bluuebunny/crossref_metadata_2025 huggingface dataset:
Nucleate and film pool boiling of ethane‐ethylene mixtures
Authors: Wright R. D. , Clements L. D. , Colver C. P.
Published: June 2004

Experimental results are presented for saturated nucleate and film pool boiling heat transfer to ethane, ethylene, and three binary ethane‐ethylene mixtures containing approximately 25, 50, and 75 mole % ethylene. Data were obtained at reduced pressures from 0.05 to 0.75. The nucleate boiling data are compared with several predictions; the film boiling data are favorably compared with the Sciance, Colver, and Sliepcevich correlation.
Suboptimal control of nonlinear systems: II. Constrained
Authors: Weber A. P. J. , Lapidus L.
Published: June 2004

The previous development in suboptimal control of nonlinear unconstrained systems is extended to constrained systems by the use of penalty functions in an augmented sense. This converts the constrained control problem into an unconstrained one with all of the advantages previously discussed. Numerical examples are presented.
Mass transfer with homogeneous chemical reaction in turbulent pipe flow
Authors: Randhava S. S. , Wasan D. T.
Published: June 2004

Mass transfer with chemical reactions in fully developed turbulent pipe flows has been studied theoretically. The pipe walls are assumed to remain at a constant prescribed concentration. The effect of arbitrary reaction orders and of Reynolds and Schmidt numbers upon the transfer coefficients was investigated. Radial and longitudinal concentration profiles were obtained to show the effect of reaction orders and dimensionless rate constants. Effects of concentration levels on these phenomena were also studied and proven significant. The ratio of the transfer coefficients with chemical reactions to those without chemical reactions increases as a function of the downstream aspect ratio.
Linear analysis of liquid film flow
Authors: Rushton Eric , Davies Graham A.
Published: June 2004

Analyses of the flow of thin Newtonian liquid films over vertical plane surfaces at low Reynolds number in the wavy flow regime have been considered. The results of a linear analysis of the equations of motion, seeking a steady periodic solution to characterize the wave profile, are presented. The solutions derived in this work give better agreement with experimental results than previously published solutions using a linear analysis. Predictions of the wave properties (wave celerity, wave number, and wavelength) as functions of the flow conditions are derived from the theory.
Measurement of velocity in gas mixtures: Hot‐wire and hot‐film anemometry
Authors: Wasan D. T. , Baid K. M.
Published: June 2004

This paper extends the use of hot‐wire and hot‐film anemometry to the measurement of velocities in gas mixtures. It is demonstrated that the velocity data in binary gas mixtures can be satisfactorily predicted by calibration tests in pure systems alone or at any two convenient composition conditions. Furthermore, the actual transport properties of a fluid mixture may be inferred from direct calibrations of hot‐wire, or hot‐film anemometers in the mixture with known compositions.
An exact analysis of low peclet number thermal entry region heat transfer in transversely nonuniform velocity fields
Authors: Hsu Chia‐Jung
Published: June 2004

A theoretical method is described for obtaining the exact solution to the problem of thermal entry region heat transfer which takes into account both transverse non‐uniformity in the velocity field and axial conduction. To allow for the effect of upstream conduction, the fluid temperature was taken to be uniform at × = – ∞, and the first 20 eigenvalues and the corresponding eigenfunctions were determined separately for the heated and adiabatic regions. Both the temperatures and temperature gradients were then matched at × = 0 by constructing a pair of orthonormal functions from the nonorthogonal eigenfunctions.

Nusselt numbers calculated for pipe flow subject to the boundary condition of uniform wall heat flux show virtually perfect agreement with those reported recently by Hennecke, who solved the governing partial differential equation numerically. To illustrate its general applicability, the present method was further employed to analyze the corresponding problem in parallel‐plate channel flow, for which no solution has hitherto been reported.
The role of wakes in the mechanism of extraction in spray columns
Authors: Kehat Ephraim , Letan Ruth
Published: June 2004

Extraction in spray columns is reexamined in view of recent information on wakes of drops and the role of wakes in the mechanism of heat transfer in spray columns. In the proposed mechanism, mass is extracted from a highly mixed drop to a highly mixed wake in the wake growth zone. Elements of wakes are shed, mixed with continuous phase, and are replaced by the continuous phase in the wake shedding zone. A narrow mixing zone exists at the entrance of the continuous phase and above it the coalescence zone.

A mathematical model for extraction in spray columns is presented. This model was used to calculate the top concentrations from the bottom concentrations, for 258 runs from nine papers covering very wide ranges of columns, systems, and operation parameters. Better than 20% agreement was obtained for 10 runs and the poorer agreement of most other runs can be attributed to the sensitivity of the calculations to the uncertainties in the average distribution coefficients of the solute between the two liquid phases, and, to a lesser extent, to the uncertainties in the length of the wake shedding zone and wake parameters. For very large or very small values of the distribution coefficient, the assumption of local equilibrium between drop and wake, used in the model, does not hold.
Concentration distribution, effectiveness factor, and reactant exhaustion for catalytic reaction with volume change
Authors: Lin Kan , Lih Marshall M.
Published: June 2004

Analytic expressions for the concentration distribution of reactant and for effectiveness factor have been obtained for zero‐order catalytic reactions of the type A → bB. They can be summarized for various physical forms of catalyst to be

and

where

, and Mi are differently defined for thin‐disk (i = 1), infinite‐cylinder (i = 2), and spherical (i = 3) geometries. The results are also presented graphically for rapid calculation of these quantities. The phenomenon of reactant exhaustion associated with a zero‐order reaction and the criteria for its occurrence are also discussed.
Nucleation and crystal proliferation kinetics: Amorphous‐crystalline transformation of basic copper carbonates
Authors: Hsu Andrew C. T.
Published: June 2004

The transformation of amorphous basic copper carbonate precipitates into the crystalline form in aqueous solutions was experimentally studied. The unique blue‐to‐green color change and drastic volume reduction of the precipitates in transition made continuous observation and quantitative determination of the transformation process feasible. The transformation, which involves both nucleation and crystal growth proliferation, was autocatalytic. Experimental results are in good agreement with the rate equation formulated on the two‐stage kinetics model postulated for the system. Also studied were the effects of temperature and precipitate concentration on the rate of transformation. In the temperature range between 34° and 39°C., the apparent nucleation activation energy was 19.8 kcal./g.‐mole.
Optimal operation of a tubular chemical reactor
Authors: Newberger Mark R. , Kadlec Robert H.
Published: June 2004

A theoretical and experimental study was conducted on the optimal steady state operation of a jacketed, tubular, liquid‐phase reactor in which consecutive second‐order reactions occurred in turbulent flow. To verify the proposed mathematical model, diethyl adipate was saponified with sodium hydroxide in aqueous solution. The 150 ft. long reactor jacket was divided into 5, 30 ft. sections. Hot water flow rates in the jacket sections were chosen to maximize the concentration of monoethyl adipate ion at the reactor exit. The plug‐flow model and a position‐dependent heat transfer coefficient accurately described temperature and concentration profiles. The Pontryagin maximum principle was used to choose idealized reactor temperature and wall heat flux profiles which would maximize the exit concentration of monoester. The maximum principle was shown to be an effective tool for this type of reactor optimization. A technique is given for optimizing more complex reaction systems.
A study of unidirectional versus tridirectional heat flux models and the effect of particle size on heat conduction in composite solids
Authors: Fidelle Thomas P. , Kirk R. S.
Published: June 2004

The effect of the assumption of unidirectional heat flux was determined for a well‐known unit cell model used to predict effective thermal conductivities of particulate composites. Predictions obtained for the condition of unidirectional heat flux were compared with those obtained for the more rigorous case of tridirectional heat flux. The latter case required a digital simulation of the model to obtain three‐dimensional temperature distributions. Comparisons were made for two different values of pure component thermal conductivity ratio and for a broad range of phase compositions. Results in each case suggest that the unidirectional heat flux assumption is not a serious limitation.

Experimental studies were made of the effects of composition, particle size, and pure component thermal properties on the effective thermal conductivity of three different composite systems. Cylindrical samples of each system were cast from various proportions of their basic constituents. Effective thermal conductivities were calculated from effective thermal diffusivities. The latter were obtained experimentally from the thermal response of the center of each composite sample as it was cooled from room temperature to 0°C. by means of an agitated ice bath. Effective conductivities so obtained were compared with conductivities predicted by the tridirectional simulation and three previously published models. Results show that a recent model that utilizes unidirectional heat flux but permits random phase distribution provides the best predictions of the experimental data presented in this work.

Results of the particle size study indicate that there is a minimum ratio of system dimension to particle dimension below which a particulate composite can no longer be considered macroscopically homogeneous and isotropic.
Boundary‐layer flow on a rotary vane
Authors: McCarthy H. E. , Olson J. H.
Published: June 2004

The boundary‐layer flow on a rotating vane is investigated with the integral momentum approximation. A parabolic velocity profile is approached over a significant portion of the vane. The assumption of a parabolic velocity profile yields a closed analytical solution for the radial dependence of the surface velocity. Experimental data obtained agree with the predicted average velocity at the exit of the vane.
The motion of vapor bubbles growing in uniformly superheated liquids
Authors: Pinto Yuda , Davis E. James
Published: June 2004

The motion of simultaneously rising and growing vapor bubblesin a uniformly superheated liquid is analyzed, and the predicted bubble velocities are shown to be in good agreement with available data. Using a quasisteady state approximation to describe the drag, and existing bubble growth theory to describe the growth rate, the equation of motion is solved for two ranges of bubble size encountered in nucleate boiling. For smaller bubbles (R<0.04 cm.) an analytical solution is obtained, and for larger bubbles (R>0.07 cm.) a numerical solution and analytical asymptotic solutions are obtained.
The stability and dynamic behavior of a continuous crystallizer with a fines trap
Authors: Lei Shang‐Jen , Shinnar Reuel , Katz Stanley
Published: June 2004

Working equations are developed for the operation of a continuous crystallizer with a fines trap. A linearized stability analysis reveals that proper operation of the fines trap can stabilize the crystallizer at large crystal product sizes that would otherwise lead to instability. Dynamic studies for the full nonlinear equations are carried out numerically, and stable limit cycles are exhibited around unstable equilibrium points.
Removal of colloidal pollutants by microflotation
Authors: Cassell E. Alan , Matijevíc Egon , Mangravite Francis J. , Buzzell Timothy M. , Blabac Stephen B.
Published: June 2004

The removal of various colloids (humic acid, silica, polystyrene latex, and bacteria) by microflotation in the presence of aluminum salts has been studied as a function of pH. The conditions for efficient separation have been correlated to the stability of these colloids, and it was shown that in all cases rapid flotation occurred when the aluminum salt concentration and the pH adjustment rendered the sols unstable. Particularly high removals were observed over the pH range of aluminum hydroxide floc formation. Microflotation could be utilized as a nonspecific method for simultaneous removal of mixtures of colloidal pollutants.
Multicomponent mass transfer in turbulent flow
Authors: von Behren G. L. , Jones W. O. , Wasan D. T.
Published: June 2004

A general treatment of entry region multicomponent mass transfer between a fully developed turbulent flow and a smooth pipe wall has been developed from a basis first derived by Toor.

The couled multicomponent equations were reduced to an equivalent binary system by the method of undetermined constants. Numerical solutions for a forced convection, binary diffusion system involving gas‐phase, nonequimolal diffusion were applied to a ternary system. These solutions have been found to compare well with these authors entry region mass transfer data on a ternary acetone‐methonal‐air mixture and with the earlier analogy theories derived for the case of an infinitely long test section.

We conclude that there is a significant interaction in some multicomponent systems, enough that the binary theory can not be satisfactorily applied in the design of multicomponent mass transfer systems.
Radiation efficiency of photoreactors
Authors: Hancil V. , Schorr V. , Smith J. M.
Published: June 2004

Theoretical expressions are derived for the fraction of the energy, emitted from a UV lamp, which strikes the reactor wall in systems where a reflecting surface is included. Two geometries used in photoreactors are considered: a cylindrical lamp located at the focus of a superimposed parabolic reflecor. The predicted efficiencies are low, particularly for the elliptical reflector—reactor system, because of the energy that escapes through the ends of the system. Experimentally determined efficiencies for the elliptical type are in reasonable agreement with predicted values, suggesting that the theoretical method may be used for estimating efficiencies for different reactor systems.
Effect of inert venting on the stability of autorefrigerated batch reactors
Authors: Luyben W. L.
Published: June 2004

Removal of the exothermic heat of chemical reactons by autorefrigeration (vaporization of a liquid phase) is frequently used in continuous and batch chemical reactors. The vapor thus generated is usually liquified in a condenser and the condensate returned to the reactor.

This paper studies the effects of the formation of an inert gas by‐product on the stability and control of batch autorefrigerated reactors.

Stability is shown to be strongly influenced by the production of these inerts because their buildup in the condenser reduces heat removal capacity. Inert buildup can be reduced by venting, but excessive venting results in a loss of not only inerts but also of the volatile components in the system. This leads to higher reactor temperaturs, faster reaction rates and instability.

Digital simulation of a numerical example illustrates the effects of various parameters.
The permeation of carbon dioxide, oxygen, and nitrogen through weakly basic polymer membranes
Authors: Tajar Joseph G. , Miller Irving F.
Published: June 2004

Permeation, diffusion, and solubility coefficients were measured for carbon dioxide, O2 and N2 in the four component membrane system, polyethlenimine–polyvinylbutyral—epoxy (Epon 834)—water, using a variable pressure technique. Extremely high CO2/O2 and CO2/N2 selectivity ratios were obtained. This can be attributed to reversible reactions between the carbon dioxide, water, and polyethylenimine which markedly increases the carbon dioxide solubility in the membrane with respect to those of O2 and N2. The O2 and N2 permeation occurs in the classical manner.

The high carbon dioxide selectivity coupled with the good O2 permeability of this membrane makes it potentially useful in an atmospheric control system or in a blood oxygenator.
Kinetics of propane pyrolysis
Authors: Herriott G. E. , Eckert Roger E. , Albright Lyle F.
Published: June 2004

A kinetic model based on the most important free radical reaction steps has been developed for propane pyrolysis. The kinetic and product distribution data were obtained over a wide range of conversions at temperatures from 700 to 850°C. and with various amounts of steam or other diluents. The results of the investigation clarify the important reaction steps and the effect of the critical operating variables.
Vapor‐liquid equilibrium in alcohol‐water systems containing dissolved halide salts and salt mixtures
Authors: Meranda David , Furter William F.
Published: June 2004

Isobaric vapor‐liquid equilibrium data at atmospheric pressure are reported for 17 systems, each consisting of water, an alchol (methanol or ethanol), and either a salt or a mixed pair of salts having a common anion, dissolved to saturation in the boiling liquid phase. The matris of four salts employed consisted of the sodium and potassium bromides and iodides. Solubility data are reported in terms of saturation salt concentration as a function of alcohol‐water proportionality in the liquid.

Some of these salts and salt mixtures were found capable of eliminating the ethanol‐water azeotrope completely. Relative volatility was observed to be enhanced by as much as threefold in certain cases. Orders of effectiveness of both the cations and anions were in agreement with those observed by previous investigators of the effects of electroytes in mixed solvents. The value of the salt effect parameter was observed to undergo major variation as a function of alcohol‐water mixed solvent proportionality in the methanol‐water‐salt systems, but to be remarkably constant throught the ethanol‐water‐salt systems. Synergistic effects of mixed salts on vapor‐liquid equilibrium were observed in certain systems despite their apparent lack in the corresponding salt solubility relationships. In systems where synergistic effects did exist they were found to be dependent stronly on liquid composition, largely lacking in water‐rich regions, and evident only in midrange and alcohol‐rich regions of binary solvent composition. In some of these systems the salt appeared to cause both salting out and salting in of the alcohol in differing composition regions of the same system, the predominating effect depending on the relative proportions of alcohol and water present. This latter effect is in general contradiction with the accepted theories of salt effect in vapor‐liquid equilibrium.
Activity coefficients at infinite dilution for ternary system
Authors: Kojima Kazuo
Published: June 2004

A simple thermodynamic expression determining the infinite dilution activity coefficients from the dew point isobar is presented. A flow method measuring the dew point temperature for ternary and binary isobaric systems is proposed. An analysis determining the infinite diluvion ternary activity coefficients for ethanol‐isopropyl alcohol‐water system at 1 atm. is illustrated.
Analysis of entrance and exit effects in a falling cylinder viscometer
Authors: Chen M. C. S. , Swift G. W.
Published: June 2004

A variational method has been used to study the entrance and exit effects in a falling cylinder viscometer for creeping and noncreeping flow. The computed result indicate solution convergence for NRe less than 100 and agree with experiment within ± 0.5% for NRe less than 25.
Radiative transfer through a cloud of absorbing‐scattering particles
Authors: Sanders C. F. , Lenoir J. M.
Published: June 2004

An experimental study was made of radiative transfer through a plane‐parallel enclosure of micron‐sized, sphercal aluminim oxide particles and flake‐like graphit particles. By suspending the particles in both carbon tetrachloride and carbon disulfide, transmission measurements were made at wave lengths from 2 to 11 microns with both collimated and diffuse incident radiation. In correlating the diffuse results, the two‐flux model was rearranged so that the cloud transmission was experessed in terms of two cloud scattering parameters. The values of the scattering parameters as determined from the data were correlated with the properties of the cloud.
Thermodynamics of multicomponent reactive nonuniform systems (adsorption)
Authors: Brunet Jean
Published: June 2004

Certain systems are characterized by a nonuniform distribution of matter in space. Examples of such systems are liquid‐fluid (1 to 3) and the solid‐fluid interfaces (4). It is the main purpose of this paper to extend thethermodynamics of nonuniform systems to multicomponent reactive mixtures in the presence of an external field and to apply the above formalism to physical adsorption. This amounts to an extension of Hart's original analysis (5 to 7) as well as an improved analysis of the solid‐fluid interface presented recently by Metiu and Ruckensteein (8). Furthermore, various approximate solutions for the solid‐fluid interface are considered, all of which reduce properly to known results.
Optimal feedback control of a class of linear tubular processes
Authors: Lim H. C. , Fang R. J.
Published: June 2004

Optimal output feedback control low requiring measurment of the output only has been considered for a class of tubular processes. The advantage of this formulation, which requires a single measurement of the output only, over a previous result which requires an infinite number of measurements, has been demonstrated through a heat exchanger example. However, when the terminal time is grater than the residence time of fluid, a time‐delay element is needed.
Local and macroscopic thermal transport from a sphere in a turbulent air stream
Authors: Galloway T. R. , Sage B. H.
Published: June 2004

The local and macroscopic thermal transport from a calorimeter‐instrumented sphere 1.5 in. in diameter located in an air steram ws measured experimentally in the subcritical flow regime. The Reynolds number was varied between 5,200 and 70,200 with artificially induced turbulence level varying from 0.013 to 0.256. Higher turbulence increased thermal transport through the laminar bundary layer prevailing in the forward hemisphere, and significantly retarded the point of separation from about 87° to 106° as measured from stagnation. An increase in the Reynolds number shifted the point of separation forward and altered the behavior in the wake. In the separated wake region, the experimental evidence indicated that the vortex reattached to the rear surface and formed a new boundary layer that resulted in a decrease in the local thermal transfer.
The role of the liquid phase in the performance of a trickle bed reactor
Authors: Satterfield Charles N. , Way Peter F.
Published: June 2004

The effect of the addition of an inert liquid into a gas‐phase reaction occurring on a solid catalyst was studied using the isomerization of cyclopropane to propylene on a sukuca‐alumina catalyst as the model reaction and one of three hydrocarbon solvents as the liquid. With a nonadsording liquid the intrinsic reaction rate constant is the same in both the gas and the gas‐liquid systems but adsorption of impurities from the liquid or adsorption of the liquid itself can have an enormous retarding effect on the reaction rate. Even i the absece of these effects the addition of a liquid phase decreases the percet conversion and increses the likelihood of occurrence of mass transfer limitations.
Stability studies in pipe flows unsing water and dilute polymer solutions
Authors: Berman Neil S. , Cooper Eugene E.
Published: June 2004

The response of water and 20 ppm. solutions of Separan AP‐30 and Polyox WSR 301 to the periodic motion of a thin sleeve was measured using a laser Doppler velocimeter. The sleeeve was moved in an axial direction by an external coupling at frequencies from 1/4 to 1.O Hz and at amplitudes of 1/2 to 2 in. The flow filed downstream of the distrbance was found to consist of three regions: 1. a near field with a separation wake from the sleeve moving toward the piep centerline; 2. an intermediate field in which alternate laminar and turbulent slugs passed a point; and 3. a far field with decaying turbulent lfow. Defferences in the behavior of water flows and polymer flows appeared in each region. In the near field, wakes spread faster in water flows. In the intermediate field, the laminar slugs disappeared into turbulence more rapidly in water flows. And in the far field, the turbulence was not as developed in the polymer flows.

Detailed statistical evaluations were made on the signals in each region for a Reynolds number of 2000. The response of the dilte polymer polymer solutions appeared to be governed by the initial interaction with the sleeve. Fewer high frequencies were generated than in the pure solvent so the periodic disturbance persisted downstream. In pure water the eddies from the separation wake interacted strongly with the periodic distrurbance leading to rapid decay of the periodic portion. Shear rates were not high enough to attribute the dilute polymer differences to viscoelastic effects.
Friction coefficients and self‐diffusivity reduced state correlations and interrelationship
Authors: Ramanan P. , Hamrin C. E.
Published: June 2004

Theretical equations for the transport properties of donse gases and liquids require knowledge of the contact pair‐correlation function g2 (σ) and the friction coefficient ζ. Usually this latter quantity is made up of a hard‐core contribution ζH and a soft‐repulsion contribution ζS. Correlations are presented for the reduced friction coefficients ζrH, ζrS, and ζr in terms of reduced density ρ* and reduced temperature T*. These correlations were found to predict the dependence of self‐diffusivity of several substances on temeratures and density in the dense gas region.
Interactions of inter‐ and intraphase gradients in a diffusion limited catalytic reaction
Authors: Kehoe J. P. G. , Butt J. B.
Published: June 2004

The experimental measuremet of inter‐ and intraphase temperature gradients in a single pellet reactor for the Ni‐kieselguhr catalyzed benzene hydrogenation reaction is described. Experimental variables were temperature, feed composition, flow rate (hence heat and mass transfer coefficients) and intrinsic catalytic activity. All parameters required for carrying out calculations were either measured in separate experiments or compared with available independent information. The rather complex interactions between inter‐ and intraphase gradients are well represented by the theory except at conditions of high reaction rate and low convective transport rate. The discrepancies observed at these conditions are apparently due to the development of nonuniform external boundary layers.
Stability of time‐delay systems
Authors: Landis J. G. , Perlmutter D. D.
Published: June 2004

A direct method is presented for determining both local and regional stability of systems described by nonlinear differential‐difference equations. Prediction of stability is with respect to a general class of initial curves. The practical as well as the conservative nature of the procedure is demonstrated by a numerical example.
Local stability of tubular reactors
Authors: Clough David E. , Fred Ramirez W.
Published: June 2004

Liapunov analysis techniques employing a general quadratic functional are used to derive stability conditions for tubular reactor systems. The adiabatic tubular reactor without axial dispersion is shown to be locally stable, which excludes the possibility of multiple steady states, and the reactor with axial dispersion is proven locally stable if a condition involving only system parameters and steady state values is satisfied. Peclet numbers for heat and mass transfer are not specified equal for the latter proof.

Results of simulation studies are used to confirm the validity of the derived stability condition, and it is shown that the parametric region of multiplicity is quite well defined. For the nonlinear equations, single steady state cases appear to possess nonuniform stability.
A method of representing the nonisothermal effectiveness factor for fixed bed calculations
Authors: Jouven J. G. , Airs Rutherford
Published: June 2004

A parametric representation of the effectiveness factor for a first‐order, nonisothermal irreversible reaction in a catalyst pellet has geen devised that amply covers the realistic range of parameters for the exothermic case. Given the Thiele modulus, Prater temperature, and dimensionless activation energy, the effectiveness factor can be recovered in about 1/1000 sec. (CDC 6600) to an accuracy of better than 5% over most of the range. When heat and mass transfer resistance at the surface is added the time required is about 0.03 sec. This makes fixed bed calculations more than 50 times faster than would otherwise be possible.
Mass transfer of water from single thoria sol droplets fluidized in 2‐ethyl‐1‐hexanol
Authors: Clinton S. D. , Whatley M. E.
Published: June 2004

The rate at which water is extracted from thoria sols was investigated by fluidizing single thoria sol droplets in 2‐ethyl‐1‐hexanol (2EH) and measuring the diameter of a droplet over a period of time until shrinkage no longer occurred. Diameter data from both water and sol drops were obtained at 25°C. The experimental variables were initial drop diameter (0.1 to 0.2 cm), sol molarity \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm (0 to 2}{\rm .5 }\underline M {\rm ThO}_{\rm 2}) $\end{document}, and water concentration in the 2EH (2–12 mg./cc.). The water and sol droplet data were correlated by Equation (5). The single relationship for the fluidized water and sol drops verified that an organic‐phase film surrounding the drop is the rate‐controlling resistance. The sphere Reynolds number was based on the approach velocity and varied from 0.4 to 14. The Schmidt number for the system was fixed at 35,700. During the extraction of water, the mass transfer coefficients for fluidized sol drops were found to depend only on the molarity of the sol. By expressing the mass transfer coefficients as a function of the density difference between the aqueous sol and the organic phase, an equation was derived to predict the gelation time required for any initial sol molarity and drop diameter fluidized in 2 EH at 25°C.
Experimental determination of residence time distributions on commercial scale distillation trays using a fiber optic technique
Authors: Bell Richard L.
Published: June 2004

A fiber optic technique for obtaining multiple, simultaneous, point residence time distributions on operating, commercial scale distillation trays is described. The method has sufficient resolution to yield residence time profiles on the tray and to separate tray and downcomer effects. The results indicate severe flow nonuniformities on the tray, which are not accounted for in present models of distillation.
Developed turbulent transport in ducts for large prandtl or schmidt numbers
Authors: Hanna Owen T. , Sandall Orville C.
Published: June 2004

The problem of developed turbulent heat or mass transfer in a duct is considered for the limit of large σ (Prandtl or Schmidt number). The limiting results depend on the behavior of the eddy diffusivity near the solid surface. Since there is a question about whether this variation begins with ϵ ∝ y+3 + … or ϵ ∝ y+4 + … for y+ near zero, both possibilities are considered. In each case the first three terms of the asymptotic expansion for σ → ∞ are obtained. The first term of the asymptotic expansion agrees with limiting results derived earlier, while the correction terms indicate the errors associated with earlier simplifying assumptions.

By proper scalling, it is demonstrated that in the limit of σ → ∞ the results are independent of geometry and boundary conditions for situations involving parallel plates, circular tubes and concentric annuli with either constant surface heat flux or temperature. The correction terms to the σ → ∞ asymptote can be significant, although the effect of Reynolds number on the correction terms is very small.

A comparison between a typical numerical integration and the asymptotic formula shows excellent agreement. The asymptotic formulae are used to correlate large Schmidt number mass transfer data.
Optimal design and control in a class of distributed parameter systems under uncertainty–application to tubular reactor with catalyst deactivation
Authors: Nishida N. , Ichikawa A. , Tazaki E.
Published: June 2004

Unpredictable variations in the values of plant parameters around their nominal values are often encountered in actual operation of process plants. In order to assure that process performance meets specifications, it is preferable to design and control the process, taking into account the uncertainty in the values of the plant parameters. In this paper, a method to minimize the maximum decrease in the process performance caused by the hypothetical worst parameter variations is proposed. Necessary condition for the worst parameter variations is derived for a class of distributed parameter systems by means of the maximum principle, and then the method for obtaining the optimal design and control subject to the worst parameter variations are discussed. The method is applied to the design of a tubular reactor associated with catalyst activity decay. The reactor obtained is fairly insensitive to the variations in the process parameters while maintaining fairly good performance even at the nominal values of parameters.
The dynamics of a packed gas absorber by the pulse response technique
Authors: Sakata Norihiko , Prados John W.
Published: June 2004

The dynamic response of a packed gas absorber to inlet gas composition changes was investigated by the pulse response technique for the case where absorption was accompanied by pseudo first‐order irreversible chemical raction.

The solute‐carrier‐solvent system was carbon dioxide‐air‐0.07 normal aqueous sodium hydroxide solution. The column used was 6.5 in. I.D. Plexiglass packed to a height of 6.15 ft. with either ¼‐in. Raschig rings or ¾‐in. Berl Saddles. Gas flow rates ranged from 1.5 to 10 lb.‐moles/hr./sq.ft. and liquid flow rates ranged from 0 to 200 lb.‐moles/hr./sq.ft. A pulse of carbon dioxide was injected into the inlet air stream and monitored as it entered the packed section. The outlet gas and liquid phase concentrations were continuously monitored as the resulting pulses left the packed section. The pulse response data were reduced to frequency response by digital computer calculations. Reliable data could be obtained over the frequncy range 0 to 5 radians/second.

The experimental results were compared with theoretical predictions from the slug flow, axial diffusion, and mixing cell models. Both the mixing cell model and the axial diffusion model satisfactorily predicted the experimental frequency responses over the entire frequency range covered. The slug flow model was found unsatisfactory for predicting gas‐phase amplitude ratios at high frequencies, where axial mixing affected the amplitude ratios. Gas‐phase particle Peclet numbers and overall mass transfer coefficients based on the gas‐phase driving force determined in the present absorption system were in reasonable agreement with the values reported in the literature.
Kinetics of anion exchange accompanied by fast irreversible reaction
Authors: Graham E. E. , Dranoff J. S.
Published: June 2004

The kinetics of binary anion exchange accompained by a fast irreversible reaction at the exchanger surface was studied. Dowex 1, X‐8, in the hydroxyl form was contacted with a strong acid in a well‐stirred batch reactor and concentration‐time data were obtained by electrical conductivity measurements. The process was analyzed assuming rate control by film diffusion, intraparticle diffusion, and a combination of both mechanisms. The results indicated that models based on the individual mechanisms gave quite satisfactory representations of the data under appropriate conditions, but the combined model appears superior in the nominally intraparticle diffusion controlled range. It was also found that severe particle cracking occurs, particularly with larger resin particles, at high solution concentrations. This results in degradation of the particles as well as apparent intraparticle diffusion coefficients that vary during the exchange process. Care must be taken to avoid or to account for this phenomenon.
The kinetics of alkylation of isobutane with propylene
Authors: Langley J. Randolph , Pike Ralph W.
Published: June 2004

A 17‐reaction mechanism model was postulated to describe the alkylation of isobutane with propylene using sulfuric acid as the catalyst. The scheme was based on the Schmerling carbonium ion mechanism with modifications introduced to account to iC9 and iC10 formation. Solving the steady state rate equations for the rate constants a set of 17 equations of the form ki = f(rcj, rC k, …)/g (Ci, Ck, …) were obtained. Experimental measurements were made in an ideally mixed, continuous‐flow stirred‐tank reactor, and the necessary data were obtained to compute the rate constants from 65°F to 135°F. The reaction model was found to be valid in the range of 81°F to 135°F using a 95% sulfuric acid catalyst since the rate constants obeyed the Arrhenius theory. The results obtained at 65°F and 95% sulfuric acid showed significant departure from the model. This was possibly due to a change in reaction mechanism. There was an apparent change in selectivity of the catalyst when the concentration was lowered to 90% sulfuric acid. This resulted in increased rates of formation of iC9's and iC10's and decreased rates of formation of iC5's, iC6's and iC8's.
Kinetics of water vapor sorption in a model freeze‐dried food
Authors: Bluestein P. M. , Labuza T. P.
Published: June 2004

Sorption kinetics experiments were performed at 37 C with microcrystalline cellulose held between dryness and 51% water activity in the absence of other gases. Effective diffusion coefficients (<10−4 cm2/s) were greater than any previously reported for similar experiments. A model based on heat and mass transfer properties of the sample is proposed. The vapor space permeability calculated by application of this model is related to the structure of the microcrystalline cellulose as determined from water desorption isotherm analysis, mercury intrusion porosimetry, and steady state permeability techniques. Microcrystalline cellulose, like some freeze‐dried foods, contains micropores and macropores. During sorption, the macropores are important in determining the balance between the internal and environmental control during the first half of sorption. The micropores, which account for less than 1% of the void volume of the porous matrix but approximately 40% of the surface area, control the mass transfer properties of the sample during the latter stages of sorption. Because of the great difference between their mass transfer properties, the macropores approach local equilibrium faster than the micropores; this phenomenon suggests that changes in the effective diffusion coefficient and permeability as sorption proceeds are related to the structure of the sample rather than to the moisture content itself.
Liquid sorption equilibria of selected binary hydrocarbon systems in type Y zeolites
Authors: Satterfield Charles N. , Cheng Chon S.
Published: June 2004

On NaY and HY, aromatic compounds are selectively adsorbed in preference to paraffins and naphthenes. Smaller aromatic compounds are adsorbed in preference to larger aromatic compounds. All the compounds studied can be sorbed into the pore structure of the zeolites and the selectivies are primarily a reflection of relative affinity for the zeolite and steric effects rather than a sieving effect.
An integral analysis of condensing annular‐mist flow
Authors: Berry Maurice R. , Goss William P.
Published: June 2004

The application of integral techniques to the analysis of a high vapor velocity, two‐phase, annular‐mist, single‐component condensing flow system is presented. A time‐averaged annular liquid film thickness is defined, and appropriate interfacial and wall shear stress correlations are employed to account for the wavy nature of the interface between the entrainment‐laden gaseous core and the axisymmetric annular liquid film. An empirical entrainment correlation is utilized to determine the amount of liquid flowing as entrained particles in the high velocity core region. The velocity and enthalpy distributions in the gaseous core and the annular liquid film are assumed as the power‐law type. The resulting set of four nonlinear ordinary differential equations is solved numerically with the use of a digital computer. A comparison with experimental data for condensing steam is obtained. The analytical model accurately predicts the condenser length necessary for complete condensation and also predicts the dynamic quality, the heat transfer characteristics, and the static pressure distribution throughout the condensation length. The integral analysis presents some insight into the complex mechanisms and interactions which occur in high vapor velocity, two‐phase, annular‐mist flows and also indicates the need for improved experimental techniques to further this understanding.
Convective instability in the presence of a catalytic chemical reaction: Part II. Oscillatory instability
Authors: Wankat P. C. , Schowalter W. R.
Published: June 2004

This is an extension of earlier work in which a linear analysis of hydrodynamic stability was applied to a fluid mixture contained between two horizontal planes. One species diffuses to the lower plane where it is destroyed by a rapid exothermic or endothermic catalytic reaction. In the present work, Galerkin's method has been used to study the importance of oscillatory instability in a system with the more dense species concentrated near the top plane. Results show that, for cases likely to be of physical interest, oscillatory instabilities are not expected.
The computation of optimal singular bang‐bang control I: Linear systems
Authors: Edgar T. F. , Lapidus L.
Published: June 2004

A general algorithm for the solution of both singular and bang‐bang control problems is presented. The algorithm utilizes a limiting process and the solution of a constrained linear‐quadratic control problem. The algorithm is applied to problems with both fixed and nonfixed final times. General numerical results for several linear system examples are presented, and two minimum time examples are discussed in detail.
The computation of optimal singular bang‐bang control II. Nonlinear systems
Authors: Edgar T. F. , Lapidus L.
Published: June 2004

A general algorithm for the computation of singular/bang‐bang control, previously applied to linear systems, is extended to nonlinear systems. The minimum time control of a two‐stage CSTR is demonstrated.
Coupled heat and mass transport in unsteady sublimation drying
Authors: Fox E. C. , Thomson W. J.
Published: June 2004

Sublimation drying is analyzed by considering coupled heat and mass transport at the ice‐vapor interface. Since, the typical model of sublimation drying assumes a pseudo steady state heat transport limited process, these assumptions are critically analyzed to determine whether they are the cause of some of the limitations of the simplified model. It is shown that although total drying times can be substantially increased if there is heat leakage into the ice core and coupled heat and mass transport, this is not a problem in the conventional sublimation drying of foods. However, the results indicate that consideration of both coupled transport and heat leakage into the core result in time‐varying ice temperatures which could exceed the triple point. In addition, the application of this analysis to the analogous heterogeneous chemical reaction problem is pointed out and appropriate conclusions can be drawn by inference.
Accelerating diffusion with mixed solvents
Authors: Cussler E. L. , Breuer M. M.
Published: June 2004

The experiments reported here show how diffusion rates in liquids can be increased by as much as an order of magnitude by use of coupled diffusion fluxes in mixed solvents. Solutes whose diffusion can be accelerated in this way include simple electrolytes, essential oils, dyes, and antibiotics. These increases are primarily caused by thermodynamic interactions and can be estimated from solubilities.
Salt effect in vapor‐liquid equilibria: Correlation of alcohol‐, water‐, salt systems
Authors: Rousseau R. W. , Ashcraft D. L. , Schoenborn E. M.
Published: June 2004

The isobaric data of Johnson and Further for the systems methanol‐water, ethanol‐water, and 1‐propanol water, each saturated with a variety of common inorganic salts, can be effectively correlated by means of the van Laar, the Wilson, or the Renon equations if pseudo‐activity coefficients for the volatile components are computed using a modified reference fugacity for the liquid phase. This reference fugacity takes into account the lowring of the vapor pressure due to the dissolved salt. Furthermore, the activity coefficients are normalized as required by the above equations.
The extraction of mercuric chloride from acid chloride solutions with trioctylamine
Authors: Caban Reinaldo , Chapman Thomas W.
Published: June 2004

The equilibrium distribution of mercuric chloride between aqueous sodium chloride solutions and a solution of tri‐isooctylamine in xylene has been measured. The dependence on pH, amine concentration, mercury level, and temperature has been determined. At low pH mercury is extracted quite effectively with a distribution coefficient as high as 2,000. At high pH the mercury can be stripped from the organic solution. This extraction system offers the possibility of an effective mercury separation process for chlorine plant brines or chloride‐based mercury leach liquors.

A theoretical model of the extraction equilibria is developed to facilitate interpolation of the experimental data.
Mass transfer into dilute polymeric solutions
Authors: Wasan D. T. , Lynch M. A. , Chad K. J. , Srinivasan N.
Published: June 2004

Mass transfer into dilute polymeric solutions was studied by using a short wetted‐wall column. Oxygen was absorbed into thin films of water and aqueous polymeric solutions. The polymer systems studied included dilute solutions of carboxymethylcellulose, polyethylene oxide, Carbopol, and Cyanamer. All of the above systems were moderately non‐Newtonian with power law indexes less than unity. Methocel (a Newtonian fluid with a power law index of one) was also studied. The flow of liquid films was well within the laminar flow regime.

The rheological properties of these solutions as well as equilibrium solubility of oxygen in these solutions were determined. In all of the polymer systems studied except Polyox the equilibrium so ubility of oxygen decreased with an increase in polymer concentration. In Polyox solutions, however, the equilibrium solubility of oxygen increased with an increase in polymer concentration.

For all of the systems investigated (including Polyox) the mass transfer coefficient for absorption of oxygen at a given flow rate decreased with an increase in polymer concentration. The mass transfer coefficient was highest for water at all flow rates.

The diffusivity of oxygen in all of the systems considered except Polyox was lower than that in water. This was attributed to the increased viscosity of the polymeric solutions. The diffusivity of oxygen in Polyox solutions was higher than it was in water. This was found to be due to the complex chemical reactions which occur in this system. In all of the pseudoplastic systems studied the diffusivity of oxygen increased with increasing wall shear rate (decreasing viscosity).