

Theoretical predictions for the growth rate of a spherical bubble tangent to a wall were carried out with a digital computer. The predictions included the diffusion equation and the continuity equation. The energy equation was neglected; viscosity and surface tension were assumed nil. The results are compared with existing predictions for a 90‐deg. contact angle. For extremely slow growth, the theoretical growth coefficient is about 30% smaller for a bubble with zero contact angle compared to one with a 90‐deg. contact angle. For fast growth the difference is much less.

Experimental growth rates were determined photographically for bubbles of carbon dioxide coming out of solution from water at an artifical nucleation site. Different contact angles from 15 to 89 deg. were obtained by coating the wall with various nonwetting agents. Every bubble showed changes in its contact angle during growth. No effect of contact angle on the growth rate could be detected.
Application of the Benedict‐Webb‐Rubin equation of state to argon
Authors: Zudkevitch David , Kaufmann Thomas G.
Published: June 2004

The coefficients of the Benedict‐Webb‐Rubin equation of state have been developed for argon. By employing these coefficients, the volumetric behavior of argon has been predicted with an average deviation of 0.241% for five hundred ninety‐seven smoothed and experimental data points in the superheated region.

At temperatures below the critical, two sets of Co's, one for the liquid and one for the vapor, were needed to relate the vapor pressure to the densities of saturated argon. However, consistent fugacities for the saturated vapor and liquid argon could not be predicted with these Co values. Therefore, another set of Co's was developed by equating the pure component vapor and liquid fugacities along the vapor pressure curve. These values were used to test the applicability of the equation of state to predict derived thermodynamic properties.

The original BWR expression for calculating isothermal pressure effects on enthalpy was modified to include explicitly the temperature dependence of the coefficient Co. Vapor‐liquid equilibrium relations for the argon‐nitrogen system predicted by the standard BWR procedure were compared with experimental data.
Local thermodynamic consistency of vapor‐liquid equilibrium data for binary and multicomponent systems
Authors: Stevenson F. D. , Sater V. E.
Published: June 2004

The Gibbs‐Duhem equation, integrated over specific concentration ranges, is used to determine local thermodynamic consistency of vapor‐liquid equilibrium data. Several specific applications of the test are given for binary systems, although the method is equally applicable to linear paths in multicomponent systems. The test is particularly useful for evaluating the consistency of incomplete data, that is, data measured over only part of the concentration range.
Skin friction of power law fluids in turbulent flow over a flat plate
Authors: McDonald A. T. , Brandt Harry
Published: June 2004

An analysis is presented for skin friction of power law fluids in turbulent flow over a flat plate. A momentum balance is combined with a logarithmic velocity profile and the resulting equation is integrated. Skin friction is shown to be a function of non‐Newtonian Reynolds number and power law shear rate exponent. Closed form solutions for viscous drag are obtained for some values of shear rate exponent, but in general a numerical integration is necessary.

The equations and curves presented are valid for any power law fluid. Computations may be carried out once the fluid viscosity and shear rate exponent are known. As an example, the results are applied to a power law fluid consisting of Carbopol in water. It is shown how viscous drag is affected by changes in the polymer concentration.
Film boiling of liquid nitrogen from porous surfaces with vapor suction: Experimental extensions
Authors: Pai V. K. , Bankoff S. G.
Published: June 2004

Previous work on film boiling of liquid nitrogen on flat horizontal porous surfaces with porous ceramic flow control elements is extended to tubular geometries and to very thin (asbestos paper) flow control members. At no loss in stability it is demonstrated that heat transfer coefficients more than five times greater than those in conventional film boiling can be obtained. An approximate model for a single liquid tongue breaking through the heating section at the critical flow rate is also presented. The upper (complete breakthrough) and lower (local breakthrough) limits on critical flow rate can be obtained theoretically. The experimental points lie between these two limits and, in general, are fairly close to the upper limit.
Response of a gas‐liquid interface to concentration pulses
Authors: Whitaker Stephen , Pigford R. L.
Published: June 2004

Frequency response techniques have been applied to the study of the absorption of sulfur dioxide in water contaminated with surface‐active material. The response of a 0.004‐in. thick liquid film to a sinusoidally varying sulfur dioxide pressure was determined for frequencies ranging from 1 to 10 cycles/sec.

The total quantity of sulfur dioxide dissolved was observed continuously by measuring the amount of light absorbed by the film, which contained a colored hydrogen ion indicator, cresol red. The experimental data indicate the presence of a surface phase of absorbed material through which sulfur dioxide molecules had to pass as they were transferred between gas and liquid. In addition to creating a resistance to the passage of the solute molecules, the surface phase apparently was capable of storing the molecules temporarily.
Continuous ion flotation of dichromate
Authors: Grieves Robert B. , Schwartz Stephen M.
Published: June 2004

An experimental investigation is presented of the continuous ion flotation of dichromate, with the use of a cationic surfactant, ethylhexadecyldimethylammonium bromide. The feed streams contain concentrations of dichromate (Cr2O72−) ranging from 10 to 100 mg./liter, and feed ratios of surfactant to dichromate from 2.5 to 6.0 (on a weight basis) are employed. The effects of feed concentration of dichromate, of feed concentration of surfactant, of liquid detention time, of air rate, and of feed into and above the foam phase are established. Results are presented in terms of the effluent concentrations of dichromate and surfactant, the ratios of effluent flow rate to feed flow rate, removal ratios, and enrichment ratios. For threecolumn series operation, predictions show that a feed stream containing 100 mg./liter dichromate may be separated (with approximately 400 mg./liter of surfactant) into an effluent steream containing 8 mg./liter of dichromate and a collapsed foam stream containing 468 mg./liter of dichromate.
Heat transfer to a subliming solid‐vapor mixture of hydrogen below its triple point
Authors: Jones M. C. , Nagamoto T. T. , Brennan J. A.
Published: June 2004

Heat transfer coefficients have been measured over a range of Reynolds numbers for a solid‐vapor mixture of parahydrogen discharging through a heated brass tube below the triple point pressure. A correlation is given which is shown by a formal analysis of a simple model to account for most of the system variables.
Interfacial tensions of binary and ternary two‐phase liquid systems
Authors: Pliskin Irwin , Treybal Robert E.
Published: June 2004

A theory is developed to enable prediction of interfacial tension in unsymmetrical, regular, binary liquid systems from solubility data. This is also shown to be applicable to nonregular aqueous binary systems by using solubility parameters and molar volumes calculated from mutual solubilities as substitutes for true molar volumes and the solubility parameters obtained from energies of vaporization.

The theory is extended to include unsymmetrical, regular, ternary liquid systems, and is shown to be applicable to systems consisting of perfluoro‐n‐hexane and other nonpolar organic liquids. The theory is not adequate for aqueous ternary systems.
Optimality and computational feasibility in transient control: Part I. A modified criterion for optimality
Authors: Paradis W. O. , Perlmutter D. D.
Published: June 2004

The notion of optimality with regard to transient control is critically examined with a particular view toward the computational difficulties of solving the optimal control problem, and the arbitrary aspects of the usual objective functions. Realizing a need for effective approximations, a criterion for transient control is developed which requires a minimum of computational effort to apply in practice. Optimality is achieved in an instantaneous sense, and it is argued that overall optimality is well approximated for many cases of practical interest. To demonstrate its use, the criterion is applied to the transient control of a stirred‐tank reactor. Numerical examples are given and the results are discussed and compared with those obtained by alternative methods.
Measurement of phase equilibria at high pressures by tracer‐pulse chromatography
Authors: Peterson D. L. , Helfferich Friedrich , Carr Robert J.
Published: June 2004

Tracer‐pulse chromatography allows the accurate measurement of sorption isotherms even at elevated pressures and in systems with more than one solute. Vapor equilibria of normally liquid solutes are best measured by scintillation counting of a liquid in which the column effluent and the emergent radioactive pulse are absorbed. An example is the equilibrium adsorption of n‐heptane by molecular sieves at 200°C. and at pressures up to 3 atm. Sorption equilibria of permanent gases are measured by use of a more conventional differential technique wherein the column effluent passes through an ion chamber. Its use is illustrated by the equilibrium adsorption of methane by activated charcoal at pressures up to 70 atm.
Hydrodynamics of rivulet flow
Authors: Towell G. D. , Rothfeld L. B.
Published: June 2004

A theoretical analysis of the hydrodynamics of liquid rivulets flowing down an inclined surface is presented. Steady state solutions are developed for the laminar flow case which relate the flow rate to the rivulet width, the physical properties of the liquid, and the contact angle. Excellent verification of the theoretical predictions was obtained in a number of experiments with various liquids on an inclined glass plate. All constants in the equations were derived from theory. These results will be useful in obtaining a better understanding and correlation of such phenomena as liquid flow over packings and catalysts and flow along walls and tube surfaces, as in condensation and evaporation.
Slip velocity of particulate solids in vertical tubes
Authors: Jones Jennings H. , Braun Walter G. , Daubert Thomas E. , Donald Allendorf H.
Published: June 2004

An equation using only easily determined physical properties of particles has been developed for calculating the slip velocity of nonspherical particulate solids falling in fluid media in the intermediate flow range where neither the Stokes nor Newton law applies. The variation in Reynolds numbers covered by this work ranged from 12 to 460. Slip velocities calculated from the equation differed from experimental data by an average deviation of only 3.7% when solids of a wide range of diameters (156 to 1,247 microns), densities (71 to 475 lb./cu. ft.), surface shape factors (0.40 to 0.97), and gases of a wide density range (0.01 to 0.31 lb./cu. ft.) were utilized. Thirty‐eight different gas‐solid systems were studied.
Flow in concentric annuli at high reynolds numbers
Authors: Rothfus R. R. , Sartory W. K. , Kermode R. I.
Published: June 2004

A method is proposed and developed for predicting velocity profiles in smooth, concentric annuli at high Reynolds numbers from the profiles in equivalent tubes. Experimental data for the flow of water in two annuli with diameter ratios of 14.8 and 38.2 at Reynolds numbers up to 226,000 strongly support the predictions. Published data show the method to be successful over a very wide range of diameter ratios.
Turbulence determination and blockage correction for immersed cylinder heat transfer at high reynolds numbers
Authors: Talmor Eliyahu
Published: June 2004

Transitional immersed cylinder heat transfer measurements are used in conjunction with the theory of boundary‐layer transition of van Driest and Blumer to determine the corresponding free‐stream turbulence intensity. The consistency of the results is demonstrated by comparison to other investigations where the free‐stream turbulence intensity was directly measured with a favorable pressure gradient present. Successful determination of the turbulence level for high blockage data and proper correction for channel blockage effects for all data compared lead to an improved and extended correlation of immersed cylinder average and stagnation point heat transfer results. Concurrently, a boundary‐layer transition theory is extended from zero pressure gradient and moderate turbulence levels to conditions of high turbulence and high pressure gradient.
Thermal convection in a completely confined fluid layer
Authors: Mitchell W. T. , Quinn J. A.
Published: June 2004

Experimental observations are reported on convective motion in a laterally confined fluid layer heated from below. Measurements extend over a wide range of Rayleigh numbers which encompass several flow regimes, including remarkably stable periodic flows. The conditions necessary for the oscillatory motion as well as the qualitative nature of the flow have been explored.
On the numerical solution of problems in multicomponent distillation at the steady state
Authors: Billingsley D. S.
Published: June 2004

A part of the empirical and generally effective θ method of Holland for the numerical solution of steady state multicomponent distillation problems is placed on a sound mathematical basis. Additional analysis of two other aspects of the numerical procedure is also presented. Finally, some numerical Jacobian types of matrices are discussed for two test problems. This discussion provides a numerical comparison between the strength of convergence of Holland's approach and direct iteration.
Chemical transport in nonconvective systems
Authors: Lever R. F. , Jona F. P.
Published: June 2004

Many practical chemical vapor transport systems are gaseous diffusion limited. For a single‐reaction system under moderate supersaturations, the diffusive transport rate is readily expressed in a form which enables the effect of surface kinetic limitations to be included. Attempts to observe surface limitations in a closed‐tube experiment are described together with experiments which confirm the diffusion theory. The treatment of multireaction systems is briefly discussed.
The effect of recycle on a linear reactor
Authors: Schmeal W. R. , Amundson Neal R.
Published: June 2004

The theoretical transient behavior of an isothermal packed bed or tubular reactor with direct recycle is investigated. It is shown that the recycle effect, coupled with the phenomenon of axial dispersion, causes waves in the reactant concentration to travel through the bed when the feed concentration undergoes a step change. The waves have a length almost equal to the bed length and they travel with the velocity of the fluid. The behavior of the waves is very insensitive to the value of the Peclet number.

The pertinent linear differential equation is solved by the method of generalized Fourier transforms and the boundary conditions are such that the Sturm‐Liouville theorem cannot be used. The operator is nonself‐adjoint and the eigenfunctions are not mutually orthogonal. The eigenvalues, which are complex, are found by means of the argument principle. Sample calculations are presented of the first one hundred terms of the Fourier expansion of a solution function and this is compared to a simplified approximate series which is developed.
Stratified laminar flow in ducts of arbitrary shape
Authors: Yu H. S. , Sparrow E. M.
Published: June 2004

A method of analysis is presented for determining closed‐form solutions for two‐component stratified laminar flow in horizontal ducts of arbitrary cross section. It is demonstrated that the method is remarkably easy to apply and produces results of high accuracy. As an application, solutions are obtained for stratified flow in a circular tube. The results are compared with various limiting cases and excellent agreement is found to exist. Among the limiting cases, an exact solution was derived by Green's functions for the problem in which the interface between the flow components is situated at the horizontal diametral plane.
Thermal diffusion in a flat‐plate column inclined for improved performance
Authors: Chueh P. L. , Yeh H. M.
Published: June 2004

Inclination of a flat‐plate thermal diffusion column from the vertical axis substantially increases the separation efficiency by reducing the remixing effect. Theoretical considerations show that when the column is at the best inclination, maximum separation, maximum production, or minimum column length may be obtained. A generalized graphical solution of the conditions for best performance is presented. Experimental results for the system benzene–n‐heptane are in excellent agreement with the theory.
Stability of a fluid in a rectangular region heated from below
Authors: Samuels Michael R. , Churchill Stuart W.
Published: June 2004

Finite‐difference methods were used to compute hydrodynamic instability due to natural convection in an enclosed horizontal rectangular region heated from below. Critical Rayleigh numbers were determined for a series of Prandtl numbers and length‐to‐height ratios. For Prandtl numbers greater than unity excellent agreement was obtained between these calculations and the values predicted by Kurzweg on the basis of a linearized theory. However, for Prandtl numbers less than unity the critical Rayleigh numbers exhibited a dependence on NPr, which was not predicted by the linearized theory. For Rayleigh numbers greater than the critical, complete temperature and velocity fields were determined.

The calculations assumed that the fluid motion is two dimensional. Experiments have indicated that the flow may be two or three dimensional depending on minor perturbations in the boundary conditions.

Although a number of metastable two‐dimensional circulations are possible for symmetrical initial conditions, the calculation always converged to a single, unique solution for any asymmetric initial condition.
Kinetics of the heterogeneous decomposition of nickel tetracarbonyl
Authors: Carlton Herbert E. , Oxley Joseph H.
Published: June 2004

The decomposition of nickel tetracarbonyl at pressures between 20 and 200 torrs was studied at temperatures from 100° to 225°C. In the cross‐flow system, the rate in the absence of appreciable dilution was primarily limited by kinetic resistances at temperatures up to about 175°C. over an effective Reynolds number range of 5 to 100. Gas phase diffusional resistances were controlling at higher temperatures. Corrections for natural convection were employed in both the kinetic and diffusional regions of control.