bluuebunny/crossref_metadata_2025_split huggingface dataset:
Skin friction of power law fluids in turbulent flow over a flat plate
Authors: McDonald A. T. , Brandt Harry 
Published: June 2004

AbstractAn analysis is presented for skin friction of power law fluids in turbulent flow over a flat plate. A momentum balance is combined with a logarithmic velocity profile and the resulting equation is integrated. Skin friction is shown to be a function of non‐Newtonian Reynolds number and power law shear rate exponent. Closed form solutions for viscous drag are obtained for some values of shear rate exponent, but in general a numerical integration is necessary.The equations and curves presented are valid for any power law fluid. Computations may be carried out once the fluid viscosity and shear rate exponent are known. As an example, the results are applied to a power law fluid consisting of Carbopol in water. It is shown how viscous drag is affected by changes in the polymer concentration.
Film boiling of liquid nitrogen from porous surfaces with vapor suction: Experimental extensions
Authors: Pai V. K. , Bankoff S. G. 
Published: June 2004

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

AbstractFrequency response techniques have been applied to the study of the absorption of sulfur dioxide in water contaminated with surface‐active material. The response of a 0.004‐in. thick liquid film to a sinusoidally varying sulfur dioxide pressure was determined for frequencies ranging from 1 to 10 cycles/sec.The total quantity of sulfur dioxide dissolved was observed continuously by measuring the amount of light absorbed by the film, which contained a colored hydrogen ion indicator, cresol red. The experimental data indicate the presence of a surface phase of absorbed material through which sulfur dioxide molecules had to pass as they were transferred between gas and liquid. In addition to creating a resistance to the passage of the solute molecules, the surface phase apparently was capable of storing the molecules temporarily.
Continuous ion flotation of dichromate
Authors: Grieves Robert B. , Schwartz Stephen M. 
Published: June 2004

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

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

AbstractA theory is developed to enable prediction of interfacial tension in unsymmetrical, regular, binary liquid systems from solubility data. This is also shown to be applicable to nonregular aqueous binary systems by using solubility parameters and molar volumes calculated from mutual solubilities as substitutes for true molar volumes and the solubility parameters obtained from energies of vaporization.The theory is extended to include unsymmetrical, regular, ternary liquid systems, and is shown to be applicable to systems consisting of perfluoro‐n‐hexane and other nonpolar organic liquids. The theory is not adequate for aqueous ternary systems.
Optimality and computational feasibility in transient control: Part I. A modified criterion for optimality
Authors: Paradis W. O. , Perlmutter D. D. 
Published: June 2004

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

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

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

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

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

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

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

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

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

AbstractThe theoretical transient behavior of an isothermal packed bed or tubular reactor with direct recycle is investigated. It is shown that the recycle effect, coupled with the phenomenon of axial dispersion, causes waves in the reactant concentration to travel through the bed when the feed concentration undergoes a step change. The waves have a length almost equal to the bed length and they travel with the velocity of the fluid. The behavior of the waves is very insensitive to the value of the Peclet number.The pertinent linear differential equation is solved by the method of generalized Fourier transforms and the boundary conditions are such that the Sturm‐Liouville theorem cannot be used. The operator is nonself‐adjoint and the eigenfunctions are not mutually orthogonal. The eigenvalues, which are complex, are found by means of the argument principle. Sample calculations are presented of the first one hundred terms of the Fourier expansion of a solution function and this is compared to a simplified approximate series which is developed.
Stratified laminar flow in ducts of arbitrary shape
Authors: Yu H. S. , Sparrow E. M. 
Published: June 2004

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

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

AbstractFinite‐difference methods were used to compute hydrodynamic instability due to natural convection in an enclosed horizontal rectangular region heated from below. Critical Rayleigh numbers were determined for a series of Prandtl numbers and length‐to‐height ratios. For Prandtl numbers greater than unity excellent agreement was obtained between these calculations and the values predicted by Kurzweg on the basis of a linearized theory. However, for Prandtl numbers less than unity the critical Rayleigh numbers exhibited a dependence on NPr, which was not predicted by the linearized theory. For Rayleigh numbers greater than the critical, complete temperature and velocity fields were determined.The calculations assumed that the fluid motion is two dimensional. Experiments have indicated that the flow may be two or three dimensional depending on minor perturbations in the boundary conditions.Although a number of metastable two‐dimensional circulations are possible for symmetrical initial conditions, the calculation always converged to a single, unique solution for any asymmetric initial condition.
Kinetics of the heterogeneous decomposition of nickel tetracarbonyl
Authors: Carlton Herbert E. , Oxley Joseph H. 
Published: June 2004

AbstractThe decomposition of nickel tetracarbonyl at pressures between 20 and 200 torrs was studied at temperatures from 100° to 225°C. In the cross‐flow system, the rate in the absence of appreciable dilution was primarily limited by kinetic resistances at temperatures up to about 175°C. over an effective Reynolds number range of 5 to 100. Gas phase diffusional resistances were controlling at higher temperatures. Corrections for natural convection were employed in both the kinetic and diffusional regions of control.
Numerical solution of the Navier‐Stokes equation for flow past spheres: Part I. Viscous flow around spheres with and without radial mass efflux
Authors: Hamielec A. E. , Hoffman T. W. , Ross L. L. 
Published: June 2004

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

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

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

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

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

AbstractLocal and average holdup and drop size distribution as function of flow rates were measured for kerosene drops and water in a countercurrent, 15‐cm. I.D., 160‐cm. long, spray column. The range of flow rates was 5 to 40 liters/min. of kerosene and 0 to 50 liters/min. of water. At the same pairs of flow rates of the dispersed and the continuous phases in spray columns, three modes of drop packings can be obtained. These are termed, in order of increasing average holdup and increasing regularity of flow patterns, dispersed, restrained, and dense packings. For dispersed packing, at low flow rates of the two phases, the holdup and the drop size are constant along the column. At high flow rates the drop size increases from bottom to top of the column and the holdup increases from top to bottom of the column. The range of flow rates for the operation of a spray column is extended by the use of a conical entry section (Elgin design) at the bottom of the column, by the formation of an equilibrium region in the conical section.The average holdup increases with increased flow rates of both phases for dispersed and restrained packings, and with decreased flow rates of both phases for dense packing.The best definitions of flooding in a spray column are either the point of maximum average specific area of the drops, which corresponds to the onset of coalescence in the column, or the start of rejection of drops from the column proper.
Influence of resin selectivity on film diffusion‐controlled ion exchange
Authors: Copeland J. P. , Henderson C. L. , Marchello J. M. 
Published: June 2004

AbstractAn analytic solution of the Nernst‐Planck equations is derived which applies to a selective resin when film diffusion controls. The selectivity has a marked effect on the rate of exchange for a wide range of diffusivities. The unit‐selectivity solution of Schlögl and Helfferich is included as a special case of the more general solution.