bluuebunny/crossref_metadata_2025 huggingface dataset:
Numerical solution of the Navier‐Stokes equation for flow past spheres: Part I. Viscous flow around spheres with and without radial mass efflux
Authors: Hamielec A. E. , Hoffman T. W. , Ross L. L.
Published: June 2004

This study was undertaken to ascertain the accuracy of finite‐difference solutions for flow around spherical particles in the intermediate Reynolds number range. Comparison of the results with experimental data on drag coefficients, frontal stagnation pressure, and wake geometry indicated good agreement. The approximate solutions, in which the Galerkin method and asymptotic analytical predictions were utilized, were evaluated by using the finite‐difference solutions as a standard. These methods were used to calculate the effect of uniform and nonuniform mass efflux on the drag and flow characteristics around a sphere. Theoretical solutions indicated that nonuniform mass efflux can significantly reduce the drag on a submerged object. Ranges of applicability of the approximate methods were established.
Adduction in the decane‐urea‐ethanol system: Part II. Kinetic studies
Authors: Tamarelli A. W. , Manning F. S.
Published: June 2004

Supersaturated solutions with randomly distributed seed crystals were formed by jet mixing of saturated slurries of urea—decane adduct and decane—urea—ethanol solutions. The resulting crystal growth rates were measured quantitatively with a rapid‐mixing, stopped‐flow calorimeter. Nucleation of additional crystals was negligible. Times required for 90% adduction ranged between 0.375 and 25.5 sec., a 68‐fold variation. A single dimensionless chronomal which adequately represented all the kinetic data was obtained. In all runs, liquid phase mass transfer appeared to control the rate of adduction, despite the fact that the rapid mixing greatly reduced mass transfer resistance. Whereas the data were consistent with several equations describing models based on diffusional rate control, the results did not support mechanisms involving surface phenomena.
Momentum transfer in climbing film flow in annular duct
Authors: Kim D. H. , Knudsen J. G.
Published: June 2004

The characteristics of upward gas–liquid flow in a vertical annular duct were investigated. The flow regime studied was the climbing film regime in which water flowed as a film up the inner core of the annulus while air flowed in the annular space, the outer wall of the annulus remaining dry. Friction losses, air velocity distributions, and film characteristics were studied, the latter by photographing the climbing film through the transparent outer tube. Friction loss and film thickness were correlated with Lockhart–Martinelli parameters, X, Φ, and RL. The presence of the climbing film caused the point of maximum velocity of the air profile to move toward the outer tube, indicating that the film created a rough wall condition. The inner portion of the velocity profile was correlated by Nikuradse's rough tube equation, while the outer portion was correlated by a logarithmic equation which previous workers have reported for single‐phase flow. Kapitza's theory of wave formation was applied to the climbing film and was found to predict reasonable values for the mean film thickness. However, it failed to predict reliable values for the wavelength of surface waves.
Turbulent flow of unstable liquid‐liquid dispersions: Drop sizes and velocity distributions
Authors: Ward J. P. , Knudsen J. G.
Published: June 2004

Friction lossess, velocity distributions, and drop size distributions were obtained for unstable liquid‐liquid dispersions in turbulent flow. The friction losses and velocity profiles were used to determine effective viscosities which were correlated by the Einstein relation for dispersions in which μd/μc ≤ 15. When μd/μc ≈ 200 the dispersion could not be considered as a single‐phase fluid and exhibited non‐Newtonian characteristics. Drop size distributions were obtained from photographs of the flowing dispersion. These drop size distributions provided information concerning drop breakup and coalescence in the circulation system. From drop size distribution and effective viscosity measurements a criterion was obtained to determine if a dispersion could be treated as a homogeneous single‐phase fluid.
Diffusion and dispersion in porous media
Authors: Whitaker Stephen
Published: June 2004

The dispersion equation for a single, nonreacting, nonadsorbing species is derived for incompressible, laminar flow in anisotropic porous media. Direct integration of the appropriate differential equations gives rise to a dispersion vector ψi and a tortuosity vector τi, both of which must be evaluated experimentally. For the dispersion vector, this is conveniently done by representing ψi in terms of the velocity and gradients of the velocity and concentration. The experimental determination of τi is not straightforward except for the case of pure diffusion. The analysis yields a result which contains all the features of previously presented dispersion equations without making any assumptions as to the nature of the flow, that is, bypassing, cell mixing, etc., except that it be laminar. Attacking the dispersion problem in terms of the differential diffusion equation provides a rational basis for the correlation of experimental data and illustrates the connection between the microscopic and macroscopic equations.
The mechanics of a spray column
Authors: Letan Ruth , Kehat Ephraim
Published: June 2004

Local and average holdup and drop size distribution as function of flow rates were measured for kerosene drops and water in a countercurrent, 15‐cm. I.D., 160‐cm. long, spray column. The range of flow rates was 5 to 40 liters/min. of kerosene and 0 to 50 liters/min. of water. At the same pairs of flow rates of the dispersed and the continuous phases in spray columns, three modes of drop packings can be obtained. These are termed, in order of increasing average holdup and increasing regularity of flow patterns, dispersed, restrained, and dense packings. For dispersed packing, at low flow rates of the two phases, the holdup and the drop size are constant along the column. At high flow rates the drop size increases from bottom to top of the column and the holdup increases from top to bottom of the column. The range of flow rates for the operation of a spray column is extended by the use of a conical entry section (Elgin design) at the bottom of the column, by the formation of an equilibrium region in the conical section.

The average holdup increases with increased flow rates of both phases for dispersed and restrained packings, and with decreased flow rates of both phases for dense packing.

The best definitions of flooding in a spray column are either the point of maximum average specific area of the drops, which corresponds to the onset of coalescence in the column, or the start of rejection of drops from the column proper.
Influence of resin selectivity on film diffusion‐controlled ion exchange
Authors: Copeland J. P. , Henderson C. L. , Marchello J. M.
Published: June 2004

An analytic solution of the Nernst‐Planck equations is derived which applies to a selective resin when film diffusion controls. The selectivity has a marked effect on the rate of exchange for a wide range of diffusivities. The unit‐selectivity solution of Schlögl and Helfferich is included as a special case of the more general solution.
Nonisothermal adsorption in fixed beds
Authors: Meyer Oscar A. , Weber Thomas W.
Published: June 2004

Removal of methane from a helium stream by adsorption on Columbia SXC activated carbon was studied experimentally and theoretically. A mathematical model for the process was developed and the governing differential equations were solved numerically. The model incorporates heat and mass transfer resistances within and around the adsorption particle. Wall effects and moderate heat loss to the surroundings are also included. The required heat and mass transfer correlations were obtained from the literature. Simple expressions were developed to determine the relative resistances for heat and mass transfer within and around the adsorption particles.
Determination of transient plate efficiencies from operational data
Authors: Groves D. M. , Tetlow N. J. , Holland C. D.
Published: June 2004

Methods are presented for the determination of the transient values of the vaporization efficiencies from the knowledge of various combinations of the transient values of operating variables. For the case where the temperature and the composition of the liquid phase for each plate are known, a direct solution for the vaporization efficiencies is presented. Also, a method is presented for the determination of the mixing parameters of a generalized plate model on the basis of known transient values of certain operating variables.
Equilibrium stage calculations
Authors: Tierney John W. , Bruno Joseph A.
Published: June 2004

Iterative methods for the determination of stage temperature and interstage flow rates in the equilibrium stage problem are discussed, and the use of the Newton‐Raphson method for solution of the systems of simultaneous equations is proposed. It is shown that the complete correction process can be divided into four independent parts, two of which are treated in the paper. The first is equivalent to the constant molal overflow problem in distillation and the second to the constant temperature extraction problem. For each of these cases the necessary partial derivatives describing the effects of temperature and flow rate changes on all material balance equations are developed. Sample problems are briefly discussed to demonstrate the feasibility of the calculation and the fact that quadratic convergence is obtained. Equation derivation is simplified by using matrix notation, which also has the advantage that any interstage flow pattern is allowed.
A stochastic mixing model for homogeneous, turbulent, tubular reactors
Authors: Kattan Abraham , Adler Robert J.
Published: June 2004

A stochastic mixing model is developed for turbulent flow in homogeneous plug‐flow reactors. The model is based on random coalescence and redispersion of fluid elements. Of special significance is its applicability when mixing and reaction rates are comparable, as well as when either rate dominates. The model's parameters may be determined by measuring conversion with instantaneous reactions. Experimental results reported by others are successfully simulated.
Prediction of the Joule‐Thomson coefficients of a gas mixture from a generalized equation of state: The nitrogen‐ethane system
Authors: Stockett A. L. , Wenzel L. A.
Published: June 2004

Using a thermodynamically consistent form of equation of state proposed by Foulkes, one can determine the virial coefficients of the pressure expansion from Joule‐Thomson coefficient data. A modification of the method has been applied for nitrogen and ethane within the temperature range from 50°C. to the normal boiling point. Mixture rules are proposed that allow reproduction of experimental data on μ for nitrogen‐ethane mixtures at pressures below the critical pressure of ethane.
A static vapor pressure apparatus for mixtures
Authors: Davison R. R. , Smith W. H. , Chun K. W.
Published: June 2004

A static vapor pressure apparatus is described which is especially suitable for mixtures. A vapor pressure flask with a built‐in condenser allows the mixture to be degassed without change in composition. The entire apparatus is assembled from simple parts. Equilibrium is rapidly attained with either an external pressure or a liquid of known vapor pressure used as a reference.
Three turbulent drag coefficients in beds of spheres
Authors: Tallmadge John A.
Published: June 2004

Form, shear, and total drag have been studied in the 2,500 to 65,000 range of Reynolds number over a wide range of porosity by using the data of Thodos and co‐workers. The effect of Reynolds number was found to be the −0.14 power for form drag, the −0.19 power for total drag, and the −0.5 and highe power for shear drag, so that the ratio of shear drag to total drag decreased from about 16% to less than 5% with increasing Reynolds numbers. For the 2,500 to 6,000 range of Reynolds number, experimental evidence supports the apparently analogous behavior between average shear drag and average heat flux. Limitations and related evidence of this behavior are also discussed. Methods are suggested for estimating drag ratios and coefficients by using the correlation of this work.
The streaming potential fluctuations in a turbulent pipe flow
Authors: Liu Henry
Published: June 2004

Accompanied by a bried theoretical consideration, the results of an experimental study of the streaming potential fluctuations in turbulent pipe flows of distilled water are presented. The dependence of the streaming potential fluctuations on turbulent velocity fluctuations and other parameters as indicated by the theory is determined from the experimental data. Information on the characteristics of turbulent velocity fluctuations in the viscous sublayer near a pipe wall have been inferred from the data.
A theoretical analysis of some interrelationships and mechanisms of heat and mass transfer in dispersions
Authors: Gal‐Or Benjamin , Walatka Vernon
Published: June 2004

Some of the main interrelationships that govern heat and mass transfer in dispersions are considered. Qualitative and quantiative analyses of the effects of holdup, average residence time, surface active agents, viscosity, and average particle size on transfer rates are made for two major domains. In the first domain a convective mass transfer model is formulated for the case of low dispersed phase holdup values and a steady motion of a swarm of bubbles with clean interfaces. A second domain is established for high dispersed phase holdup values and fine dispersions that contain surfactants. A semidynamic model for unsteady state heat (or mass) transfer from a swarm of droplets in a multistage liquid‐liquid disperser is demonstrated in this domain by a simultaneous solution of two differential equations (one for each phase).
Mass transfer from large single bubbles at high reynolds numbers
Authors: Nate Takayuki , Himmelblau D. M.
Published: June 2004

Single bubbles of carbon dioxide were formed in a fixed position surrounded by a thin conical film of water flowing at average film Reynolds numbers in the range of 40 to 300. Measurements of interphase mass transfer at 32°C. and various bubble pressures agreed with predicted values only for the smallest bubbles. For larger bubbles, mixing perpendicular to the bubble interface was enhanced by waves, believed to be generated by the unstable interface. A comparison of interphase transfer coefficients between this investigation and previous work indicated that the bubbles at the lowest flow rates qualitatively fell in line with other measurements, but that the highest water flow rates gave distinctly higher coefficients.
Diffusion coefficients of hydrogen and helium in water
Authors: Ferrell R. T. , Himmelblau D. M.
Published: June 2004

Measurements of laminar dispersion in a capillary have been used to determine the molecular diffusion coefficients of hydrogen and helium dissolved in water over the temperature range of 10° to 55°C. Literature correlations did not predict realistic values of the diffusivities for the hydrogen—water and helium—water binaries. A statistical analysis of the experimental diffusion coefficients indicated that they could be related to the absolute temperature by a semiempirical correlation, which may be considered an extension of the well‐known Wilke‐Chang correlation. This relation was based on the absolute reaction rate model of liquids.
Normal freezing of eutectic forming organic mixtures
Authors: Cheng C. S. , Irvin David A. , Kyle B. G.
Published: June 2004

Normal freezing of several organic systems exhibiting simple eutectic behavior has been studied experimentally, and the occurrence of constitutional subcooling has been clearly established. This phenomenon, previously observed in systems of metallurgical interest, results in the instability of a planar solid‐liquid interface and leads to solute trapping. This trapping mechanism quantitatively explains why eutectic forming systems exhibit solid phase concentration profiles identical to those expected of systems which form solid solutions. The onset of constitutional subcooling can be correlated and reliably predicted by theoretical equations.

Although the process of normal freezing with no liquid phase agitation would appear to be well described by a diffusion model, free convection induced by concentration gradients renders a boundary‐layer model more appropriate when the liquid density of the solvent exceeds that of the solute and freezing is in an upward direction.
A gravity corrected theory for cylinder withdrawal
Authors: White David A. , Tallmadge John A.
Published: June 2004

The speed range of the low‐speed theory for cylinder withdrawal is extended by a correction for gravity and a modified use of the thin meniscus assumption. Experimental evidence indicates that this gravity corrected theory holds over a 3,000‐fold range of speed, in terms of capillary number. This gravity corrected theory reduces, as special cases, to several other previously published theories as well as to the low‐speed theory.
Incorporation of ionic impurities in crystals growing from solution. The case of lead ions in potassium chloride crystals
Authors: Botsaris G. D. , Mason E. A. , Reid R. C.
Published: June 2004

Single seed crystals of potassium chloride were grown from aqueous solutions under conditions of constant temperature, supersturation, and impurity concentration. With emission spectrography as the method of analysis, the distribution of various metal ion impurities between the grown potassium chloride crystal and the solution was studied. The distribution coefficients of Pb++, defined as the ratio of the impurity concentration in the crystal to the concentration in solution, were found to be greater than unity at very low concentrations. The lead distribution coefficients varied between 2,700 for solutions containing 10−8 moles of lead/mole of potassium chloride to 28 (for solutions of 10−5 moles of lead/mole of potassium chloride).

The results suggest a mechanism of nonequilibrium capture of the impurity. The magnitude of the distribution coefficient is shown to depend on the equilibrium distribution coefficient between the solution and surface of the crystal, the rate of growth of the crystal, and the rate of diffusion of the impurity through the crystal lattice. These results are believed to be of significance in the purification of materials by fractional crystallization. For instance, they indicate that in order to produce crystals of lead‐free potassium chloride, the conventional techniques or recrystallization should be modified to include rejection of the first crystals grown.
The injection method of determination of partial volume at infinite dilution
Authors: Hensel B. H. , Edmister W. C. , Chao K. C.
Published: June 2004

A new experimental method of determining partial volume is described. The method requires the measurement only of a series of absolute and differential pressures. It is applicable to the determination of the partial volume of an infinitely dilute solute in a gas mixture up to high pressures. Measurement by this method can be readily performed at conditions of temperature and pressure so far unexplored to yield essential data for equation of state analyses.
Thermal dynamics of a distributed parameter nonadiabatic humidification process
Authors: Stewart Richard R. , Bruley Duane F.
Published: June 2004

Results of a theoretical and experimental study of the thermal dynamics of a distributed parameter nonadiabatic humidification process are presented. A wetted‐wall column was selected for study to ensure standard and reproducible velocity profiles and a definable area for heat and mass transfer. Four mathematical models which consider various heat and mass transfer. Four mathematical models which consider various heat and mass transfer effects were derived in the time domain and solved in the frequency domain. All models, including a simple model previously tested for the adiabatic humidification case, were in good agreement with experimental results obtained by pulse testing.
Mixing and contacting models for fluidized beds
Authors: Mireur John P. , Bischoff Kenneth B.
Published: June 2004

Parameters of the two‐phase model for mixing in fluidized beds were evaluated from a large amount of available literature data. The dense phase dispersion coefficients and the cross flow, or interphase transfer, coefficients, based on the consistent model calculations, were correlated with operating conditions. A strong effect of bed length‐to‐diameter ratio was found for the dense phase mixing but not for the cross flow. On the basis of the given kinetics information with the mathematical model parameter correlations, some chemical reactor conversions from the literature were predicted by a priori calculations.
Viscosities and densities of methane‐propane mixtures at low temperatures and high pressures
Authors: Huang E. T. S. , Swift G. W. , Kurata Fred
Published: June 2004

The viscosities and densities of methane‐propane mixtures were determined at pressures to 5,000 lb./sq.in.abs. for 22.1 and 50.0 mole % methane over a temperature range from −120 to 37.78°C. and for 75.3 mole % methane over a temperature range from −150° to 37.78°C. Reproducibility of the viscosity data was ± 2%, and the agreement with literature values was, on the average, within ± 2%. The reproducibility of the density data was ± 0.8%, and the agreement with literature values was ± 1.2%.
Transport of gases through insoluble monolayers
Authors: Sada Eizo , Himmelblau D. M.
Published: June 2004

The reduction in gas desorption through surface active monolayers on a water substrate has been investigated for five compounds (1‐hexadecanol, 1‐octadecanol, 1‐docosanol, 1‐eicosanoic acid, and 1‐docosanoic acid) and four gases (oxygen, nitrogen, methane and carbon dioxide) at 25°C. Gas transport was retarded significantly at high surface coverage and decreased nonlinearly with change in surface coverage past the point equivalent to zero surface pressure.

Interphase mass transfer coefficients for transport through the films were calculated, but no simple correlation could be discovered which could be used to predict film coefficients or the reduction as a function of surface coverage.
A study on stability and incipient turbulence in poiseuille and plane‐poiseuille flow by numerical finite‐difference simulation
Authors: Dixon T. N. , Hellums J. D.
Published: June 2004

A difference method for treating the complete two‐dimensional Navier‐Stokes equations in time‐dependent form is applied to the prediction of incipient turbulence. A steady laminar flow profile is disturbed and the propagation of disturbances in time and space is calculated. Changes occur in amplitude and in character much as would be observed in a laboratory experiment. The classical paradox of stability of Poiseuille flow to low amplitude disturbances at all Reynolds numbers is studied and contrasted to plane‐Poiseuille flow. The amplitude dependence of stability is demonstrated. The results are shown to be consistent with prior theoretical and experimental work. The work lends strong support to the difference approach to difficult stability problems.
Third virial coefficients of nonpolar gases and their mixtures
Authors: Chueh P. L. , Prausnitz J. M.
Published: June 2004

While much attention has been given to second virial coefficients of nonpolar gases, experimental and theoretical studies on third virial coefficients are scarce. This work presents a correlation of third virial coefficients within the framework of the corresponding states principle. The correlation is useful for estimating third virial coefficients of pure and mixed nonpolar gases, including the quatum gases helium, hydrogen, and neon. The importance of third virial cross coefficients in phase equilibrium predictions is illustrated with calculations for the solid‐gas, methane‐hydrogen system at 76°K.

Brief attention is given to the pressure series form of the virial equation. Because of fortuitous cancellations, it is shown that for reduced temperatures above 1.4, the pressure series, truncated after the second term, is applicable to a wider range of density than the density series truncated after the second term. However, when both series are truncated after the third term, the density series appears to be superior regardless of reduced temperature.
Photochlorination of propane
Authors: Cassano Albert E. , Smith J. M.
Published: June 2004

The chlorination of propane was studied in a tubular flow reactor, with outside illumination, at atmospheric pressure. At chlorine concentrations of less than 1.5 mole % (and inert nitrogen above 94%) a second‐order (in chlorine) rate expression was indicated. At higher chlorine or propane concentrations propane affects the rate. Two rate equations, based upon different termination steps for the chain carriers, were found to fit the data. For the low concentration region the apparent activation energy for the overall reaction was 3.4 kcal./g.‐mole. Most of the measurements were carried out with polychromatic light, but data taken with a narrow band of radiation, over the range 2,200 to 5,400Ā, showed an increase in rate with decreasing wave length. As a first step toward reactor design, differential reactor data were used to predict the conversion for laminar flow, integral reactor conditions. A reactor model which included the effects of residence time distribution and radial variation in light intensity gave good agreement with experimental data. A plug‐flow model was less satisfactory.
The optimality of an easily implementable feedback control system: An inverse problem in optimal control theory
Authors: Denn Morton M.
Published: June 2004

In most control applications in the chemical process industries it is not realistic to attempt to define a unique mathematical statement of the control objective, for many criteria will satisfy the physical requirement of the rapid elimination of errors in the product stream as the result of an upset. The strong dependence of the structure of an optimal control system on the choice of objective then makes optimal control theory irrelevant in such situations, since the control engineer has no assurance that a complicated controller is a necessity of the process, rather than a consequence of an unfortunate choice of objective. In this paper an inverse problem is considered, in which an easily implementable feedback control system is first chosen and then is shown to be optimal for a physically meaningful objective in a large class of systems.
Kinetics of complex isothermal reversible first‐order reaction systems involving three components
Authors: Faith Larry E. , Vermeulen Theodore
Published: June 2004

A new calculation method presented here for interpreting batch or tubular‐flow reactor data (and also CSTR data) on three‐component, three‐reaction reversible systems is based upon the general analyses of Jost and of Wei and Prater. With advance knowledge of the pertinent equilibria, even a very few experimental points can be matched easily and rapidly to the given figures and equations. The simplification involved when one reaction disappears, with the divariant system thus becoming monovariant, is also described. Representative concentration‐time curves are given for design purposes.
Concentrated polymer solutions: Part III. Normal stresses in simple shear flow
Authors: Williams Michael C.
Published: June 2004

A molecular theory for the stress P in a concentrated polymer solution is evaluated for simple shear flow. Three rheological functions (P12, P11 − P22, P11 − P33) are predicted to be dependent on shear rate γ in a very complicated fashion, and are displayed graphically. A unique feature is that P22 − P33 is shown to have the same sign as P11 − P33 at low shear, a result in agreement with most experimental data and not predicted by other theories. A comparison with two sets of data verifies the prediction of relative behavior of shear and normal stresses at low γ, but the theory fails to fit data at high γ. Reasons for the success of the reducing factors c2 or c3 (where c is mass concentration) in constructing master curves for normal stress are suggested.
Transient multicomponent diffusion with heterogeneous reaction
Authors: Hudson J. L.
Published: June 2004

The problem of transient multicomponent diffusion of an arbitrary number of components in one‐dimension with heterogeneous reaction has been solved exactly by means of the Laplace transform. Linearized expressions for the diffusion and reaction were used. Numerical evaluations of the solution are given and a comparison made with results derived by use of an effective diffusivity.
The control of nonlinear systems: Part IV. Quasilinearization as a numerical method
Authors: Rothenberger B. F. , Lapidus Leon
Published: June 2004

Five different variations on the basic quasilinearization algorithm for optional control are applied to a six‐variable nonlinear gas absorber system. Convergence of the algorithms to the optimal trajectory with better than 1% accuracy is achieved in less than ten iterations. The region of initial starting points which yield convergence is quite large. The main difficulty encountered is due to instabilities of the maximum principle equations. This limitation is, however, not severe and it is possible to predict a priori when the difficulty will occur. It is concluded that quasilinearization is a feasible algorithm for the optimization of nonlinear unconstrained systems.
Convective diffusion in stagnation flow with an imperfect semipermeable interface
Authors: Zeh Dale W. , Gill William N.
Published: June 2004

In this note convective diffusion in stagnation flow is discussed in the context of membrane separation processes, reverse osmosis in particular. It is shown that this is a desirable configuration for determining the rejection parameter R, a measure of how imperfect the semipermeable membrane interface is, because the dimensionless concentration function depends only on η.

A simple approximate analytical solution is developed for (wsw/wse) which applies to separation processes in general. For reverse osmosis, NSc ≃ 560 and in this case the approximate results are compared with exact numerical calculations. It is found that the analytical solution is very accurate up to a polarization of (wsw/wse) ≃ 4 which constitutes a wide range of practical interest. For completeness, numerical results are reported up to a polarization of about 30.
Quasilinearization in optimization: A numerical study
Authors: Lee E. Stanley
Published: June 2004

The quasilinearization technique is used to obtain numerical answers for optimization problems formulated by the calculus of variations and the maximum principle. The optimum temperature profile in a tubular reactor, together with its initial optimum pressure, is obtained by this technique. Various variations of this problem such as control variable inequality constraints and the presence of pressure drop in the reactor are also discussed.
Diffusion in liquid metals
Authors: Pasternak A. D. , Olander D. R.
Published: June 2004

Mutual diffusion coefficients in dilute liquid metal solutions have been correlated by methods based upon absolute rate theory and the theory of corresponding states. Both correlations reproduce the experimental data to approximately ±25%, but the absolute rate theory method is simpler to use and is applicable to a larger number of systems.
Washing of the liquid retained by granular solids
Authors: Han Chang Dae , Bixler Harris J.
Published: June 2004

A mathematical model termed the blind side channel model is developed to describe the washing performance of liquid retained in a bed of granular solids. The effects of operating variables and system's parameters, such as the flow rate of wash liquor, the diffusivity of the liquid system, and the thickness of the bed, are discussed. The experimental washing study was carried out with granular solids such as glass beads, sand, and crystalline solids, and application of wash liquors miscible in all cases with the residual liquid in the bed, drained by centrifuging. Results from the developed model showed very good agreement with the experimental results. The developed model would be valuable in analyzing the washing performance for process improvement and in designing washing systems.
Translation of continuous phase in the wakes of single rising drops
Authors: Hendrix Charles D. , Dave Shashikant B. , Johnson Homer F.
Published: June 2004

Volumes translated in wakes of single drops of organic liquids rising through aqueous media have been measured. Organic drops studied comprised methyl isobutyl ketone, toluene, and toluene‐carbon tetrachloride mixtures. Aqueous media comprised water and water‐sugar solution. Distance of drop rise varied from 10 to 20 in. Drop size was varied such that Reynolds numbers of 40 to 800 were obtained. Volumes translated were nearly independent of distance for nonoscillating drops and decreased rapidly with distance for oscillating drops. Transition from nonoscillating to oscillating drops occurred at Reynolds number of 200. Measurements of drop velocities were also made.
Continuous flow in packed thermal diffusion columns
Authors: DiCave Sergio , Emery Alden H.
Published: June 2004

A parallel‐plate thermal diffusion column packed with glass wool was operated in continuous flow. The standard equation used for continuous flow through nonpacked columns satisfactorily correlates separation and flow rate. The packed‐column theory correctly gives the effects on the regression coefficients of plate spacing and packing permeability, the two variables unique in the packed column. The theory gives poor approximations of the absolute magnitudes of the coefficients, however, which is the same situation found in results from nonpacked columns.
Dynamic behavior of the well‐mixed isothermal crystallizer
Authors: Sherwin M. B. , Shinnar Reuel , Katz Stanley
Published: June 2004

Under some conditions, continuous crystallization exhibits cyclic changes of the particle size even with constant input conditions. A linearized stability analysis has been performed to determine under what conditions this behavior can be expected. Numerical solutions of the actual nonlinear system equations were carried out to follow the cyclic behavior and to compute the cycle time and the amplitude of the fluctuations. The effect of seeding on the stability limits and product distribution was also evaluated.
A predictive theory for diffusion in mixed solvents
Authors: Cullinan Harry T. , Cusick M. R.
Published: June 2004

A relationship for the diffusion coefficient of a dilute species in a mixture of two solvents is developed. The result, based on the linear additivity of the frictional activation energy which is valid for completely miscible, nonassociated systems, predicts the diffusion coefficient of the solute in terms of the limiting values of the diffusion coefficient of the solute in each of the solvents, the limiting values of the solvent pair diffusion coefficient, and two thermodynamic factors. The equation is confirmed for some recent experimental data.
Heat transfer in packed and fluidized beds by the method of cyclic temperature variations
Authors: Lindauer George C.
Published: June 2004

Particle‐to‐gas heat transfer coefficients were determined in packed and fluidized beds with large diameter particles and high mass velocities using the cyclic temperature method.

Experimental results for packed beds were satisfactorily correlated within 10% deviation as εjh vs. NRe and were found to compare favorably with results of other experimenters obtained with much lower mass velocities and larger particles. The particle‐to‐gas heat transfer coefficient varied as G0.60 for the steel spheres vs. G0.66 for the tungsten spheres, and as Dp−0.44.

Heat transfer coefficients obtained at minimum fluidization were in good agreement with those obtained with packed beds. As the mass velocity was increased above that required for minimum fluidization, heat transfer coefficients remained essentially constant.
Motion of spherical particles in a Bingham plastic
Authors: Ansley Ralph W. , Smith Terence N.
Published: June 2004

This paper describes an investigation of the settling characteristics of spherical particles in Bingham plastic fluids. A stress analysis is used to derive a nondimensional parameter which describes the laminar settling regime. The terminal velocities of spheres in the Reynolds number range of 2 to 130 have been determined. These, together with published data at higher Reynolds numbers, are shown to substantiate the theoretical argument.

A correlation of drag coefficient as a function of the settling parameter indicates the transition from laminar to turbulent settling.
Kinetics of physical adsorption of propane from helium on fixed beds of activated alumina
Authors: Rimpel Auguste E. , Camp David T. , Kostecki John A. , Canjar Lawrence N.
Published: June 2004

The kinetics of physical adsorption of propane from helium on fixed beds of activated alumina at 30°C. and at atmospheric pressure was studied. Two grades of activated alumina with the same average pore size distribution but different pore size distributions were used. Gas concentration, flow rate, and adsorbent particle size were also varied. The rate of internal diffusion controlled the adsorption process and was best described by Ficks' equation for unsteady state diffusion into a sphere. The internal diffusion appeared to be by a pore diffusion rather than by a surface diffusion mechanism.
Nonlinear feedforward control of chemical reactors
Authors: Luyben William L.
Published: June 2004

This paper illustrates the synthesis of nonlinear feedforward controllers for chemical reactors. In most of the theoretical development and application of feedforward control only linear systems have been considered. There are, however, no inherent linear limitations in feedforward control. Since chemical reactors are usually nonlinear, the effectiveness of control should be improved by including nonlinearities in the design of feedforward controllers. This is particularly true for batch reactors because of the large changes in variables during a batch cycle. Continuous stirred‐tank reactors are studied with single and consecutive reactions of first and higher order. Effectiveness of linear and nonlinear feedforward controllers is compared for disturbances of various magnitude and direction. Feedforward control of batch and tubular reactors is also discussed.
Mass transfer through horizontal liquid films in wavy motion
Authors: Goren Simon L. , Mani R. V. S.
Published: June 2004

The effect of standing waves of controlled amplitude and frequency on the steady state rate of mass transfer through thin horizontal liquid layers is studied experimentally. The variables studied are the film thickness, the amplitude and frequency of the waves, and the spacing between the probes generating the waves. A bulk motion of complicated pattern known as drift is caused by the finite amplitude of the waves. The rate of mass transfer in the absence of imposed vibration is two to three times greater than that expected by molecular diffusion alone. Vibration increases the rate up to an order of magnitude or more, depending on the hydrodynamic conditions. The data at low frequencies are correlated by an expression of the form (i‐io)/idiff = KAf3/4h1/2L−1/2.
A kinetic approach for polymer solution data
Authors: Kim H. T. , Brodkey Robert S.
Published: June 2004

The phenomenological theory previously prsented for describing the rheological properties of non‐Newtonian materials was applied to two polymer solution systems. The basic shear diagram is needed over a wide range of shear rates and polymer concentrations, and such data are not readily available; however, what could be found supported the analysis. In order to confirm the theory further, ten solutions of polymethylmetacrylate in diethyphthalate with concentrations up to 55% were investigated at 40°C. The results indicated that the forward and reverse orders were 1 and 2 respectively and that the two parameters of the theory (a susceptibility to shear term and an equilibrium type of constant) were constant over the range of concentrations investigated. The flow data were reproduced to within a few percent for all solutions, although the errors were large for the very dilute concentration, where experimental difficulties precluded obtaining reliable data. The method allows correlation of polymer solution data over the range from lower to upper Newtonian viscosities and over a wide concentration range.
Studies of intramembrane transport: A phenomenological approach
Authors: Kaufmann Thomas G. , Leonard Edward F.
Published: June 2004

The intramembrane transport properties of carbohydrates were investigated in cellophane. The experiments performed were the measurement of net volume transfer under a concentration and pressure gradient and the solute transfer due to a concentration difference together with the physical properties of the membrane. The matrix of phenomenological coefficients characteristic to the transport was established after the phase boundary contributions were extricated from the experimental transport data. These thermodynamic coefficients were then interpreted through the Spiegler‐Kedem‐Katchalsky frictional model.

The analysis of the frictional coefficients clearly indicated the importance of solute‐polymer interactions. The magnitude of solute‐solvent frictional coefficients in the membrane were compared with the corresponding interactions in free solutions. Their differences were explained in terms of the interaction of the solute with the macromolecular network and were quantitatively expressed by introducing two reduced frictional coefficients. The tortuosity factor was shown to be related to these interactions and not a simple geometric property of the membrane. The temperature dependence of the frictional coefficients was established.
The effect of eccentricity on the terminal velocity of the cylinder in a falling cylinder viscometer
Authors: Chen M. C. S. , Lescarboura J. A. , Swift G. W.
Published: June 2004

The theoretical equations for the flow of Newtonian fluids in a falling cylinder viscometer with eccentricity are developed. The error in fall velocity of the cylinder caused by eccentricity is determined and presented in tabular form. An approximate method to determine the error in fall velocity caused by eccentricity for non‐Newtonian fluids of the power law type is also presented. For the Newtonian case, n=1, the approximate method is shown to give excellent agreement with the exact method.
Effect of pressure gradient on sonic‐point heat transfer
Authors: Talmor Eliyahu
Published: June 2004

An analytical investigation of gas side heat transfer in high contraction, high convergence flows is presented. A partical criterion for retransition of a turbulent boundary layer is derived from the integral momentum equation and the effect of pressure gradient in the turbulent boundary‐layer flow regime is described with the help of external flow relations. The validity of the analytical results is demonstrated by comparison to available internal and external flow, throat heat transfer data.

Accordingly, various turbulent boundary‐layer heat transfer levels are obtained depending on the sonic‐point pressure gradient, the specific heat ratio, the reference‐to‐stagnation temperature ratio, and the exponent of the viscosity‐temperature function. Furthermore, the pressure gradient and the superficial mass velocity have opposite effects on the onset of retransition of a turbulent boundary layer.
Creeping flow of power‐law fluid over newtonian fluid sphere
Authors: Nakano Yoshisuke , Tien Chi
Published: June 2004

A technique which is a combination of Galerkin's method and variational principle was developed and used for the approximate solution of creeping flow of power‐law fluid over a Newtonian fluid sphere. The stream functions (both internal and external) and drag coefficient are expressed in terms of three parameters: the flow behavior index of the power law fluid, the external Reynolds number, and a viscosity ratio parameter \documentclass{article}\pagestyle{empty}\begin{document}$${\rm X} = \frac{{\mu ia^{n - 1} }}{{KV_{\alpha ^{n - 1} } }}$$\end{document}. Comparisons with existing experimental data are also given.
Analysis of optimal composite feedback‐feedforward control
Authors: Luecke R. H. , McGuire M. L.
Published: June 2004

We have developed analytic design methods for combination feedback‐feedforward control systems and have evaluated systems yielding optimal performance while subject to constraints commonly encountered in the chemical industry. Using the mathematical techniques pioneered by Wiener for the solution of the design equations, we have based the optimization on minimization of the mean square output of a system subject to a random disturbance. Side conditions for the constraint on mean square control effort, signal‐to‐noise ratio in the feedback system, and minimization of error output caused by misidentification of plant parameters were found to be necessary to give physically realizable and meaningful designs. The analytic design methods are useful for analysis of control system performance and capabilities under a variety of constraints, but the optimal designs are marginally superior to ideal or invariant feedforward controllers coupled with tuned proportional feedback controls. The principal improvement in the optimal design is in conservation of control effort when compromises in system performance are necessary because of this restriction.
The rise velocity of bubbles in tubes and rectangular channels as predicted by wave theory
Authors: Maneri Charles C. , Mendelson Harvey D.
Published: June 2004

In a previous paper, an analogy was presented which related the rise velocity of bubbles in liquids of infinite extent to the velocity of surface waves over infinitly deep liquids. In the present paper, a corresponding analogy is found which relates bubble velocities in bounded liquids to wave velocities over liquids of finite depth.
Pool boiling heat transfer to cryogenic liquids; I. Nucleate regime data and a test of some nucleate boiling correlations
Authors: Kosky P. G. , Lyon D. N.
Published: June 2004

Pool nucleate boiling heat transfer curves for pure nitrogen, oxygen, argon, methane, and carbon tetrafluoride have been measured on a horizontal, flat, circular, platinum plated disk for saturation pressures ranging from 1 atm. or less to the immediate vicinity of the critical pressure for each liquid. The results have been compared with various suggested nucleate boiling correlations, and the correlations of McNelly, of Kutateladze, and of Borishanskiy‐Minchenko are found to be roughly equally successful and all distinctly superior to those of Rohsenow, of Gilmour, and of Forster and his collaborators for these liquids. For oxygen, argon, methane, and carbon tetrafluoride, boiling hysteresis of a type not previously reported was observed at intermediate and high saturation pressures on this surface.
Quasilinearization, difference approximation, and nonlinear boundary value problems
Authors: Lee E. Stanley
Published: June 2004

A finite difference method combined with the quasilinearization technique is used to solve the nonlinear two‐point boundary value problems. This method does not have the stability problem connected with the marching integration techniques. A scheme which can be used to reduce the rapid access memory requirements of digital computers is also proposed. The steady state equations resulting from mass and energy balances in a tubular reactor with axial diffusion are solved by this method. With very poor initial approximations, only three to seven iterations are needed to obtain the correct answer.