bluuebunny/crossref_metadata_2025 huggingface dataset:
Self‐diffusion measurements in methane by pulsed nuclear magnetic resonance
Authors: Dawson Rapier , Khoury Fouad , Kobayashi Riki
Published: June 2004

The self‐diffusion coefficient of methane has been measured from 150° to 350°K. and from 200 to 5,000 lb./sq. in. abs. At constant temperature, the density‐diffusivity product is constant up to neighborhood of critical density and decreases sharply above that density. The temperature dependence of the low density data agrees with Chapman‐Enskog theory. The Lennard‐Jones (6‐12) parameters determined from the low density data (ϵ/k = 130°K., σ = 3.85Å.) are in good agreement with those determined by other methods. A correlation for the self diffusion coefficient for methane has been developed which may provide predictions of other spherical nonpolar gases.
Virial coefficients and critical properties of perfluorohexanes
Authors: Taylor Z. L. , Reed T. M.
Published: June 2004

Compressibility measurements of the gas phase are reported for the compounds n‐C6F14, 2‐CF3C5F11, 3‐CF3C5F11, 2,3‐(CF3)2C4F8, and cyclo C6F12. The measurements range from 1 to 18 atm. pressure and from 80° to 180°C. Second and third virial coefficients and critical properties have been calculated and are reported.
The influence of intraparticle diffusion in fixed bed catalytic reactors
Authors: Liu Shean‐Lin
Published: June 2004

By using curve fitting techniques, mathematical formulas are obtained for the catalyst effectiveness factors for nonisothermal first‐order and second‐order irreversible chemical reactions. The effects of intraparticle mass and heat diffusion upon the concentration and temperature profiles in adiabatic and nonadiabatic catalytic reactors are examined. A relation between the maximum interstitial adiabatic temperature and the maximum intraparticle temperature in the reactor is obtained. For some sets of parameters in a nonadiabatic reactor, the concentration and temperature and, consequently, the reactor effluent are sensitive to small changes in the properties of catalyst particles.
Feedforward computer control of a class of distributed parameter processes
Authors: Paraskos J. A. , McAvoy T. J.
Published: June 2004

A finite difference technique has been developed which is suitable for the derivation of feedforward control algorithms for the control of distributed parameter processes. The method embodies both steady state and transient feedforward compensation.

An experimental study, involving closed loop, on line, analogue computer control of a simple distributed parameter process proves the feasibility of the finite difference technique. The process under study is a steam water heat exchanger subject to inlet temperature forcing and controlled by flow rate manipulation. The new technique yielded significantly improved results when compared with the performance of a conventional two‐mode feedback controller, or a linearized feedforward control algorithm.
Forced convection in three‐dimensional flows: II. Asymptotic solutions for mobile interfaces
Authors: Stewart W. E. , Angelo J. B. , Lightfoot E. N.
Published: June 2004

Boundary‐layer solutions are given for heat and mass transfer at mobile interfaces. The results are asymptotically valid for small thermal and material diffusivities, or for short exposure times. Phase breakup and coalescence are formally included, but Marangoni effects are not. Effects of rapid mass transfer, chemical reactions, and variable boundary conditions are evaluated. The treatment is a generalization of the penetration and surface‐renewal theories.
Mass transfer across a nonequilibrium interface
Authors: Dang Vi‐Duong , Gill William N.
Published: June 2004

The problem of mass transfer with nonequilibrium at, and significant convection across, the interface has been studied by the method of matched asymptotic expansions. The inner solution for small values of t or z/Um was found in terms of fk functions which were obtained in closed analytical form. The outer solution for large values of t or z/Um was found in terms of gk functions which had to be determined numerically. With these solutions, calculation of concentratration distributions or instantaneous rates of mass transfer is straightforward, but determination of the total amount of mass transfer as a function of time is complicated by the lack of an intersection wherein the inner and outer solutions overlap and converge. To avoid the need for graphical interpolation and integration of the interfacial concentration as a function of time to obtain the total mass transferred, the constant of integration M1 is found to be (−kγ\documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt \pi $\end{document}/2h) by assuming that the ratio of mass transferred with an equilibrium interface to that with a nonequilibrium interface is independent of whether or not Vy convection is negligible in the system as t → ∞.

The effect of a nonequilibrium interface is greatest for small t in unsteady systems and z/Um in steady state systems. This occurs because the departure from their equilibrium values of the interfacial concentrations of the phases in contact is greatest when they are first brought into contact. The larger the interfacial mass transfer coefficient α, the smaller is the time required for the interfacial concentrations to achieve their equilibrium values.

Other things being equal, the rate of mass transfer is greatest when the driving force xA*‐x is greatest. Since the departure from equilibrium at the interface is greatest for small values of time, it follows that nonequilibrium interfacial phenomena can be observed most easily in systems where the rate of mass transfer is high. This is also the case when one cannot neglect the effect of finite velocity at the interface which is shown in the present work to be a significant effect.

The method of analysis can be used to study a variety of problems in addition to the specific system considered here. In particular, both batch and flow reverse osmosis problems can be attacked by the present approach.
Methanol synthesis catalysis in an internally recycled reactor
Authors: Brown C. E. , Bennett C. O.
Published: June 2004

A gradientless reactor has been tested by measurement of the chemical reaction rate in the synthesis of methanol from carbon monoxide and hydrogen. The reactor behaves as a well‐stirred tank, and data have been obtained at 3,000 lb./sq.in.abs. over the temperature range 300° to 400°C.

Rate data have been obtained for commercial zinc chromite catalyst in particle form and for the commercial ¼‐in. pellets. The effectiveness factors derived from these experiments have been used to estimate the tortuosity of the pellets; it is found to agree qualitatively with the value measured from experiments on pure diffusion in a catalyst pellet.
Rate of coalescence of the dispersed phase in a laboratory mixer settler unit: Part I
Authors: Jeffreys G. V. , Davies G. A. , Pitt K.
Published: June 2004

The rate of coalescence of large swarms of drops of a dispersed phase in the settler of a stage, laboratory mixer settler has been studied in order to establish the parameters that determine the dimensions of settlers used in extraction processes and effluent treatment. Part I is devoted to a description of the apparatus, experimental technique, and presentation of experimental results. Part II describes the development of a mathematical model which has been employed to analyze the results and is submitted as the basis for the design of settlers.
Diffusion in the ternary system d‐tartaric acid—l‐tartaric acid‐water at 25°C
Authors: Bremer M. F. , Cussler E. L.
Published: June 2004

Ternary diffusion coefficients at 25°C. of the system 0.5 g./cc. d‐tartaric acid—0.5 g./cc. l‐tartaric acid‐water are reported. The results allow experimental verification of the theory for the diffusion of two indistinguishable solutes and clearly illustrate the difference between mutual and tracer diffusion. Moreover, the results allow calculation of ternary mass transfer coefficients and ternary tray efficiencies for the case of two similar species dissolved in a third.
Simultaneous noncatalytic solid‐fluid reactions
Authors: Wen C. Y. , Wei L. Y.
Published: June 2004

Solid‐fluid reactions often involve two or more simultaneous reactions because either the feed contains multiple fluid reactants or the fluid products are reactive with the solid. Three types of simultaneous reactions, independent, parallel, and consecutive, are examined in terms of the selectivity and the effectiveness factor based on the unreacted core shrinking model under isothermal conditions. Criteria for high selectivities are derived, and effects of diffusion and chemical reaction are discussed.
Evaporation and drying of drops in superheated vapors
Authors: Trommelen A. M. , Crosby E. J.
Published: June 2004

The evaporation of pure liquid drops and the drying of drops containing suspended and dissolved solids in an atmosphere of superheated vapor were studied. Changes in the weight and temperature of approximately 2 μliter drops of four food products, five miscellaneous materials, and pure water were measured as evaporation and drying proceeded at different drying temperatures. Evaporation of water was found to take place more slowly in superheated steam than in air. However, the medium, in which faster drying occurred, depended upon the material being dried. No major differences between the final products were observed for these two drying media except that some materials yielded denser particles in superheated steam than in air.
Withdrawal of flat plates from power law fluids
Authors: Tallmadge John A.
Published: June 2004

A new one‐term withdrawal expression for power law fluids is developed from theoretical equations. Comparison with film thickness data for three carbopol fluids of α = 1.79 to 2.68 indicates agreement similar to that observed with valid Newtonian theories. The agreement was verified by comparison with independent measurements of entrainment flow rate.
Laminar flow in the entrance region of a cylindrical tube: Part II. Non‐Newtonian fluids
Authors: Sylvester N. D. , Rosen S. L.
Published: June 2004

The laminar flow of dilute aqueous polymer solutions was studied in the entrance region of a cylindrical tube. In laminar, fully developed, steady tube flow, elastic and inelastic fluids were indistinguishable. Viscoelastic fluids exhibited much higher entrance pressure losses than did inelastic fluids with comparable viscous properties. A method has been developed for separating the elastic portion of the overall entrance loss and shows that in some cases the elastic contribution represents as much as 80% of the total. An analysis is also presented which allows calculation of the elastic entrance loss in terms of a Hookean shear modulus.
numerical investigation of free convection between two vertical coaxial cylinders
Authors: Schwab Thomas H. , De Witt Kenneth J.
Published: June 2004

Free convection between two vertical coaxial cylinders was studied by solving the governing transport equations as an initial‐value problem. The coupled, nonlinear, partial differential equations were converted into a set of difference equations by use of an alternating‐direction implicit finite‐difference numerical scheme. Twenty‐four different combinations of Prandtl and Grashof numbers, and height to annular spacing ratios were used to characterize the problem. The results are presented primarily in the form of contour maps for the steady‐state isotherms and streamlines.

For Rayleigh numbers greater than 5 × 103, a fully developed boundary‐layer flow was found to exist in the cavity. The interior region of the annulus was found to be thermally stratified and to possess a nearly uniform vertical temperature gradient, with a unicellular flow pattern being generated.

With Rayleigh numbers of 5 × 104 and greater, it was found that the flow patterns could not be properly described with a grid spacing of 1/10. The variation of the steady‐state mean Nusselt number with Prandtl and Rayleigh numbers and with geometric ratios was also investigated.
Unsteady state behavior of multicomponent distillation columns: Part I: Simulation
Authors: Howard G. Michael
Published: June 2004

A very general form of the basic column equations is presented which allows a wide choice in the form of the specifications of variables required to define the column operation. Variable plate holdups, variable plate efficiencies, heat losses from the column, and finite time liquid flow dynamics are some of the specifications considered. The values of the implicit column variables during the unsteady state period are found by a method which is independent of the numerical procedure chosen to solve the differential equations. Computer runs with the Kutta‐Merson method used to solve the differential equations were made for a column approaching steady state at total reflux. The effect of different variable specifications on this computer column are discussed.
Feedback control of an enriching column
Authors: Shoneman Keith F. , Gerster Jack A.
Published: June 2004

The transient behavior of a 24‐in. diameter, 10‐tray enriching column was investigated experimentally while the column was operated under closed‐loop, feedback control. This behavior was compared with that of a perturbated linear model with the column open‐loop behavior being represented with simple transfer functions in the frequency domain. Comparisons showed that control parameters determined with the predictive linear model were conservative and permitted stable and smooth responses of the experimental column.
Saturated liquid enthalpies of ethane–n‐butane‐n‐pentane system with multicomponent clapeyron equation
Authors: Lee Byung‐Ik , Edmister Wayne C.
Published: June 2004

Enthalpies of the coexisting equilibrium vapor and liquid mixtures of the ethane‐n‐butane‐n‐pentane system are computed at several pressures. Saturated liquid enthalpies are obtained by using a new multicomponent Clapeyron equation with the B‐W‐R equation of state and the experimental temperature‐composition data for the ternary mixture. Saturated vapor enthalpies are calculated by applying the B‐W‐R equation to the vapor mixture. Ideal gas state enthalpies are used in both vapor and liquid enthalpy calculations.
Green's functions for the Graetz problem and interfacial concentrations
Authors: Gidaspow Dimitri
Published: June 2004

Green's functions for various Graetz problems are identified. Multiple forms of Duhamel's formula with improved convergence were obtained, using particular solutions to unit flux, linear prescribed flux, and similar problems. The method makes it possible to quickly calculate interfacial concentrations from a knowledge of outlet concentrations at several flow rates. The analysis is illustrated with experimental combustion data from a tubular reactor.
Optimal control policies for tubular reactors experiencing catalyst decay. Part 1. Single bed reactors
Authors: Ogunye A. F. , Ray W. H.
Published: June 2004

The optimal control problem is formulated, and a weak maximum principle for such distributed parameter systems is derived. From this principle an efficient computational algorithm is presented which allows the simultaneous solution of the problems of both catalyst distribution (along the reactor) and optimal control. Detailed numerical examples are worked for isothermal reactors, adiabatic reactors, and adiabatic reactors with both a catalyst distribution problem and an optimal control problem. For irreversible reactions constant conversion policies are found to be optimal a significant portion of the time.
Mass transfer and drag coefficients of bubbles rising in dilute aqueous solutions
Authors: Raymond Delmar R. , Zieminski Stefan A.
Published: June 2004

The effects of aliphatic alcohols on mass transfer and drag coefficients of a carbon dioxide bubble were investigated in very dilute aqueous solutions. A high speed photography technique provided an almost continuous record of the bubble volume, shape, and oscillation, as related to the height of the bubble in the liquid and the time elapsed from the moment of its release. The results showed that the concentration, molecular size, and structure of the investigated alcohols have a pronounced effect on mass transfer as well as drag coefficients of the rising bubble. The significance of these effects with respect to idealized models of a highly circulating bubble and a solid sphere was considered, and a functional relationship was found to exist. This relationship may be applied to systems more complex than a single bubble.
Vapor‐liquid phase behavior of the hydrogen‐propane and hydrogen‐carbon monoxide‐propane systems
Authors: Trust D. B. , Kurata F.
Published: June 2004

Vapor‐liquid equilibria data for the hydrogen‐propane binary system and the hydrogen‐carbon monoxide‐propane system were taken at temperature of −185° to +75°. and under pressures as high as 3000 psi. Vapor‐liquid data for the hydrogen‐carbon monoxide‐propane system are reported at −50°, 0°, and +50°. at pressures of 500, 1000, and 2000 lb./sq.in. abs. for each of the three temperatures. The Krichevsky‐Kasarnovsky equation adequately correlated the solubility data of hydrogen in the liquid phase of the hydrogen‐propane system. Hydrogen‐propane data are compared with the data of two previous studies.
Stretching of viscoelastic liquids
Authors: Denn M. M. , Marrucci G.
Published: June 2004

Analyses of stretching of a viscoelastic liquid have been interpreted as showing that there is a maximum stretch rate to which the material can be subjected, and several physical phenomena have been explained on this basis. It is shown here theoretically and experimentally that the concept of a limiting stretch rate does not have general validity.
A stochastic model of packed‐bed mixing and mass transfer
Authors: Schmalzer D. K. , Hoelscher H. E.
Published: June 2004

A new model of packed‐bed behavior based on a second‐order stochastic process is developed and examined. The model takes as the basis process the transitions of fluid “packets” among allowed velocity states. The observable phenomenon, that is, the spatial distribution of packets, is a projection of the velocity state process.

Results from the model compare well with results from experiments for mixing in packed beds. Model parameters are consistent, and correlate with the physical parameters of the systems. Present results under mass transfer conditions are inconclusive but encouraging.
Trajectory optimization techniques in chemical reaction engineering: I. Boundary condition iteration methods
Authors: Jaspan R. K. , Coull J.
Published: June 2004

A new generalization of boundary condition iteration (BCI) methods is developed, based on a suggestion of Denn and Aris. This simplifies to Horn's equation for up to two state equations and to previous boundary iteration methods when

is explicitly soluble for

as a function of the constants, the state and the adjoint variables. The new general method is also applicable when this latter function is unobtainable.

Distinct improvement in the convergence rates of the existing BCI methods has been obtained through the introduction of a correction specific to each state variable.

A convergence procedure for use with Horn's equation is proposed and the resultant algorithm has desirable properties.
Liquid bridges between cylinders, in a torus, and between spheres
Authors: Erle Michael A. , Dyson D. C. , Morrow Norman R.
Published: June 2004

The stability of a capillary liquid bridge of given volume between two small, solid, equal, separated spheres is investigated by formulating and treating a minimum energy problem in the calculus of variations and by experiment. A conjecture is made that in the case of two solutions one and only one is minimizing, and that the case of one solution represents the limiting stable bridge. This theory agrees accurately with our stability experiments. Furthermore, it is possible to predict the cohesive force. For the case of spheres in contact, the theory presented here is in agreement with some experimental work and also with the theory of Fisher and calculations of cohesive force based on Melrose and Wallick's solution to the bridge problem. For the case of separated spheres, the agreement with the only available experimental data is excellent except for close separations.
Bubble growth by coalescence in gas fluidized beds
Authors: Argyriou Dimitris T. , List Harvey L. , Shinnar Reuel
Published: June 2004

Bubble size and distribution of bubble sizes were studied in an air fluidized bed, 11.5 in. in diam. and 3 ft. high, by taking motion pictures of the bubbles breaking the top surface of the bed and by determining the size of the bubbles from the film. The distribution of bubble volumes at a given bed height was expressed as a gamma distribution with parameters obtained from the observations. A statistical mechanical method proposed by Hulburt and Katz for studies in agglomeration of particles was used in the mathematical formulation of the problem. A proposed mechanism of bubble growth by coalescence in gas fluidized beds resulted in a one parameter model. Comparisons of the distributions predicted by the model to the experimentally obtained profiles yielded the parameter of the model.
Interfacial mass and heat transfer during evaporation: I. An experimental technique and some results with a clean water surface
Authors: Navon Uri , Fenn John B.
Published: June 2004

A vacuum sweeper probe of a type introduced by previous investigators was evaluated for use in the study of heat and mass transfer during evaporation. A simple theory of the probe behavior was formulated and checked by experimental measurements over a substantial range of operating conditions. The results revealed that in the interpretation of experimental data the validity of some assumptions usually made is strongly dependent upon seemingly minor features of probe construction and operation. Errors as large as 200% were encountered when the gas flow distribution in the probe was not symmetrical. Consequently, some results now in the literature are open to question.

To test the technique and theory as well as to introduce a subsequent study of the effect of monolayers on evaporation, the evaporation rate from a clean water surface was measured over a temperature range of 2° to 22°C. The role of natural convection was clearly reflected in the increase of Nusselt number as the water bulk temperature passed through the density inversion at 4°C. A relation between Nusselt and Rayleigh numbers was determined and found to be consistent with earlier results of others.
Multicomponent separation calculations by linearization
Authors: Naphtali Leonard M. , Sandholm Donald P.
Published: June 2004

A new approach to separation calculations has been developed which has many practical advantages. The equations of conservation of mass and energy and of equilibrium are grouped by stage and then linearized. The resulting set of equations has a block‐tridiagonal structure which permits solution by a simple technique. Thus a new way to apply the Newton‐Raphson technique to separation calculations is devised. The method has been tried on a number of problems chosen to exhibit characteristics which cause other solution technique to fail. Most problems are solved with ten iterations or less.
Transient creeping flow around fluid spheres
Authors: Sy Francisco , Lightfoot E. N.
Published: June 2004

A description of transient behavior of a spherical liquid drop rising or falling in a quiescent continuous field has been obtained by numerical methods. It is found that for the same disperse phase to continuous phase density ratio, the transient behavior of a liquid drop is usually intermediate between that of a gas bubble and a solid sphere. However, at the region where V/V∞ of a solid sphere is approximately equal to that of a gas bubble, the liquid drop generally has a higher value of V/V∞ than either the gas bubble or the solid sphere.

For short times, behavior of a liquid drop is shown to be in agreement with that obtained from potential flow theory.
Laminar dispersion in Jeffery‐Hamel flows: Part I. Diverging channels
Authors: Gill William N. , Güceri Ülkü
Published: June 2004

Dispersion in flow in diverging channels, where the velocity decreases with axial distance is studied. Numerical experiments indicate:

At sufficiently large values of the angle of divergence and Peclet number, both axial and transverse molecular diffusion play minor roles in the dispersion process, and the system is dominated by convection. This is in marked contrast to parallel wall systems.

A dispersion model, given by Equation (15), is shown to exist for such flows for limited ranges of the Peclet number and angle of divergence.

At sufficiently large values of dimensionless time, the dependence of concentration on both axial position and time can be represented by a single similarity coordinate. This behavior is predicted by both the numerical solutions of Equation (3) and analytical solutions of the dispersion model.
On the thermodynamics of nonuniform systems
Authors: Metiu H. , Ruckenstein E.
Published: June 2004

Two methods are presented for the treatment of the nonuniform systems. Both have as a starting point the approximation of the real system by a succession of uniform systems (cells). In one of them, the nonuniformity is taken into account by attributing a free energy to the separating surfaces between the cells, while in the other by considering that the cells are under the action of an “external field” created by the nonuniformity.

A distinction between small and large nonuniform systems is made by comparing the thickness of the nonuniform system with the length of the interval in which the nonuniformity is decaying. For small systems the intensive properties depend on the thickness of the system and thus some supplementary effects, as for instance the disjoining pressure, occur.

An expression for the “external field” based on the formalism of the radial distribution function is proposed.

A large number of phenomena, such as surface tension, adsorption, disjoining pressure, nucleation, the vapor pressure of a liquid imbibing a porous medium, the influence of a solid surface upon a chemical reaction, are treated in a unitary manner by means of the present approaches.

Some previous equations such as those of Cahn‐Hilliard and of Hill are derived in a different manner or justified.

The objections raised by Widom against the continuous approaches are discussed.
A Lagrangian algorithm for equality constrained generalized polynomial optimization
Authors: Blau Gary E. , Wilde Douglass J.
Published: June 2004

A procedure for optimizing generalized polynomial functions occurring widely in engineering design problems is presented. Equality constraints of the same form can be handled. The technique involves driving to zero the gradient of a Lagrangian function by a Newton‐Raphson method. A nonlinear transformation so simplifies the derivatives needed for Newton‐Raphson iteration that they are given in closed form. The initial estimate needed to start the algorithm need not be feasible. Successive systematic adjustment of Lagrange multipliers is accomplished, and an unambiguous procedure for starting multipliers is given. All implicit computations are linear. Convergence is not proven, but successful computational results for the design of a reactor exchanger pump system in eight variables and with five constraints are presented.
Catalytic reduction of nitric oxide with various hydrocarbons
Authors: Ault J. W. , Ayen R. J.
Published: June 2004

Conversion data for the reduction of nitric oxide with C1 to C8 hydrocarbons over a bariumpromoted copper chromite catalyst were obtained in an integral flow reactor operated at atmospheric pressure and temperatures of 225°C to 525°C. In general, an increase in carbon number in the hydrocarbon studied resulted in a decrease in the required temperature for a given nitric oxide conversion. For a given carbon number the required temperature for a given nitric oxide conversion decreased with degree of saturation. The data were fitted to empirical rate expressions.
Thermal conductivity of mixtures of argon‐helium, argon‐nitrogen, and argon‐neon
Authors: Peterson Jon N. , Hahn Thomas F. , Comings E. W.
Published: June 2004

A secondary concentric cylinders cell was used to measure the thermal conductivity of binary mixtures of argon‐nitrogen, argon‐helium, and argon‐neon approximately 20, 40, 60, and 80 vol. % at 75°C, and pressures to 2,800 atm. Measurements were made also on the pure gases argon and nitrogen.
Van der Waals forces in a three‐phase system
Authors: Sherony D. F. , Kintner R. C.
Published: June 2004

An analysis is made of the Van der Waals forces of two different species when separated by a third continuous component. Results show that under certain circumstances, attractions as well as repulsions can exist between the two different species. The theory is applied to a fibrous bed coalescer to determine what type of material would best serve as a coalescence medium.
Transient flow in the hydrodynamic entrance regions of long closed ducts
Authors: Downing Carl G.
Published: June 2004

Velocity profiles were calculated for transient fluid flow in the hydrodynamic entrance regions of a long narrow slit and of a long tube. The solutions were obtained by use of a linearized momentum equation. An estimate was also made of the manner in which the resistance to flow of the entrance region develops with time.
Multiparameter adaptive process control via constrained objective functions
Authors: Ryan Philip J. , Crandall Edward D.
Published: June 2004

A method has been developed for applying classical minimization techniques to forms of algebraic performance indices for use in optimal adaptive control systems. Essentially, the derivative of a general objective function is constrained to be equal to the integrand of a desired integral performance index. This generates a set of linear algebraic equations, the solution of which results in an algebraic objective function which is explicit in the system parameters. Derivatives of this function can be taken with respect to the controllable parameters, set equal to zero, and solved for the settings which minimize the performance index over time. Alternatively, the function itself may be searched for its minimum on the controllable parameters.

The method has been applied to a stirred tank chemical reactor with an exothermic first‐order reaction in which heat removal was accomplished by cooling coils. The cooling water flow rate was controlled by a proportional‐plus‐integral controller and by a three‐mode controller. The adaptive control system adjusted the controller settings periodically. The plant, which was third‐order, was controlled to a second‐order dynamic reference model. The responses to both initial offsets (start‐up problem) and disturbances in system parameters were investigated. In all cases, the adaptive control system performance was markedly superior to that for the unadapted, ordinary feedback control system.
Turbulent momentum transfer in two‐phase cylindrical Couette flow
Authors: Gandhi Ravi , Estrin Joseph
Published: June 2004

Torque measurements were made in experiments carried out using a cylindrical Couette apparatus with the inner cylinder rotating and the outer one stationary. The fluid systems employed consisted of distilled water, 50% distilled‐water glycerine solutions, and these with several concentrations of suspended polystyrene spheres (through 40 on 70 mesh). The parameters employed by Bjorklund and Kays were found to correlate the data successfully when suspension viscosities were used for the two‐phase systems.
Fugacity and vapor pressure of nonpolar liquids at low temperatures
Authors: Chao K. C. , Greenkorn R. A. , Olabisi Olagoke , Hensel B. H.
Published: June 2004

Available generalized correlations of fugacity coefficients of nonpolar liquids are reexamined in their lower temperature ranges, and these correlations are extended to a reduced temperature of 0.35. Generalized functions are constructed from literature data on vapor pressures and liquid densities. Two sets of functions are presented with w and zc, respectively, as third parameter. The results fulfill a need for basic information in the engineering of cryogenic systems.

The same vapor pressure data are correlated in a generalized form down to Tr = 0.35 to give a one‐parameter family of reduced vapor pressures curves. The correlation is compared with data on simple fluids, normal fluids, polar substances, and quantum fluids.
Diffusion and reaction in ideal multicomponent systems: II. Behavior away from equilibrium
Authors: Solomon R. L. , Hudson J. L.
Published: June 2004

An analysis is made of diffusion and chemical reaction in an isothermal multicomponent fluid. Transient gas‐phase reaction in a one‐dimensional nonflow system and steady state gas‐phase or surface reaction in a tubular reactor are considered. The equations are linearized around some state away from equilibrium. Multicomponent and binary diffusivity expressions are used and a series of reactions of varying complexity is considered. The possibility of oscillations increases as the complexity of the reactions is increased. These oscillations occur with time in the nonflow system and with space‐time in the tubular reactor, and it appears that any reacting mixture which oscillates in one of these two systems will also oscillate in the other.
Sufficiency conditions for constrained extrema
Authors: Law Victor J. , Fariss Robert H.
Published: June 2004

Sufficiency conditions for equality constrained extrema are formulated in terms of a transformed set of coordinates by means of a generalized inverse of the constraint Jacobian matrix. This procedure produces a computationally simple and efficient method for testing sufficiency of a previously established stationary point. Computation of Lagrange multipliers is also facilitated by the method.
Rates of sorption and diffusion of hydrocarbons in zeolites
Authors: Riekert Lothar
Published: June 2004

The kinetic patterns of sorption, desorption, and sorbate exchange have been studied for several C2‐C5 hydrocarbons in synthetic zeolites of the mordenite, T and Y structures. The rate observations can best be represented by a model of sorption on interstitial sites in the solid, rather than by a model based on the analogy with macroporous sorbents. Two cases of interstitial diffusion have to be distinguished for this purpose. The number of vacant sites changes in time during the process of sorption, whereas it can remain constant if one sorbate is exchanged against another one. Rate measurements for both types of processes are reported and their interrelation is discussed.
Mass and energy transfer between a confined plasma jet and a gaseous coolant
Authors: Smith Dean L. , Kadlec Robert H. , Churchill Stuart W.
Published: June 2004

Mass and energy transfer between confined plasma and coolant gas streams was studied experimentally. Argon was used as the plasma gas and nitrogen was used as the coolant gas. The temperature profiles present in the mixing region were determined by optical‐spectrographic methods. Both the electronic excitation temperature of the argon atoms and the rotational temperatures of the nitrogen molecules were determined. The compositions and axial velocities present in the plasma coolant mixing region were determined by sampling probe methods.

The measured nitrogen temperatures were found to be much lower than the argon temperatures present at the same point in the flow. The difference could be explained on the basis of incomplete mixing and thermal equilibration on the microscopic scale. The composition profiles indicated that direct induction of coolant into the high‐velocity plasma jet and the formation of a recirculation eddy increased the mixing of plasma and coolant.

From the standpoint of carrying out a chemical reaction in the plasma jet, the results indicate that the mixing of a reactant injected into a plasma jet reaction chamber with the plasma would be very rapid but that the internal energy modes of the reactant molecule might not be fully excited during the short residence time in the high‐velocity flow.
Mathematical model of heavy water extraction and distillation
Authors: Burgess M. P.
Published: June 2004

A mathematical model of the heavy water production facility at the Savannah River Plant, an installation of the U.S. Atomic Energy Commission at Aiken, South Carolina, operated by E. I. du Pont de Nemours and Company, was developed because measured production rates, even when averaged over one‐month periods, are inadequately precise for process control. With this model the instantaneous steady state production rate for any set of process conditions is calculated with precision. Therefore the model is used to establish process set points for achieving production goals, to study the effect of important process variables on these goals, and to evaluate proposed changes of equipment. In fact, with only minor changes in the computer program, several features of a newly designed heavy water plant are being evaluated.
Absorption and desorption accompanied by a reversible reaction
Authors: Porter K. E. , Cantwell A. D. C. , McDermott C.
Published: June 2004

The processes of absorption and desorption with reversible reaction are compared theoretically for reactions of the type A ⇌ nB. With the same concentration difference between bulk and interface, it is found that in general, the rate of desorption is lower than that of absorption. Under certain conditions the difference may be as much as 35%.

The analysis is based on the penetration theory. The numerical solution introduces a new transformation of the time and distance variables (based on the error function) which reduces the computing time required. An analytical examination of the penetration theory equations provides an explanation of the results of the numerical solution.
Correlation of second virial coefficients through potential function parameters
Authors: Kunz Robert G. , Kapner Robert S.
Published: June 2004

An analytical technique based on the method of least squares has been developed to fit experimental second virial coefficients to the functional form derived from the Lennard‐Jones (6–12) potential. Both the functional form and the normal equations of the least squares fit are rigorously derived. Because of the implicit, nonlinear dependence upon one of the adjustable parameters, a computer solution of the normal equations is required. Second virial coefficient data for a large number (60) of materials, including hydrocarbons, halides, alcohols, and cyclic compounds, have been extracted from published sources, carefully evaluated for consistency, and fitted to the Lennard‐Jones potential function.

Force constants for these materials as determined from fitting the data in this uniform manner have been found to be related to structural parameters. The final correlation, with the potential well‐depth related to critical temperature and the collision diameter calculated from a set of group contributions with appropriate corrections for polarity and/or association, produces average deviations between computed and experimental second virial coefficients of 10 to 15% or 100 cc./g.‐mole, whichever is greater. In many cases the agreement is much better.
Induced transport in pulsating flow
Authors: Horn F. J. M. , Kipp R. L.
Published: June 2004

The dispersion coefficient is evaluated in a general linear chromatographic system in which the velocity field is time periodic. Computations are carried out in detail for two examples. In the first example there are two phases and the flow pattern is simple. In the second example there is only one phase and the flow pattern is complex. The latter example is closely related to Taylor diffusion. Depending on the relative size of certain dimensionless parameters, one can distinguish four regions of different qualitative behavior of the system: molecular diffusion region, Taylor region, constant amplification region, and boundary transport region.
Synthesis of system designs: III. Toward a process concept generator
Authors: Siirola J. J. , Powers G. J. , Rudd D. F.
Published: June 2004

Principles are developed for the computer‐aided generation of initial process flowsheets. The invention of a process concept is analogous to the proof of a multihypothesis/multiconclusion theorem, a mental activity which has been simulated on the computer. Techniques of artificial intelligence are combined with the concept of equivalence class matching and information flow logic to develop a working, computerized process synthesizer. This is part of a continuing project on the development of principles of process invention.
Confined jet mixing in the entrance of a tubular reactor
Authors: Seider Warren D. , Churchill Stuart W.
Published: June 2004

The equations for the conservation of momentum and mass were solved numerically for the region downstream from the exit of an axial jet into a confined annular stream of the same fluid. An implicit, alternating direction method was used. Numerical results were obtained for radius ratios of 0.281, 0.470, and 0.563 over a range of jet‐to‐annular velocities from 0.85 to 2.77. The values for the limiting case of the entrance region in pipe flow are in good agreement with the values of Christiansen and Lemmon and Ventras, Duda, and Bargeron. Solution of the equations for the conservation of chemical components produced results for component transfer in agreement with the experimental compositions obtained by Wood for jet mixing. Representative calculations were carried out for a chemical reaction. The results indicate the efficiency of the mixing process for this type of reactor.

Experiments were carried out with water and dye to define the conditions under which the assumption of steady, laminar jet mixing is valid. The experiments also indicated the conditions and location of turbulent breakup of the jet.
Mixing and product distribution for a liquid‐phase, second‐order, competitive‐consecutive reaction
Authors: Paul Edward L. , Treybal Robert E.
Published: June 2004

Mixing effects for the homogeneous, liquid‐phase, second‐order, competitive‐consecutive reaction of iodine (B) with L‐tyrosine (A) to form 3‐iodo‐L‐tyrosine (R) and 3,5‐diiodo‐L‐tyrosine (S) were determined for the following conditions: vessel volume, 5 and 36 liters (baffled and unbaffled); turbine diameter (2 to 6 in.) and speed (95 to 1,600 r.p.m.); feed inlet locations (3), addition rate (0.25 to 18 min.), and distribution; temperature (11° to 43°C.); initial A concentration (0.1 to 0.4 g.‐mole/liter); and kinematic viscosity (0.765 to 6.35 centistokes). A was initially charged to the reactor and an equimolar quantity of feed B was added over a time period. Yields of R are less than that expected for perfect mixing owing to local regions of excess B concentration that exist for time periods during which R over‐reacts to S.

Agitation power for a given yield is less in unbaffled vessels without an air‐liquid interface than for baffled vessels. The local fluctuating velocity u′ where feed is introduced correlates the mixing variables and predicts mixing requirements for maintaining yields of R on scale‐up. Regions of excess B concentration are related to a concept of partial segregation. The extent of reaction occurring under this condition is correlated by the dimensionless group (k1bτ) (a0/b), where τ is a microtime scale of mixing related to u′ and the characteristic length of a microscale eddy. The magnitude of this group provides a criterion for predicting the importance of mixing effects on other reaction systems.
Flow of dilatant (shear‐thickening) fluids
Authors: Griskey Richard G. , Green Richard G.
Published: June 2004

The conduit laminar flow of dilatant (shear‐thickening) fluids was investigated. It was found that such flow agreed with the Metzner‐Reed (friction factor‐modified Reynolds number) correlation previously verified only for pseudoplastic fluids. The agreement was found to hold even for cases where the flow behavior index was 2.0 or greater, which caused the velocity term V in the modified Reynolds number Dn′ V2−n′/gc8n−1 K′ to be raised to the zero or a negative power. It was also demonstrated that conduit laminar flow for dilatant (shear‐thickening) fluids could be described solely with the Metzner‐Reed correlation and rheological data taken with a small‐scale laboratory viscometer. Studies of flow through fittings (90‐deg. elbows, globe valves, and couplings) showed a definite effect for non‐Newtonian fluids contrary to previous reports for pseudoplastics which indicated essentially Newtonian behavior.
Effect of dissipation and compression work on the eddy conductivity calculated from experimental temperature data for gases
Authors: Blanco Jose A. , Gill William N.
Published: June 2004

The effect of dissipation and compression work on the eddy conductivity calculated from experimental temperature distribution data for gases is examined in detail, and it is shown that these effects are significant even in relatively low Reynolds number flows, say greater than 30,00. The inclusion of dissipation and compression work in the energy equation for gaseous flows is shown to lead to the determination of symmetrical eddy diffusivities from experimental data.
Experimental heats of mixing for gaseous nitrogen and methane
Authors: Klein R. R. , Bennett C. O. , Dodgge B. F.
Published: June 2004

The excess enthalpy of binary gas phase mixtures has been measured by direct experiment, using a continuous flow, isothermal colorimeter. Heat of mixing data are presented for the methane‐nitrogen system for compositions of 25 to 80 mole % methane in nitrogen, at temperatures of 40°, 0°, −20°, −40°, −60°, and −78°C. and pressures from 250 to 1,50 lb./sq. in. abs. These data are in agreement with the literature to within the experimental uncertainty of this work, 4%.

The experimental results agree well with values predicted using the Benedict‐Webb‐Rubin and the Redlich‐Kwong equations of state. The virial equation of state truncated after the third coefficient fits the low density data only. The liquid theories of Scott predict the enthalpies of the mixtures in a qualitative way.
Langmuir‐hinshelwood kinetics of the dehydration of methanol catalyzed by cation exchange resin
Authors: Gates B. C. , Johanson L. N.
Published: June 2004

Rates of the dehydration of methanol to dimethyl ether catalyzed by cation exchange resin (polystyrenesulfonic acid) were measured with a differential flow reactor and gas chromatographic analysis. Reaction temperature was 119°C., pressure was 1 atm., and feeds were methanol and mixtures of methanol with argon, dimethyl ether, and water.

Rata data for the methanol reaction as well as the previously investigated ethanol dehydration reaction are well represented by Langmuir‐Hinshelwood kinetics with adsorption parameters in the rate equations approximately equal to corresponding values of Langmuir adsorption equilibrium constants estimated from or available in the literature. The reaction model is consistent with previous conclusions regarding mechanism. Its pertinence suggests that at reaction conditions the ion exchange resin offers a nearly homogeneous array of catalytic sites.