bluuebunny/crossref_metadata_2025 huggingface dataset:
Mixing effects in a spray‐column heat exchanger
Authors: Letan Ruth , Kehat Ephraim
Published: June 2004

Temperature profiles were measured in a spray‐column heat exchanger 7.5 cm. in diameter and 167 cm. long between the inlets of warm kerosene and cold water. The temperature jump, at the inlet of the continuous phase, is a measure of the amount of mixing in the column and is a function of holdup and ratio of flow rates of the two phases. At holdup the temperature jump had a minimum value of 0.24.

A physical model for heat transfer in a spray column based on hydrodynamic principles is proposed. Heat is transferred from drop to wake downstream of drop. Wakes are shed and mixed with the bulk water flow. New material enters the wake and is spilled out at higher temperatures.

The physical model is applied to explain the data on temperature jumps in spray‐column heat exchangers and the data on concentration jumps in spray‐column extractors.
Adsorption kinetics in fixed beds with nonlinear equilibrium relationships
Authors: Tien Chi , Thodos George
Published: June 2004

Previous work by the authors on ion exchange kinetics for systems having nonlinear equilibrium relationships has been extended. Computer studies have produced additional concentration—bed length–time relationships for values of αo  5, 10, and 50. This information and the results obtained previously for values of αo  100 and 1,000 provide an extensive variation of the parameter αo for design applications. The composite results are represented graphically.
Suction nucleate boiling of water
Authors: Wayner P. C. , Kesten A. S.
Published: June 2004

Suction nucleate boiling (consisting of saturated pool boiling on a porous heat source with the generated vapor exhausting through the pores) was investigated experimentally and theoretically. The experimental results demonstrated that: (1) interfacial free energy can be used to direct the flow of liquid and vapor in a desired direction and to separate vapor from liquid at the point of vapor generation; (2) the heat transfer coefficient for suction nucleate boiling is higher than that associated with normal boiling; and (3) a porous heat exchanger can be designed to give stable transition from nucleate to film boiling. The theoretical analysis, which was based on experimental observations, indicated that extremely high heat fluxes and heat transfer coefficients are possible with small pores. Comparison of the experimental and theoretical results demonstrated that the full potential of suction nucleate boiling was not attained in the experiments and indicated some of the experimental refinements neededto attain this potential.
Gas‐liquid mass transfer in cocurrent froth flow
Authors: Heuss J. M. , King C. J. , Wilke C. R.
Published: June 2004

The absorption of ammonia and oxygen in horizontal cocurrent gas‐liquid froth flow in a 1‐in. I.D. pipe has been investigated. At superficial liquid rates between 2 × 106and 3.2 × 106lb./(hr.)(sq.ft.) and superficial gas rates between 5 × 103and 18 × 103lb./(hr.)(sq.ft.), the length of a transfer unit in both systems was between 0.5 and 4.0 ft. The effects of distance and temperature were also investigated.

With the use of James and Silberman's data on bubble size and distribution in froth flow to estimate average bubble sizes, the gas‐phase‐controlled ammonia absorption data could be explained by the model of unsteady state transfer from a stagnant sphere. With the use of an interfacial‐area estimate from the ammonia results, the liquid‐phase‐controlled oxygen absorption data were correlated by a Sherwood number characterizing the transfer from the bubbles, a Reynolds number characterizing the turbulence within the system, and the void fraction.
Analysis of heterogeneous catalytic reactions by nonlinear estimation
Authors: Lapidus Leon , Peterson T. I.
Published: June 2004

Integral conversion catalytic data have been studied by nonlinear estimation to determine whether the Langmuir‐Hinshelwood heterogeneous catalytic models are more valid than the simpler homogeneous noncatalytic forms, and whether it is possible to discriminate among models. The experimental system chosen for this study was the vapor phase dehydration of ethanol. Data for a similar hypothetical catalytic system were also generated and analyzed to highlight the effects arising in the ethanol dehydration case.

Nonlinear estimation is shown to be a valuable adjunct in the study of reaction kinetics and mechanism. For the hypothetical system, the correct model was found to provide the best fit to the data. Linear regression, coupled with the usual criterion that models are acceptable if all parameter estimates are positive, did not provide this discrimination. For the experimental system of ethanol dehydration, as corroborated by the hypothetical system, such problems as degeneracy of the heterogeneous rate equations and comparatively large errors in measurement are shown to be obscuring factors in determining the best model. When these effects are involved, it is doubtful that the Langmuir‐Hinshelwood equations are more warranted than the simpler homogeneous forms.
Vapor‐liquid equilibrium in the methane–n‐hexane–nitrogen system
Authors: Poston Robert S. , McKetta John J.
Published: June 2004

Because varying amounts of nitrogen are found in hydrocarbon mixtures, a knowledge of vapor‐liquid equilibrium ratios for hydrocarbon‐nitrogen system is needed for petroleum reservoir studies and refinery calculations. Presented here are results of a quantitative investigation which shows how the K values of methane and n‐hexane change when varying amounts of nitrogen are added to mixtures of the two hydrocarbons.

Analyses of equilibrium phases at different conditions of temperature and pressure in order to completely describe the phase equilibria of the system are presented. Temperature intervals of 60°F., starting at 100°F., and going up to 340°F. were used. At each temperature equilibrium samples were taken at 500 lb./sq.in.abs. and the pressure increased in 500 lb./sq.in.abs. intervals with samples taken at each interval up to 5,000 lb./sq.in.abs. or the critical pressure, whichever was lower.
Correlations of selectivity parameters for separations extractions of hydrocarbons with fluorochemicals
Authors: Munson M. S. B.
Published: June 2004

The equation In β12  ε12 xs2/T adequately represents the variation of the separation factors for the extraction of hydrocarbon mixtures with fluorochemicals. The selectivity parameter ε12 is a measure of the selectivity of a solvent for hydrocarbons 1 and 2 which is independent of the experimental conditions. With a given solvent it is possible to develop a correlation between εji for pairs of hydrocarbons and the heats of vaporization of these hydrocarbons. A group contributions method is also successful in correlating the selectivity parameters. The three fluorochemicals in these experiments, (C4 F9)3N, C7 F14, and C8F16O, had essentially the same selectivity for hydrocarbon separation which one would expect on the basis of their essentially identical solubility parameters.
Flow behavior of viscoelastic fluids in the inlet region of a channel
Authors: Metzner A. B. , White J. L.
Published: June 2004

The behavior of viscoelastic fluids in the inlet region of a channel formed by two parallel flat plates has been analyzed with a Rivlin‐Ericksen approximation to describe the fluid properties. It was found that viscoelasticity changed the entry length; both the magnitude and direction of this change predicted to depend upon the detailed fluid properties. These predictions of the change in the entry length were seen to find some qualitative support in available experimental evidence.

The directions for further analysis, based primarily on the important observation that these materials may exhibit solidlike behavior in the immediate vicinity of the entrance, are indicated. This solidlike behavior is seen to be closely related to “melt fracture” and similar instability phenomena common to these materials; it serves to explain directly the otherwise perplexing observations concerning the similarity of such fluid fracture phenomena in materials as divergent in their properties as viscoelastic polymeric systems and inelastic dilatant slurries.
Entrance region flow
Authors: Christiansen E. B. , Lemmon H. E.
Published: June 2004

The results of rigorous numerical solutions of the general equations of motion are presented for isothermal, laminar, Newtonian flow in a tube entrance region for a uniform entrance velocity. Computed velocity profiles, entrance length, and pressure gradients are compared with previous theoretical and experimental results.
Effective wall heat transfer coefficients and thermal resistances in mathematical models of packed beds
Authors: Crider J. E. , Foss A. S.
Published: June 2004

Expressions are derived for an effective wall heat transfer coefficient useful in one‐dimensional representations of heat transport in packed beds. These expressions are obtained with two mathematical models of a cylindrical packed bed: a partial differential model and a finite stage model. These expressions relate the effective wall heat transfer coefficient, which is a local coefficient, to the actual wall heat transfer coefficient and the bed diameter (and the radial Peclet number in the partial differential model) in regions of the bed where similar temperature profiles obtain. These relations involve a single dominant root of an equation characteristic of the heat balance equations of each model.

From these relations, expressions for an effetive thermal resistance of the bed are obtained. For each model, this bed resistance is found to be an approximately linear function of the bed diameter and to be rather insensitive to the actual wall heat transfer coefficient. For each model, an approximate bed resistance is found that is not dependent upon the actual wall heat transfer coeficient and with which the effective wall heat transfer coefficient can be estiamted with an error of less than 7%.
Analysis and design of gas flow reactors with applications to hydrocarbon pyrolysis
Authors: Trombetta Michael L. , Happel John
Published: June 2004

The analysis and design of gas flow reactors are customarily based on a plug flow model. Because of transverse concentration and temperature gradients, however, kinetic constants and reactor lengths based on the plug flow model may be in gross error. This paper presents an approximate method of analysis which accounts for the effects of these gradients. We examine a gas in laminar flow which supports a first‐order irreversible reaction. Compressibility effects are considered, and the diffusion fluxes are calculated with the full ternary diffusion equations. Instead of solving exactly the full equations of change which describe this system, the well‐known Pohlhausen technique is adapted and approximate solutions which satisfy the integral forms of these equations are sought. This reduces the problem to the solution of a set of ordinary differential equations, which are integrated numerically. The main result is a set of graphs giving correction factors to be applied to plug flow kinetic constants and reactor lengths. Although primary interest is in hydrocarbon pyrolysis systems, the integral method graphs are applicable to other reaction systems.
Evaporation from falling saline water films in laminar transitional flow
Authors: Unterberg Walter , Edwards D. K.
Published: June 2004

An analytical and experimental study was made of the evaporation from pure and saline water films flowing down a heated vertical surface at Reynolds numbers between 160 and 600. Visual observation showed free surface evaporation. Film continuity was poor for pure water, but good for saline water, because of the influence of temperature and salinity on surface tension gradients. Evaporation rates were predicted by (1) a constant‐property boundary‐layer type of laminar analysis; (2) the constant‐property Dukler “eddy” treatment; and (3) a variable property laminar analysis that took into account the boiling point elevation due to salinity. The experimental evaporation rates could be correlated by dimensionless moduli arising out of the laminar analyses, but best quantitative agreement was found with the Dukler eddy treatment.
Direct contact heat transfer with change of phase: Effect of the initial drop size in three‐phase heat exchangers
Authors: Sideman Samuel , Hirsch Gideon , Gat Yehuda
Published: June 2004

The initial drop size of volatile fluids evaporating within immiscible, nonvolatile liquids was experimentally related to the overall heat transfer coefficient in single and multiparticle systems. Coalescence and turbulence diminish the effects of the initial size, which are thus limited to the lower part of the exchanger where single‐drop characteristics are maintained. Condensation data of single bubbles are in good agreement with the single‐drop relationship.
The influence of gravitational force on gas absorption in a packed column
Authors: Vivian J. E. , Brian P. L. T. , Krukonis V. J.
Published: June 2004

Carbon dioxide was desorbed from water in a packed column mounted on a large centrifuge. By varying the centrifuge rotational speed, the total body force acting upon the liquid was varied from 1 to 6.4 times the normal gravitational force. The results, obtained for ¾ in. Rasching ring packing, showed kLa varying with the body force to a power between 0.41 and 0.48, the exponent being larger at lower liquid flow rates. This effect of gravity is compared with penetration theory predictions and with those inferred from dimensional analysis and the effect of packing size.
Partial oxidation of o‐xylene in melts containing vanadium pentoxide
Authors: Satterfield Charles N. , Loftus Jordan
Published: June 2004

o‐Xylene vapor in nitrogen was partially oxidized by bubbling it through a melt of the 39 wt. % vanadium pentoxide‐potassium sulfate eutectic at temperatures from 528° to 598°C. The principal product was o‐tolualdehyde; some benzene and traces of phthalide were formed but no organic acids. These products are similar to those found in o‐xylene oxidation over a solid vanadium oxide catalyst, except for the absence of acid products but are far different from the product distribution found from homogeneous oxidation with air. The rate of reaction per unit of gas‐melt interface was approximately equal to that reported for oxidation of o‐xylene in air on an unsupported fused vanadium oxide catalyst. With o‐xylene‐air mixtures bubbled through either a vanadium pentoxide‐potassium sulfate eutectic melt or vanadium pentoxide‐potassium pyrosulfate melt, homogeneous reaction obscured any contribution from heterogeneous processes.
Obtaining precise parameter estimates for nonlinear catalytic rate models
Authors: Kittrell J. R. , Hunter W. G. , Watson C. C.
Published: June 2004

A method is reviewed which allows data points to be chosen in such a fashion that precise estimates of the parameters in nonlinear reaction rate models can be obtained. This method allows each future data point to be selected such that the confidence region of the estimated parameters is smaller with it than with any other possible data point within the region of experimentation. This procedure is applied for Hougen‐Watson models with hypothetical experimental data which were generated with the guidance of an example from the current chemical engineering literature. It is found that, for the same number of data points, the parameters in the model can be estimated eighteen times more precisely by using this suggested experimental design than by another commonly used design. Confidence regions are presented for the parameters of the Hougen‐Watson models with two types of designs.

It is found that the positions of the data points in the well‐designed experiments are more sensitive to the functional form of the model than to the current estimates of the magnitudes of the parameter values.
Mechanism of dispersed‐phase mass transfer in viscous, single‐drop extraction systems
Authors: Johns L. E. , Beckmann R. B.
Published: June 2004

The theory of solute extraction in viscous single‐drop systems is extended to show (1) the dependence of the asymptotic Nusselt number on the Peclet number from NPe = 0, the molecular diffusion limit, to NPe = ∞, the Kronig and Brink limit, and (2) the dependence of the diffusion entry region Nusselt number on the Peclet number and the initial concentration profile.

A numerical solution of the diffusion equation, limited to dilute solute concentrations and solute transport by viscous convection and molecular diffusion, is presented from which the nature of the Nusselt number is deduced. The observed oscillatory behavior of the Nusselt number in the diffusion entry region, as NPe → ∞, is given a simple physical interpretation in terms of the circulation period of the drop liquid.

The model is based upon the Hadamard stream function which theoretically is limited to creeping flow; however some experimental evidence indicates that flow fields similar to the Hadamard stream function exist at continuous phase Reynolds numbers of the order of ten.
Momentum, heat, and mass transfer in turbulent non‐Newtonian boundary layers
Authors: Skelland A. H. P.
Published: June 2004

The boundary‐layer equations and a Blasius type of relationship between f and NRe gen are used to derive expressions for velocity distribution, local boundary‐layer thickness, local shear stress, and total drag force for the turbulent boundary‐layer flow of a power law non‐Newtonian fluid across a flat plate at zero incidence. Relationships are derived for the velocity at the edge of the laminar sublayer and for the thickness of the laminar sublayer.

An analogy between heat and momentum transfer is then used to obtain expressions for local and mean values of the heat transfer coefficient in a turbulent thermal boundary layer for power law materials flowing over flat plates. Analogous extensions to mass transfer are indicated.

A tentative criterion is suggested for characterizing the transition from laminar to turbulent boundary‐layer flow of power law fluids.

Relationships combining the effects of a part laminar, part turbulent boundary layer are presented.
Identification and adaptation in control loops with time varying gain
Authors: Mellichamp D. A. , Coughanowr D. R. , Koppel L. B.
Published: June 2004

A method is presented to apply the gain identification procedures developed in a companion paper to a control system. The method employs a small identification tank which follows the control tank; the identification tank is perturbed to estimate the gain of the process (controlled tank system). The effects of load changes on the identification system are minimized by this approach.

The results of analog and digital computer simulations of this adaptive process are given. Both a general system with linear change in gain and a pH control system with a step change in concentration of the buffer species are studied. Process gain changes up to 20:1 are introduced.

It is concluded that an adaptive control system of this type can be designed to maintain good control characteristics in a process experiencing wide gain variation. Criteria are presented to aid in the design of an adequate identifier.
Effect of ultrasonic waves on mass transfer rates of selected fluids
Authors: Fogler H. Scott , Timmerhaus Klaus D.
Published: June 2004

The application of ultrasonic energy to a fluid in a capillary has resulted in greatly increased rates of mass transfer (of the order of 800 to 2,000% above that without insonation) to occur at specific heights in the capillary. Reproducible results with several selected fluids (carbon tetrachloride, acetone, ethanol, and methanol) have shown that these specific heights are always at the half wavelengths of the particular fluid investigated. The mathematical model developed herein predicts that at these half wavelengths, the fluid particle displacement of the ultrasonic wave becomes quite large, exceeds the threshold value necessary for the stability of the surface waves, and causes droplets to be ejected into the vapor above the surface in the form of a fog. The resulting decrease in the diffusional path length of the ejected fluid provides the final mechanism for an increased mass transfer from the capillary tube.
A generalized equation for computer calculation of liquid densities
Authors: Yen Lewis C. , Woods S. S.
Published: June 2004

A generalized equation explicitly relating reduced density to reduced temperature and reduced pressure has been developed for calculating liquid densities of pure compounds on a digital computer. The analytical formulation is based mainly on a modified corresponding states principle and the graphical correlation of Lydersen, Greenkorn, and Hougen. The calculated densities from the equation reproduce the literature data within 2% for sixty‐two saturated liquids and nineteen compressed liquids.

With the aid of a pseudocritical method and a generalized equation of vapor pressure, the same equation is readily applied to the estimation of liquid mixture densities. The method of Prausnitz and Gunn is chosen for the evaluation of pseudocritical constants. For fifteen binary systems, one ternary system, and one quinary system, the one hundred fifty‐nine calculated densities agree with the literature data to within 3%. This method is limited to pseudoreduced temperatures less than 1.0.
Column height required for continuous chromatographic separation: A probabilistic model
Authors: Sciance C. T. , Crosser O. K.
Published: June 2004

A probabilistic model is used to develop the mathematical theory of a continuous chromatographic column. Equations are developed relating column height, feed location, degree of separation, and flow rates. Necessary sorption data can be obtained from a fixed‐bed chromatographic column.
The stability of Couette flow between rotating cylinders in the presence of a radial temperature gradient
Authors: Walowit J. A.
Published: June 2004

The effects of viscosity and density variations due to an imposed radial temperature gradient on the stability of Couette flow between rotating cylinders are investigated. The annular spacing between the cylinders is assumed to be small compared with the mean radius. The fluids considered are water and 50% aqueous glycerol. Free convection due to gravity is not considered.

Approximate solutions to the stability equations are obtained by the Galerkin method. Computations are restricted to the case where the outer cylinder is at rest. For the cases studied, the effects of radial convection were found to be small but the effects of the temperature dependence of viscosity were appreciable. The critical Taylor number based on the mean temperature viscosity was found to decrease as the viscosity variation became more pronounced and as the Prandtl number increased.
Tracking function approach to practical stability and ultimate boundedness
Authors: Paradis W. O. , Perlmutter D. D.
Published: June 2004

A graphical method of analysis is presented for studying the practical stability and ultimate boundeness of autonomous second‐order systems. It is argued that these measures of stability are in many cases more germane to design than Liapunov stability. The method incorporates much of the geometric character of a Liapunov analysis, but it is shown that a Liapunov function, relatively difficult to obtain, can be replaced by a set of easily postulated scalar functions which collectively yield the required stability information. Examples are given which demonstrate the use and effectiveness of the method.
Rates of hydrogen chloride oxidation
Authors: Jones Alva M. , Bliss Harding , Walker Charles A.
Published: June 2004

Rates of oxidation of hydrogen chloride (the Deacon process) were measured in a recycling reactor with chromic oxide catalysts. The temperatures were 325° to 355°C., and a wide range of reactant compositions was used. The reverse reaction was also explored at 355° to 370°C. The experimentation was carefully tested to be sure that the construction material did not affect the results and that diffusional effects were absent.

An empirical equation is described which correlates well the rates of oxidation and fits the original observed data. It is capable of predicting reasonably well some of the observed rates of the reverse reaction.
Direct contact heat transfer with change of phase: Spray‐column studies of a three‐phase heat exchanger
Authors: Sideman Samuel , Gat Yehuda
Published: June 2004

Transfer characteristics are presented for a perforated plate‐spray column in which a volatile dispersed phase evaporates while rising in the continuous, counterflowing, immiscible phase. Optimal column heights, volumetric transfer coefficients, holdup, and foam heights are reported as functions of flow rate and temperature approach for a pentane‐water system, A comparison with related studies is presented.
The dehydrogenation of isopropanol on catalysts prepared by sodium borohydride reduction
Authors: Mears David E. , Boudart Michel
Published: June 2004

Nickel catalysts reduced with sodium borohydride have been found to be active for the liquid phase dehydrogenation of isopropanol. The activity, per unit weight of catalyst, is at least as high as that of Raney nickel. Promotion of the new catalyts with small amounts of chromium has been explained by an increase in surface area. Indeed, the activity per unit surface area of the unpromoted and promoted nickel catalysts is constant over a sevenfold range of surface area.
Axial laminar flow of a non‐Newtonian fluid in an annulus
Authors: McEachern Donald W.
Published: June 2004

The equation of motion has been solved for steady axial, laminar, isothermal flow of an Ellis model fluid in a conduit of annular cross section. Tables are presented which may be used to obtain flow curves for annular flow of fluids whose Ellis parameters are known.

The Ellis fluid predictions are compared to experimental data on dilute polymer solutions flowing in annuli. Ellis fluid predictions of flow curves are also compared to those predicted by the generalized Newtonian fluid and the power law fluid.
Catalytic hydrogenation of propylene and isobutylene over platinum. Effect of noncompetitive adsorption
Authors: Rogers G. B. , Lih M. M. , Hougen O. A.
Published: June 2004

A mathematical and kinetics model is presented for reactions catalyzed by solid surfaces where both competitive and noncompetitive adsorption take place, a situation that may be general in reactions between large and small molecules catalyzed by solid surfaces.

In the adsorption of large molecules steric hindrance or multiple site adsorption cause maximum surface coverage of such molecules before all sites are occupied. This does not, however, preclude further adsorption of small molecules on the remaining isolated vacant sites nor does it preclude further surface reaction. The overall reaction model for such conditions may be expressed as
equation image
This particular model has been evaluated for the catalytic hydrogenation of propylene and isobutylene with the expectation that it may be useful in reactions that are of industrial importance. A reaction model based on either competitive adsorption or noncompetitive adsorption alone fails to correlate the experimental data.

In these two reactions maximum rates occur at olefin concentrations below 5 mole % and the catalytic adsorption constants for the olefins are a hundredfold greater than for hydrogen. This reaction model is similar to that proposed by Bond and Turkevich (15), who have further demonstrated through the deuteration of propylene that the actual mechanism of the reaction is much more complicated.
The prediction of liquid mixture enthalpies from pure component properties
Authors: Osborne Adam
Published: June 2004

The paper presents a procedure for calculating liquid mixture enthalpies, whereby a liquid heat of mixing is added to the molal average of the pure liquid enthalpies. The heat of mixing for the mixture is calculated from the heats of mixing of the binary systems at infinite dilution, which in turn are determined with a proposed molecular model for liquid mixing, and a postulate of acceptance. The two cases where the solute in the binary system is more volatile and less volatile than the solvent are treated separately. The case is also considered where a component of the liquid mixture is above its critical temperature; a pure liquid enthalpy is defined and justified for such pseudo liquids, and heats of mixing are then calculated as for actual liquids. Results are compared for four nonpolar binary systems, three with experimental data, and one with data calculated by other means. Data for a number of gases dissolved in water are also considered. The agreement in all cases is excellent.
Turbulent flow in annular pipes
Authors: Macagno Enzo O. , McDougall David W.
Published: June 2004

An extension to annular conduits of the well‐known method of calculating the resistance coefficient for turbulent flow in circular pipes is presented. The method is new in that it does not borrow any information from laminar flow theory; it gives, therefore, a location for the maximum velocity based only on turbulent flow characteristics. Expressions and a few essential graphs are given for the average as well as inner‐ and outer‐wall resistance coefficients for both hydraulically smooth and rough regimes and also for the transitional regime. A comparison with available experimental information for fully developed turbulent flow is presented.
Modified description of wave motion in a falling film
Authors: Massot Claude , Irani Farhad , Lightfoot E. N.
Published: June 2004

The presence of gravity‐capillary waves at the surface of a viscous falling film has been studied theoretically by a more rigorous linear treatment than presently available.

The present analysis is based on the assumption of steady state periodic solutions of the complete Navier‐Stokes equations. It provides methods of prediction, to a first order of approximation, for the wavelength, celerity, and wave number, in terms of the Weber number which emerges as the governing dimensionless group. This treatment includes as special cases the low Weber number analyses of Yih, Benjamin, Hanratty and Hershman, and Kapitza, as well as the high Weber number theory of Ishihara, Iwagaki, and Iwasa. Agreement with experimental observation is improved over that obtained from previous analyses.

The stream function of the system has been derived and the instantaneous streamlines have been constructed for application to heat and mass transfer.
Spinning of a Noll simple fluid
Authors: Slattery John C.
Published: June 2004

Previous results for a class of flows dynamically possible in a Noll simple fluid are the starting point for a description of melt spinning or dry spinning in the limit of a rapidly extruded, small diameter polymer thread. Simultaneous energy and mass transfer, important in the real process, are not taken into account; also neglected are inertial effects, body forces, and surface tension.
A mathematical treatment of the effect of particle size distribution on mass transfer in dispersions
Authors: Gal‐Or Benjamin , Hoelscher H. E.
Published: June 2004

A mathematical model is proposed that takes into account interaction between drops or bubbles in a swarm as well as the effect of particle size distribution. The model is used to solve the equations for unsteady state mass transfer with and without chemical reaction when the drops or bubbles are suspended in a nonextraordinarily purified agitated fluid. Steady state diffusion to a family of moving drops with clean interface and without interaction and chemical reaction has been also analyzed. The model demonstrates the sort of error that may arise when one applies uniform drop size assumptions to drop populations. It is shown quantitatively that this error is usually small when one replaces the variable particle size by the mean. By using variables that can be determined and predicted, the equations presented permit the estimation of diffusion rate per unit area of interface, as well as the average concentration and the total average rate of mass transfer in the disperser under pseudo steady state conditions.
Longitudinal dispersion in rotating impeller types of contactors
Authors: Miyauchi Terukatsu , Mitsutake Hiromi , Harase Ichiro
Published: June 2004

On the basis of a back‐flow model, the rates of interstage mixing of continuous phase for RDC and Mixco columns are measured experimentally under flow and nonflow conditions. These rates are correlated into dimensionless formulas for wide combinations of operational condition, column geometry, and dimensions, and are put into a single formula by introducing the power number as an additional parameter. The final correlation covers the impeller Reynolds number from 3.5 × 103 to 1.0 × 106 and the diameter of columns from 4.1 to 218 cm.
A correlation of the frictional characteristics for turbulent flow of dilute viscoelastic non‐Newtonian fluids in pipes
Authors: Meyer Warren A.
Published: June 2004

A formula has been determined which satisfactorily represents, for the existing data, the frictional characteristics of the turbulent flow of a dilute viscoelastic non‐Newtonian fluid in a pipe. This formula contains two elastic fluid parameters, one of which is strongly dependent on both polymer solute and concentration and the other appears to be a constant and independent of the polymer solutes which were used in this report. A rheometer is proposed based on this formula which should be useful in classifying fluids of this type.
Investigation of the turbulent shear flow of dilute aqueous CMC solutions
Authors: Ernst William D.
Published: June 2004

Experimental measurements of the fully developed turbulent flow field in straight circular tubes of dilute CMC solutions are described. The viscosity of the solutions used had a non‐Newtonian power law exponent of 0.93 to 0.95 in order to eliminate most of the effects attributed to power law fluids. Both pressure drop and velocity profile measurements were made over a wide range of Reynolds numbers. The velocity data were taken in both the linear sublayer and the turbulent core, and are presented in terms of the universal velocity parameters modified by use of a viscosity defined at the tube wall. A check of the existing empirical correlations based on a power law viscosity shows that none predict the observed velocity profiles.
Simultaneous heat and mass transfer in free convection with opposing body forces
Authors: Adams J. A. , McFadden P. W.
Published: June 2004

An experimental technique which utilized a Mach‐Zehnder interferometer was used to measure local heat and mass transfer coefficients during simultaneous heat and mass transfer. The experimental model was a vertical, subliming surface ofp‐dichlorobenzene. The body force created by the heavy organic vapor in the boundary layer opposed the upward thermal body force caused by heating the surface.

The results indicated that the heat and mass transfer, under the influence of opposing body forces over the range investigated, was from 10 to 15% lower than the values predicted by present approximate analytical solutions for a constant wall heat flux boundary condition.
The surface transport of adsorbed molecules
Authors: Weaver J. A. , Metzner A. B.
Published: June 2004

A detailed mechanistic model is developed to describe the process by which adsorbed molecules migrate over the surface of an adsorbent. The migration is assumed to occur as a result of a random hopping of partially desorbed species; explicit expressions are derived for the hopping rate and the distance traversed in a single jump for the case of a gas adsorbed on a homogeneous surface. In the degree of detail developed herein experimental determinations are still required (to evaluate an otherwise unknown ratio of partition functions, and the activation free energy) but the pressure or surface concentration dependency of the transport rate is given explicity.

The predictions are tested by comparison with three sets of experimental data for hydrocarbons adsorbed on porous glass; these systems were chosen as they may be shown to meet the assumption of an adsorbate migrating over an energetically homogeneous surface under the conditions studied. Reasonable values are found for the parameters and excellent agreement between the observed and predicting trends with pressure is noted in all cases.
Entrainment of air into a liquid spray
Authors: Briffa Francis E. J. , Dombrowski Norman
Published: June 2004

An investigation has been carried out into the flow pattern existing in and around a flat spray, particular attention being paid to the region of disintegration of the liquid sheet. The mass of air entrained into the spray, the decay of air velocity along the spray axis, and the spread of the drops in the plane normal to that of the sheet have been related to the operating conditions by equations theoretically derived and experimentally confirmed. Similarities between the characteristics of air entrainment into liquid sprays and into gas jets have been noted.
Generalization of the penetration theory for surface stretch: Application to forming and oscillating drops
Authors: Angelo Jacob B. , Lightfoot Edwin N. , Howard David W.
Published: June 2004

A method is developed for predicting rates of mass or heat transfer through stretching or shrinking phase boundaries of finite lifetime at low mass transfer rates. The primary result of this development, Equation (43), may be considered as a generalization of penetration theory. It includes as special cases similar expressions developed for more restricted situations, notably those of Ilkovic (7) and of Beek and Kramers (1).

This general development is then used to refine the Rose‐Kintner analysis (13) of mass transfer to large oscillating liquid drops for the limitig case of all heat or mass transfer resistance in the droplet phase. It is found that convection normal to the phase boundary tends to offset the direct effect of surface stretch, and that the postulated mass transfer behavior can be expressed adequately by a very simple expression, Equation (68). This result yields slightly lower predictions of mass transfer rates than the correlation of Rose and Kintner, but available data are not sufficiently accurate to indicate which is the more reliable.

The surface‐stretch model is also applied to drop formation at submerged nozzles. Experimentally it was found that the growth of surface during this process is essentially linear, which simplifies calculations. The model gives predictions of the mass transfer coefficient which are in reasonably good agreement with the predictions based on the assumption of continual formation of fresh surface first used by Groothuis and Kramers (18), and later by Beek and Kramers (1). Both models show that the mass transfer coefficient is at least fifteen times as high as predicted by boundary‐layer calculatins alone. Finally, the surface‐stretch model indicates that the mass transfer behavior druing the rise period is approximately fourteen times as important as during the formation period for the equipment used in this study.

An expression was also developed for the more general situation of appreciable resistance in each phase, Equation (62), by assuming the surface‐stretch model to describe the transfer processes in both phases. The two‐resistance theory (10) is exact under such circumstances. This result was also found to correlate available data reasonably well.

More data, however, are needed if meaningful tests of the above, or other, correlations are desired.
The evaporation of drops of pure liquids at elevated temperatures: Rates of evaporation and wet‐bulb temperatures
Authors: Downingm Carl G.
Published: June 2004

The rates of evaporation and the wet‐bulb temperatures have been correlated for drops of pure liquids evaporating in streams of high‐temperature air. The four liquids studied were acetone, benzene,n‐hexane, and water. The drops were of a millimeter in diameter and were suspended in a free jet of dry, vapor‐free air that ranged in temperature from 27° to 340°C. Reynolds numbers ranged from 24 to 325. Corrections to the Nusselt number to account for the heat lost the outwardly diffusing vapor ranged up to about 35%.
A fundamental analysis of slurry grinding
Authors: Turner H. E. , McCarthy H. E.
Published: June 2004

An analytical approach to mathematical expression of the mechanisms involved in typical slurry grinders is presented. Experimental equipment performance is correlated with developed formulas. Results are expressed in terms of fundamental machine and slurry parameters useful in predicting performance and scale‐up.
A theoretical approach to nonfoaming adsorptive bubble fractionation
Authors: Lemlich Robert
Published: June 2004

A theoretical discussion is presented for the separation attainable via adsorption at the surfaces of bubbles rising up through a liquid solution. This heretofore neglected operation, which is called bubble fractionation, differs from both foam fractionation and gas desorption.
Generalized couette flow of an ellis fluid
Authors: Wadhwa Y. D.
Published: June 2004

The motion of an ordinary Newtonian fluid in a channel caused by a pressure gradient alone, or caused by the motion of one of the walls, can be obtained separately; and the problem of generalized Couette flow (the motion due to both causes simultaneously) can be obtained by superposition. For an Ellis fluid, because of the nonlineraity of the viscosity‐stress law, the principle of superposition is not applicable. This paper is devoted to the solution of this problem of generalized Couette flow of an Ellis fluid in parallel flat plate and circular annular channels.
The effect of monomolecular films on the rate of gas absorption into a quiescent liquid
Authors: Plevan R. E. , Quinn J. A.
Published: June 2004

An experimental technique has been developed for measuring the permeability (or surface resistance) of various monolayers to gases, as well as their effectiveness in hindering any substrate motion which accompanies the absorption process. Results are reported for sulfur dioxide absorbing into water and into aqueous gels in the presence of several surface‐active agents. Measured surface resistances extend from a maximum of 200 sec./cm. for a condensed layer of hexadecanol to an indeterminably small value for expanded and gaseous films. After an initial period in which transfer is by diffusion alone, convective motion sets in. The onset and magnitude of the convective motion is displayed by measured absorption rates into water covered with monomolecular films and into viscous gels. The relative magnitude of the convective retardation of the various films parallels their permeabilities, both effects being proportional to the compressibility of the monolayer.
Laminar dispersion in capillaries: Part III. Experiments in horizontal tubes including observations on natural convection effects
Authors: Reejhsinghani N. S. , Gill William N. , Barduhn Allen J.
Published: June 2004

Experimental data on the axial dispersion of a solute in laminar flow in capillaries are presented for a range of Peclet numbers from 12 to 50,000 and of dimensionless time from 0.01 to 60. They show good agreement with the mathematical solutions over all ranges of variables as long as natural convection is unimportant. For slow flows it was observed that natural convection can both enhance and depress the dispersion significantly and that extremely small density differences (Δ p/p = 10−4) are adequate to cause these phenomena. A qualitative explanation for the apparently anomalous effects of natural convection is proposed.
Longitudinal dispersion mechanisms in packed beds
Authors: Babcock R. E. , Green D. W. , Perry R. H.
Published: June 2004

A theoretical study has been made of longitudinal dispersion mechanisms during steady flow of a fluid through unconsolidated spherical beads. The mathematical model utilizes a step function input of thermal energy and presents the solution for the transient behvior of the system. The longitudinal dispersion of the step input is considered the result of eddy mixing of the fluid, molecular conduction within the fluid, and a finite time lag for heat transfer to occur between fluid and particle. The latter mechanism is characterized by both a fluid film resistance and an intraparticle resistance. The exact solution, involving an infinite integral, is approximated to an error function form. The character of the contribution of each mechanism is apparent from the form of the approximate solution, and furthermore, the contributions are shown to be additive to yield the total dispersion. The conditions for convergence to the aproximate solution are indicated. The equations are presented such that the analysis is applicable to both heat and mass transfer processes.
Theoretical study of bubble dynamics in purely viscous fluids
Authors: Yang Wen‐Jei , Yeh Hsu‐Chieh
Published: June 2004

This paper analyzes the growth or collapse of a spherical bubble in an incompressible, viscous fluid. Theoretical results include the timewise variations in the bubble size and its growth or collapse rate, the fluid pressure, and the rate of energy dissipation. The analysis is general and may be applied to both Newtonian and non‐Newtonian fluids. A comparison is given for the collapse of the bubble in several viscous fluids.
Statistical models for surface renewal in heat and mass transfer: Part I. Dependence of average transport coefficients on age distribution
Authors: Koppel L. B. , Patel R. D. , Holmes J. T.
Published: June 2004

Average transport coefficients for different transport models are computed by using widely varying distributions of residence times of elements at the transporting surface. It is shown that for typical transport models, the shapes of the residence time and age distributions have an insignificant effect on the average transport coefficient. Operational techniques for calculating average coefficients and for constructing delayed versions of age distributions are presented.
A simplified method for the prediction of multicomponent adsorption equilibria from single gas isotherms
Authors: Kidnay A. J. , Myers A. L.
Published: June 2004

The ideal adsorbed solution theory of Myers and Prausnitz (7) provides an accurate and thermodynamically consistent method for predicting multicomponent adsorption equilibria. The major difficulty in the application of this theory lies in the calculation of the spreading pressure curves for the pure adsorbates. The purpose of this article is to show that in many cases of practical interest, the spreading pressure calculations may be greatly simplified or altogether eliminated with little or no loss in the accuracy of the calculations. The problem of adsorption azeotropy is also briefly discussed.
Model calculations for capillary condensation
Authors: Melrose James C.
Published: June 2004

Capillary phenomena arising from vapor phase condensation in porous media are discussed in the light of an exact interface curvature theory and a self‐consistent thermodynamic theory. The system studied consists of liquid condensed in the form of pendular rings at the contact points between identical spherical particles. The geometrical parameters—the curvature, the confined volume, and the surface area of the liquid‐vapor interface—must be expressed in terms of incomplete elliptic integrals. In addition several corrections are introduced for the classical Kelvin relation for lowering of vapor pressure. One of these is based on the density dependence of the isothermal thermodynamic susceptibility. Since the susceptibility vanishes at large negative pressures, an upper limit to the curvature is established. The balance equation for the extensive free energy is considered from the point of view of hydrostatic principles.