bluuebunny/crossref_metadata_2025 huggingface dataset:
Longitudinal dispersion in pulsed perforated‐plate columns
Authors: Miyauchi Terukatsu , Oya Haruhiko
Published: June 2004

Experimental measurements have been performed for pulsed perforated‐plate columns of different sizes and geometry to obtain longitudinal dispersion coefficients for continuous and dispersed phases and size and holdup of liquid droplets dispersed in the columns. These quantities are correlated with operating conditions and column design, including the data published by different authors. Longitudinal dispersion coefficients for the continuous phase are shown to follow the backflow model. A superficial number of stages in series in each compartment is shown to come from inherent instability of fluid motion in the compartment. The longitudinal dispersion coefficient of the dispersed phase approaches that of the continuous phase with increasing pulse velocity. Holdup and mean size of droplets are correlated mainly on the basis of the rate of energy dissipation in the column fluid. Inclusion of dispersed‐phase viscosity is shown to correlate the holdup data successfully for different liquid‐liquid systems.
Coalescence of liquid droplets in two‐component–two‐phase systems: Part I. Effect of physical properties on the rate of coalescence
Authors: Jeffreys G. V. , Hawksley J. L.
Published: June 2004

Experimental coalescence time and time distribution studies of the coalescence of a single droplet at a plane interface are presented for four two‐component–two‐phase systems. The results have been analyzed by dimensional analysis and statistical analysis, and a correlation of coalescence time and coalescence time distribution with the physical properties of the system is proposed.
Significance of pressure gradients in porous materials: Part II. Diffusion and flow in porous catalysts
Authors: Otani Seiya , Wakao Noriaki , Smith J. M.
Published: June 2004

Diffusion and flow rates through porous catalysts were measured under the conditions of finite pressure gradients for single‐ and two‐component systems. For large pore (low density) alumina pellets the diffusion rate counter to the pressure gradient was severely depressed, while for small pore Vycor the pressure gradient had little effect.

The equations developed in Part I for flow and diffusion in a single capillary were extended to porous catalysts. The resulting prediction methods contain no parameters which require transport data for their evaluation, but pore size and void fraction information is needed. For the catalysts investigated, both the permeability and diffusion rates varied several thousand‐fold. The calculated results predict the same extensive range and show the same effects of pressure gradient and pore properties. Also the quantitative agreement between calculated and experimental results is such that the theory provides a useful method of predicting transport rates through certain types of porous media.
Vapor‐liquid equilibria in hydrogen‐benzene and hydrogen‐cyclohexane mixtures
Authors: Thompson Richard E. , Edmister Wayne C.
Published: June 2004

A new vapor‐liquid equilibrium experimental facility has been built for and operated on light gas‐hydrocarbon systems. The range of operating conditions are 3 to 1,000 atm. and 25° to 400°C. A dynamic flow type of equilibrium cell is used. This and most of the other apparatus are from designs by Michels. Solubilities of hydrogen in benzene and in cyclohexane were obtained at 150° and 250°F. and at pressures up to 10,000 lb./sq.in.abs.

Compositions of the equilibrium vapor phases were determined so the vapor‐liquid K ratios could be derived. Thermodynamic consistency tests were applied to the data with the conclusion that the new data are consistent with volumetric properties, predicted by other methods.
A study of perfectly mixed photochemical reactors
Authors: Harris Paul R. , Dranoff Joshua S.
Published: June 2004

The performance of a perfectly mixed photochemical reactor has been analyzed for systems having low light absorption coefficients. The analysis has been tested by an experimental study of the decomposition of hexachloroplatinic acid in dilute aqueous solution. Results tend to verify the analysis, but indicate the need for additional experimental work.
Turbulence effect on direct‐contact heat transfer with change of phase: Effect of mixing on heat transfer between an evaporating volatile liquid in direct contact with an immiscible liquid medium
Authors: Sideman Samuel , Barsky Zvi
Published: June 2004

The concept of local isotropy in turbulent agitation together with the particular characteristics of volatile drops evaporating while in dispersion were used to derive a simple and practical correlation relating the specific power input with the temperature driving force and the heat flow rates for all conceivable mixing regimes. The correlation was verified by experiments which indicate that dilute evaporating dispersions are controlled by viscous shear stresses.

The generality of the proposed correlation is demonstrated by its application to pilot plant and laboratory data obtained over a wide range of turbulent mixing intensities. At its lower limit the correlation reduces to the well‐known relationship of surface‐boiling heat transfer.
Analytical and numerical solutions for laminar flow of the non‐Newtonian ellis fluid
Authors: Matsuhisa Seikichi , Bird R. Byron
Published: June 2004

Because of the apparent success in the use of the three‐constant Ellis model to describe a wide variety of experimental data, a summary is given of analytical and numerical solutions for this model. The solutions include isothermal flow between flat plates, in tubes, in films, in annuli (axial, tangential, and radial) and nonisothermal flow in tubes with constant wall temperature and with constant heat flux at the tube wall.
Local parameters in cocurrent mercury‐nitrogen flow: Parts I and II
Authors: Neal L. G. , Bankoff S. G.
Published: June 2004

An experimental study was made in a cocurrent vertical mercury‐nitrogen flow of local parameters, including local liquid velocity and gas fraction. In Part I the pertinent quantities are carefully defined and power‐law continuity expressions derived. A description is given of the apparatus, including a simple local liquid velocity probe. In Part II experimental velocity and void profiles are given for the mercury‐nitrogen flow. The regime is slug flow, but the slugs are not axisymmetrical, on account of the nonwetted walls. Intensities of density and liquid velocity fluctuations are computed for the first time and a comparison made with Levy's mixing‐length theory.
The effect of concentration level on the gas phase absorption coefficient
Authors: Vivian J. Edward , Behrmann William C.
Published: June 2004

A theoretical and experimental investigation has been made to determine the effect of the concentration level on the rate of mass transfer of a solute from a nontransfering or inert carrier gas in turbulent flow.

Diffusion theory predicts the gas phase mass transfer coefficient to be inversely proportional to the first power of the mean mole fraction of the nontransferring gas and to be a possible function of the rate and direction of mass transfer.

The results of an experimental study of the absorption of ammonia from mixtures with nitrogen into distilled water and aqueous ammonia solutions in a short wetted‐wall column verified the predicted inverse relationship between the turbulent gas phase absorption coefficient and the first power of the mean inert mole fractions ranging from 0.068 to 0.934. The data also showed that for the range covered in this investigation there was no significant influence of the mass transfer rate on the product of the coefficient and the mean mole fraction of the inert carrier gas.
Second‐order chemical reactions in a nonhomogeneous turbulent fluid
Authors: Vassilatos George , Toor H. L.
Published: June 2004

Very rapid, rapid, and slow second‐order reactions were studied in an isothermal turbulent flow reactor. The two aqueous reactant solutions were separately introduced through many alternate jets and the reaction took place in the resulting nonhomogeneous mixture. Very rapid reactions were diffusion controlled and were in agreement with earlier theory. All reactions followed second‐order rate laws based on time average quantities. The apparent reaction velocity constant was controlled by the mixing for very rapid reactions, by the chemical kinetics for slow reactions, and by both mechanisms for rapid reactions.
Determination of plate efficiencies from operational data: Part II
Authors: Davis Parke , Taylor D. L. , Holland C. D.
Published: June 2004

A method for the determination of the plate efficiencies for existing conventional and complex columns is presented. Information, such as any combination of product distributions, plate temperatures, and plate compositions, which is in addition to that required to solve a problem for a fixed column is used to determine efficiencies.
Axial dispersion during pulsating pipe flow
Authors: Taylor Harry M. , Leonard Edward F.
Published: June 2004

A method is developed for the treatment of data obtained from flow systems whose performance is unsteady and periodic. Experimental results from a study of axial dispersion in pulsating turbulent flow in an open, round pipe are presented; they show that pulsations can greatly increase axial mixing.
Diffusion in the laminar boundary layer with a variable density
Authors: Hanna Owen T.
Published: June 2004

The problem of isothermal diffusion in a variable molecular‐weight binary gas mixture is considered for the case when the process occurs in a laminar boundary layer. Viscosity and diffusion coefficient are assumed constant. Solutions are given for both forced and free convection at large Schmidt numbers and large mass transfer rates toward the surface. Use of the molar average velocity considerably simplifies the results. These results suggest that the constant density solution in terms of mole fractions, evaluated at free stream conditions, may be a good approximation for variable density. This technique, improved by an approximate correction derived herein, is shown to agree reasonably well with the results of exact numerical solutions of the boundary layer equations.
Size distribution dynamics in a salting out crystallizer
Authors: Murray D. C. , Larson M. A.
Published: June 2004

A laboratory continuous mixed suspension salting out crystallizer was designed and constructed to test the dynamic crystallization model proposed by Randolph and Larson. The model relates the crystal size distribution to nucleation and growth kinetics and operating conditions. The ammonium alum‐ethanol‐water system was selected because of its ease of operation and control.

The results of this work were in agreement with the steady state model. Under the conditions of these experiments, it was found that the nucleation rate dNo/dt was related to the growth rate r by dNo/dt = k1r2. The crystallizer was also operated under unsteady state conditions which resulted from variations in the production rate. The theoretical model with experimentally determined parameters was simulated on an analog computer and solved for production rate changes. The results indicated that the model was in agreement with the dynamic data for production rate upsets.
Peak nucleate boiling fluxes for liquid oxygen on a flat horizontal platinum surface at buoyancies corresponding to accelerations between −0.03 and lgE
Authors: Lyon D. N. , Jones M. C. , Ritter G. L. , Chiladakis C. I. , Kosky P. G.
Published: June 2004

Peak nucleate boiling fluxes for liquid oxygen near 1 atm, have been measured on a 0.75‐in.–diameter flat polished horizontal platinum surface located in a known, variable magnetic‐field gradient that produced steady acceleration (which could be maintained indefinitely) on the oxygen acting in opposition to the earth's gravitation, gE. Measurements were made under condition ranging from net negative (directed away from the heated surface) accelerations of −0.03gE acting on the bulk liquid to the normal accelerations, 1.0gE. The results indicate that at zero g conditions for the bulk liquid, the peak nucleate boiling flux is ∼0.55 of the value at 1.0gE. For bulk‐liquid accelerations ranging from ∼0.25 to 1gE, the experimental results confirm the ¼ power dependence of peak flux on acceleration as predicted by various correlations. However, below 0.25gE the peak flux becomes insensitive to the acceleration, varying approximately in proportion to the 1/14 power of the net acceleration. At bulk‐liquid conditions of zero g (±0.005gE) the peak plux breaks sharply and falls by a factor of 10 between zero g and −0.03gE (for this apparatus).
Heat transfer to decomposing nitrogen dioxide in a turbulent boundary layer
Authors: Brian P. L. T. , Reid R. C. , Bodman S. W.
Published: June 2004

Heat transfer coefficients were measured for the dissociating system 2 NO2⇋ NO + O2in turbulent flow. Heat transfer rates to this reacting gas are limited by the kinetics of the decomposition and recombination reactions. Experimental results agree to within 10% with a film‐theory solution for heat transfer accompanied by a nonequilibrium chemical reaction.
Forced convection mass transfer: Part II. Effect of wires located near the edge of the laminar boundary layer on the rate of forced convection from a flat plate
Authors: Thomas David G.
Published: June 2004

The local and the average rates of forced convection through laminar boundary layers on a flat plate were shown to be markedly increased by locating small cylinders near the outer edge of the boundary layer. The local rate of forced convection was strongly peaked directly beneath each cylinder; the magnitude of the effect depended upon the free stream velocity, the spacing between cylinders, and the gap between the cylinders and the plate. Under optimum conditions, local values of the rate of forced convection were increased as much as 340%, while the average values were increased by over 190%.
Laminar dispersion in capillaries: Part I. Mathematical analysis
Authors: Ananthakrishnan V. , Gill W. N. , Barduhn Allen J.
Published: June 2004

Since 1953, when G. I. Taylor first considered the problem, numerous studies of the miscible displacement of fluids in capillaries have produced several approximate mathematical solutions which are purported to be valid under different conditions. Their form and ranges of applicability have been in conflict to some extent, since no exact solution is available to check these expressions.

This study has resulted in exact numerical solutions to this problem with both axial and radial molecular diffusion accounted for. The range of parameters investigated is wide enough for comparison with all known analytical and empirical results and covers τ from 0.01 to 30 and NPe from 1 to 23,000. It is shown that for sufficiently large values of τ the Taylor‐Aris theory is valid and thus results for all τ and NPe of any practical interest are now known.

Axial molecular diffusion is significant at lower values of the Peclet number but the magnitude of NPe at which this occurs depends on the value of τ. In general, axial molecular diffusion is important for Peclet numbers less than about 100.

Present results show that there is no justification for Bailey and Gogarty's empirical modification which yields an exponent of 0.541 rather than 0.50 for τ in Equations (35) and (36). Also, for the system studied here, no justification was found for the conjecture of Bournia et al. that Aris' low NPe modification may not account for axial diffusion properly.

Simple expressions given by Equations (48) and (50) were developed empirically and they give with good accuracy the average concentration distribution over wider ranges of NPe and τ than previously reported expressions.
Non‐Newtonian flow in porous media
Authors: McKinley R. M. , Jahns H. O. , Harris W. W. , Greenkorn R. A.
Published: June 2004

This paper describes a preliminary study of the linear flow of a non‐Newtonian fluid, a water solution of Dextra (a polysaccharide), in porous media. A modification of Darcy's law, which uses capillary rheology data, is developed to describe non‐Newtonian flow in underground reservoirs. The generalization, in effect, replaces the porous media with a capillary of equivalent radius proportional to the square root of the ratio of permeability to porosity. The constant of proportionality αo should be independent of permeability and porosity for a given type of rock. This has been partially confirmed experimentally. In principle, a capillary rheogram and a single core test permit evaluation of αo. Then non‐Newtonian flow can be predicted in this type of rock regardless of porosity, permeability, or flow rate.
The influence of surface coverage on catalytic effectiveness and selectivity. The isothermal and nonisothermal cases
Authors: Hutchings John , Carberry James J.
Published: June 2004

Both nonisothermal and isothermal catalytic effectiveness factors are computed for kinetic rate laws of the Langmuir‐Hinshelwood, Hougen‐Watson type, involving surface coverage by reactant and products. Selectivity taxation is also treated and the significant influence of interphas heat and mass gradients surrounding the catalyst is displayed. The complexities of these real kinetic systems suggest caution in the use of prior generalizations based upon simpler rate laws.
Pressure drops and void fractions in horizontal two‐phase flows of potassium
Authors: Smith Lowell R. , Tek M. Rasin , Balzhiser Richard E.
Published: June 2004

Vapor‐liquid flow of a potassium‐8% sodium mixture was studied with the use of a boiling heat transfer test loop. Pressure drop data were obtained from a 36‐in. long, 0.495‐in. I.D. unheated test section. Void fractions were measured at the midpoint of the test section with gamma ray attenuation.

Flows were essentially frictional. Quality, total flow rate, and absolute pressure were the principal variables affecting the pressure drop results, which were correlated in terms of a two‐phase friction factor. A metallic void fraction correlation was developed from previously reported data for other metallic fluids together with the potassium data of this study.

The potassium two phase friction factors fall substantially lower than values predicted by well‐known frictional pressure drop correlations. Metallic void friction values are appreciably lower than data for other fluid systems. Velocity slip ratios appear to be much higher than for other fluid systems due to high liquid‐to‐vapor density ratios and low void fractions.
Forced convection mass transfer: Part III. Increased mass transfer from a flat plate caused by the wake from cylinders located near the edge of the boundary layer
Authors: Thomas David G.
Published: June 2004

Enhanced rates of mass transfer in the wake region behind detached cylindrical turbulence promoters were investigated with the use of the naphthalene sublimation technique. The maximum increase in the average rate of mass transfer through laminar boundary layers was over 170%. The remarkable feature of these results was that the enhanced rates of mass trasfer persisted for over one hundred and thirty cylinder diameters downstream from the cylinder generating the wake. The observed effect was not only strongly dependent on the free stream velocity and the location of the cylinders relative to the mass transfer surface, but there were marked differences observed between the rate of mass transfer in the wake region behind one and behind two cylinders. These results resemble a “tuning phenomenon” and are believed to be due to Tollmein‐Schlichting instabilities and premature transition.
Velocity and pressure profiles for Newtonian creeping flow in regular packed beds of spheres
Authors: Snyder L. J. , Stewart W. E.
Published: June 2004

A theoretical analysis is made of Newtonian creeping flow through dense cubic and simple cubic beds of spheres. Velocity and pressure profiles are obtained in equation form by Galerkin's error‐distribution method. The profiles satisfy the conservation equations approximately, and the boundary conditions and symmetry conditions exactly. The calculated friction factors are within 5% of experimental values for both packing arrangements.
A computational model for the structure of porous materials employed in catalysis
Authors: Foster Richard N. , Butt John B.
Published: June 2004

A computational model for the structure of porous materials such as those employed in catalysis is proposed. The void volume within the solid is considered to be composed of two major arrays of pores, centrally convergent and centrally divergent, respectively, interconnected at specified intervals within the arrays. The exact shape of these arrays is determined uniquely from the volume‐area distribution of the porous structure.

The model is applied to computation of counterdiffusional flux through a porous solid as measured in a Wicke‐Kallenbach experiment. The effects of dead end pores and of mixing on the results are discussed, and comparison with experimental data reported for a particularly well‐defined system is given.
The effect of wave induced turbulence on the rate of absorption of gases in falling liquid films
Authors: Jepsen J. C. , Crosser O. K. , Perry R. H.
Published: June 2004

Concentration profiles for carbon dioxide diffusion into thin water films with waves flowing down an inclined plate have been determined. Film Reynolds numbers were varied from 732 to 1,834 at a cell angle of inclination of 9 deg. 44 min. Total diffusivities measured from the concentration profiles showed a marked increase in the central region of the film, with the diffusivity tending toward the molecular diffusivity at the boundaries of the film. Interferometer pictures of the concentration profile showed that the effect of the waves was to compress and expand the profile as the surface of the film changed, but indicated no direct effect on the variation of eddy diffusivity normal to the liquid surface.
Bubble motion and mass transfer in non‐Newtonian fluids
Authors: Barnett Stanley M. , Humphrey Arthur E. , Litt Mitchell
Published: June 2004

Instantaneous mass transfer coefficients were obtained for the absorption of carbon dioxide bubbles rising in an aqueous solution of sodium carboxymethylcellulose. The rheological character of the solutions was well described by the Ellis model.

Mass transfer coefficients were high initially but trailed off rapidly with bubble age. Exceptions were found at specific diameters where the bubble shape went through a transition. At about 0.2 cm. a transition from ellipsoidal to a sphere shape occurred, which has also been observed in Newtonian fluids. At a larger diameter, however, the non‐Newtonian fluid showed a shape change from a spherical “cap” to a “top” shape and finally to an ellipsoid. A sudden increase of mass transfer coefficient accompanied each shape transition.

Drag coefficient data were correlated successfully with a new Reynolds number. The Newtonian and power law portion of the Ellis model each contributed a component to the Reynolds number, which, when added together, correlated drag data for the bubbles as well as for glass spheres.

Attempts to account for transition shape changes and bubble tailing in the non‐Newtonian fluid and their effects on bubble mass transfer are included.
The kinetics of sorption by ion exchange resin beds
Authors: Colwell Charles J. , Dranoff Joshua S.
Published: June 2004

The kinetics of sorption of dilute aqueous solutions of acetone, n‐propanol, ethylen glycol, and glycerine by packed beds of Dowex 50W‐X8 (H+) resin have been investigated experimentally. Data indicate that intraparticle diffusion of the solute is rate controlling and that density mixing and nonlinear equilibrium effects must be considered in analyzing this type of operation.
Heat transfer to molten flowing polymers
Authors: Griskey Richard G. , Wiehe Irwin A.
Published: June 2004

A precise, reproducible method has been developed for measuring temperature profiles in flowing molten polymers with heat transfer. Experimental data determined by this method showed that viscous dissipation occurred, but not at the level predicted theoretically. The difference between the actual and theoretical viscous dissipation was possibly due to flattening of fluid velocity profile, changing physical properties, and fluid viscoelasticity. Nusselt numbers calculated from the data checked thoretical Nusselt‐Graetz solutions.
Velocity distributions and normal stresses in viscoelastic turbulent pipe flow
Authors: Astarita Gianni , Nicodemo Luigi
Published: June 2004

Pitot tube readings in a viscoelastic turbulent stream are discussed thoretically, and are shown to be made up by a first normal stress contribution, an integral normal stress contribution, and a kinetic contribution. These three contribution are of comparable orders of magnitude. The integral of a Pitot tube scanning curve is shown to yield a momentum average factor of direct physical relavance. Experimental data show that the normal stress contributions are not negligible even in the central region of the pipe, although turbulent flow conditions were reached. Observed values of the relevant parameters are discussed.
Mass transfer from large oscillating drops
Authors: Rose P. M. , Kintner R. C.
Published: June 2004

A mass transfer model for vigorously oscillating single liquid drops moving in a liquid field has been developed with the concepts of interfacial stretch and internal droplet mixing. The model takes into account both amplitude and frequency of drop oscillations. Experimental values of fraction extracted were predicted with an average deviation of 15%. Oscillations break up internal circulation streamlines and a type of turbulent internal mixing is achieved.
Gas bubble entrainment by plunging laminar liquid jets
Authors: Lin Tong Joe , Donnelly Harold G.
Published: June 2004

A free, vertical jet of liquid plunging into a uiescent surface of the same liquid entrains the surrounding gas into the receiving liquid to form bubbles. The entrainment characteristics of such jets of Newtonian liquids of varying physical properties have been investigated by means of high‐speed photography.

Although both laminar and turbulent jets entrain gas bubbles, the mechanisms governing the entrainment process of the two types of jets are clearly different. Entrainment by turbulent jets results from the disturbances on the free surface caused by the jet instability; entrainment by laminar jets is accomplished by the formation of a thin shell of gas around the jet at the point of entrance, by the development of oscillations in the shell, and by its subsequent breakup into bubbles.

Entrainment occurs only when the average jet velocity exceeds a certain critical value termed minimum entrainment velocity. For a laminar jet having a flat velocity profile at the point of entrance, the following correlation permits prediction of the minimum entrainment velocity:

where the dimensionless numbers are based on the liquid properties and the jet diameter at the point where the jet meets the surface of the receiving liquid.
Surface catalysis of the hydrogen‐oxygen reaction on platinum at low temperatures
Authors: Leder Frederic , Butt John B.
Published: June 2004

The reaction between hydrogen and oxygen has been investigated at low temperatures with a dilute platinum catalyst. Experimental conversion data indicate a strong effect of product water on reaction rate and a second‐order dependence of rate on hydrogen partial pressure in the presence of a large excess of oxygen. This observed behavior is considerably different from expectations based on prior literature.

Stable activity levels are much lower than those reported by Boreskov for this reaction on platinum; it is shown that present results are consistent with the effect of chemisorbed oxygen proposed by Boreskov and with the conditions imposed for reaction on a dilute catalyst. Activation energy for the reaction at 100°C. was determined to be 10± 2 kcal./g.‐mole.
The relaxation of concentration polarization in a reverse osmosis desalination system
Authors: Tien Chi , Gill William N.
Published: June 2004

An analysis of diffusional effects in a system consisting of impermeable relaxation sections placed alternately between semipermeable membrane sections indicates significant attenuation of salt concentration at the boundary in the impermeable section. The analysis employed exploits Equation (16), a relation deduced by Lighthill (4), to avoid the necessity of using orthogonal function expansions which converge slowly in the diffusion entrance region which is studied here.
Axial dispersion in liquid flow through packed beds
Authors: Miller Steven F. , King C. Judson
Published: June 2004

Step‐function injection and purging of a dilute salt tracer in water was used to measure axial dispersion for low Reynolds number liquid flow through beds of uniform sized, random packed glass spheres. The resultant data and those of several previous studies are coordinated and interpreted in terms of Reynolds, Schmidt, and Peclet numbers.
Effect of axial diffusion of vorticity on flow development in circular conduits: Part I. Numerical solutions
Authors: Vrentas J. S. , Duda J. L. , Bargeron K. G.
Published: June 2004

An entrance model is presented which extends the analysis of the flow development in the entrance region to flow regimes which are inadequately described by a boundary‐layer analysis. Results are presented for the numerical solutions of the boundary‐layer equations and the complete equations of motion at five different Reynolds numbers. The effect of the axial diffusion of vorticity on the pressure drop, entrance length, and development of the vorticity and velocity fields is demonstrated.
Constitutive equations for viscoelastic fluids for short deformation periods and for rapidly changing flows: Significance of the deborah number
Authors: Metzner A. B. , White J. L. , Denn M. M.
Published: June 2004

The proper forms and asymptotic characteristics of constitutive equations which may be useful for the description of viscoelastic fluids in flow fields of engineering interest are considered. It is seen that the Deborah number emerges as a natural ordering parameter which determines, on the one hand, whether simple approximations explicit in stress may suffice to describe the fluid properties or, on the other hand, whether implicit or integral equations are required. Methods of scale‐up are discussed.
Mass transfer in supported forths
Authors: Workman Walter L. , Calvert Seymour
Published: June 2004

Operating and mass transfer characteristics are reported for a supported froth apparatus consisting of a dual‐flow sieve plate column with eggcrate packing above the plate. The assembled packing produced a series of vertical tubes and served to support the froth generated at the plate, increasing its height and consequently the contact time. Addition of the packing improved the mass transfer efficiency. Systems studied were ammonia–air–water and carbon dioxide–air–water. Effects of liquid and gas rate as well as packing size and spacing are correlated. A model based on measurable physical parameters was developed to predict efficiency, and a generalized correlation of efficiency was developed.
Prediction of thermodynamic properties of dense gas mixtures containing one or more of the quantum gases
Authors: Gunn R. D. , Chueh P. L. , Prausnitz J. M.
Published: June 2004

Effective critical constants for helium and normal hydrogen have been determined by fitting experimental volumetric data for these gases to the generalized tables of Pitzer. The effective critical temperature and pressure are found to depend on the temperature and on the molecular mass in a simple manner permitting good estimates to be made of effective critical constants for other quantum gases for which experimental data are scarce (neon, isotopes of helium and hydrogen). Pitzer's tables are used with pseudocritical mixing rules to predict thermodynamic properties of mixtures at high pressures and low temperatures. Calculated compressibility factors and enthalpies are in excellent agreement with experimental results for dense mixtures of hydrogen‐methane, hydrogen‐argon, and helium‐nitrogen.
Turbulent dispersion in a pipe flow
Authors: Becker H. A. , Rosensweig R. E. , Gwozdz J. R.
Published: June 2004

The nearly homogeneous, isotropic turbulence field in the core of a fully developed pipe flow was chosen as the medium for turbulent dispersion of a smoke tracer injected from a point on the centerline. By using the optical probe technique the fields of the mean and fluctuating point concentration were mapped at several Reynolds numbers, and spectral analyses made of concentration fluctuations on the plume axis. With the use of sheet illumination, the mean and fluctuating components of the integral material concentration in a plume cross section were measured and the fluctuating component was spectrally analyzed. The maximum Reynolds number was 684,000, the maximum ratio of root‐mean‐square concentration fluctuation to mean concentration exceeded 100% for points and 40% for sheets, and the turbulent Peclet number was found to equal 850. The existence of standard flow conditions was confirmed by measurement of the frictional drag coefficient and the mean concentration field.
A method of getting approximate solutions to the orr‐sommerfeld equation for flow on a vertical wall
Authors: Anshus Byron E. , Goren Simon L.
Published: June 2004

A method is presented for getting approximate solutions to the Orr‐Sommerfeld equation for free surface flows. The method consists of replacing the velocity, normally a function of distance from the wall, by its value at the free surface while the second derivative of the velocity is kept at its true value. This permits a simple solution to the equation and the eigenvalues can then be determined by a simple and rapid numerical technique. Comparison of this approximate solution for the flow of a thin film on a vertical wall with existing exact numerical solutions and with analytical results valid only for small Reynolds numbers shows the approximation to be quite accurate for most practical values of the parameters and suggests that the method will be useful in investigating the stability of related flows.
Liquid surface area effects in a wetted‐wall column
Authors: Robert Reker J. , Plank C. A. , Gerhard E. R.
Published: June 2004

Vaporization of methanol and carbon tetrachloride into air and carbon tetrachloride into helium was carried out in a counterflow wetted‐wall column at 10° to 20°F. These data show an influence of liquid rate upon the mass transfer coefficients. Liquid rate influence has been empirically accounted for by a function of surface area increase caused by rippling of the liquid film.
Adsorption of hydrocarbon gas mixtures at high pressure
Authors: Preston Mason J. , Cooke C. E.
Published: June 2004

An experimental investigation was made of the adsorption or silica gel of components from light hydrocarbon mixtures, and the results were used to test a multicomponent adsorption theory. Experimental methods included a volumetric technique to measure pure component adsorption and flow techniques for adsorption from mixtures. Although the majority of measurements was made at 100°F., two mixtures were studied over the temperature range 40° to 160°F. Pressure was varied up to 1,800 lb./sq.in.abs. The Brunauer‐Emmett‐Teller (BET) theory of adsorption, as extended to mixtures by Hill, was tested against the experimental data and was found to be adequate for calculating adsorption from hydrocarbon mixtures of components heavier than methane. To account for nonideal behavior, the fugacity of each component in the gas and in the adsorbed phases was calculated by using the Benedict‐Webb‐Rubin equation of state. The differences in experimental and theoretical values for adsorption capacity were less than 10% for most of the conditions tested, but ranged up to about 25% for the highest pressures studied. Although the BET theory represents a simplified model of a complex process, it can be used to supply adsorption data for engineering application over ranges of pressure, temperature, and gas composition usually encountered in adsorption processing of natural gas mixtures.
Rate data and derivatives
Authors: Nevers Noel De
Published: June 2004

In most rate process problems, the original experimental data must be differentiated to obtain the derivatives, which are the information actually sought. For first derivatives all the commonly used methods give about the same result. However, the common methods of calculating derivatives can give very different second derivatives for the same set of starting data. Thus, in problems in which the desired result is a second derivative, the answer obtained is a strong function of the method used to calculate second derivatives. This is illustrated by several examples.
Photochlorination in a tubular reactor
Authors: Cassano Alberto E. , Smith J. M.
Published: June 2004

A method of describing the behavior of a single‐phase, photochemical reaction in a tubular flow reactor is given. A simplified form of the equations is applied to experimental data for the chlorination of propane.

The results indicate that the reaction rate is second order in chlorine concentration and first order in light intensity at the wall. Independent experimental actinometer measurements permit the determination of absolute values of the kinetic constants. Such data are rarely available for photochemical reactions. Filter solutions flowing through a jacket around the reactor is shown to be a practical method for studying the effects of light intensity, as well as for cooling the reactor. The optical efficiency of the reactor lamp system was 11%.
Reverse osmosis in annuli
Authors: Gill William N. , Zeh Dale W. , Tien Chi
Published: June 2004

The nonlinear problem of reverse osmosis in annular conduits is solved by a series expansion method which is very accurate in the diffusion entrance region near the inlet of the membrane section. It is found that polarization at the outer membrane surface is significantly greater than at the inner wall.

In the diffusion entrance region, for the problem considered, the degree of polarization depends on the three parameters, σ, and B2, which are known once the operating conditions and the physical properties of the system are specified. The quantities θi (0) are tabulated for a wide range of ηk and B2. With these quantities known one can apply Equation (17) at β = 0 to calculate the wall concentration distribution and, with Equation (4), the flux distribution along the system. Then, by using Equation (26), the water produced by the system can be determined explicitly in terms of prescribed operating conditions.
Theoretical analysis of the falling cylinder viscometer for power law and bingham plastic fluids
Authors: Eichstadt F. J. , Swift G. W.
Published: June 2004

Theoretical equations and their solutions for the falling cylinder viscometer are presented for the Bingham plastic and power law models.
Measurements of velocity profile in developing liquid flows
Authors: Atkinson Bernard , Kemblowski Zdzislaw , Smith J. M.
Published: June 2004

An optical technique for the quantitative determination of point velocities in rapidly developing laminar flows of transparent liquids is useful as an experimental tool in problems of complex geometries and fluids. The accuracy of the technique has been confirmed by comparison of experimental data with the numerical solution of the equation of motion for the entrance region problem. A distributor capable of generating a flat velocity profile has been developed for this purpose.
Axial dispersion and heat transfer in liquid‐liquid spray towers
Authors: Mixon F. O. , Whitaker D. R. , Orcutt J. C.
Published: June 2004

A radioptracer technique was utilized to measure axial dispersion in both phases in spray towers operated at and near flooding. A new method that exhibits certain advantages over methods employed in the past is presented for reducing such data. It is demonstrated that axial dispersion in flooded and near‐flooded spray towers is sufficiently severe to control completely their performance as heat exchangers.
An experimental study of nonisothermal effectiveness factors in a porous catalyst
Authors: Miller F. W. , Deans H. A.
Published: June 2004

Circulating hydrogen‐oxygen mixtures were reacted at atmospheric pressure in a single long porous catalyst cylinder which contained a thermocouple‐micromanometer probe. Rate and temperature rise data were obtained at 20°, 30°, 50°, and 60°C. in the concentration range 0 to 5% oxygen in hydrogen.

The data were used in connection with the transport equations to obtain effectiveness factors, rate constant, activation energy, and reaction order for oxygen concentration.

The necessity of considering thermal effects is exhibited clearly by this system. The maximum temperature rise observed inside the catalyst (33°C.) is associated with a 60% increase in utilization factor over the isothermal value.
Critical flow of liquid‐vapor mixtures
Authors: Cruver James E. , Moulton R. W.
Published: June 2004

A unified theory of one‐dimensional, adiabatic, separated, two‐phase flow is presented. To describe the flow adequately, four mixture specific volumes are defined. They are based on area, momentum, kinetic energy, and velocity averages. Increasing relative velocity between the phases initially lowers all mixture specific volumes except the velocity average. The momentum average specific volume minimizes when the slip ratio equals (Vg/Vf)1/2, while the kinetic energy average specific volume reaches its minimum value at a slip ratio of (Vg/Vf)1/3. Area average specific value does not minimize with slip ratio.

Because a higher slip ratio would decrease the entropy of a closed system, (Vg/Vf)1/3is the maximum slip ratio attainable in two‐phase critical flow. Based on the maximum slip ratio and isentropic flow, a new critical flow model was developed and compared with the steam‐water critical flow data of four recent investigations. While the predicted flow rates followed well the pressure behavior of the experimental data, they were too low at high qualities and too high at low qualities. The average percentage difference between experimental and predicted critical flow rates was −8.5% (three hundred and seventy‐six data points).

Differences in the approach to critical flow between a gas and a vapor‐liquid stream appear to be caused by the latter's increased frictional and gravitational pressure drops and relative velocity effects.
Gas absorption by drops traveling on a vertical wire
Authors: Rajan Shanti Mohan , Goren Simon L.
Published: June 2004

In the measurement of the absorption of carbon dioxide gas by a series of oil drops moving down a vertical wire the variables studied are drop frequency, oil viscosity, wire size, and column length. A model is proposed which assumes that the gas is absorbed by almost stagnant liquid film between and covering the drops, that the film is subsequently mixed with a drop as it moves past, and that the dissolved gas is carried from the column in circulating loops of liquid within the drops. The model leads to an equation which correlates the data and gives a good approximation to the slope of the line.
Isobaric integral heats of vaporization for methane‐ethylene system
Authors: Tully Philip C. , Edmister Wayne C.
Published: June 2004

An isobaric calorimeter has been built for measuring the integral heat of vaporization at high pressures and low temperatures simultaneously with vapor‐liquid equilibria data. The methane‐ethylene system was studied at 20 and 40 atm., with data obtained on three mixtures and the two pure components. The experimental results are compared with three different calculation methods.
Adduction in the decane‐urea‐ethanol system: Part I. Equilibrium studies
Authors: Tamarelli A. W. , Manning F. S.
Published: June 2004

Phase equilibria in the decane–urea–ethanol system were investigated between 15° and 40°C. Solubility limits for urea–decane adduct in ternary liquid solutions and for urea in ethanol were measured over the entire feasible range of compositions, thus defining the phase diagrams. Activity coefficients estimated for the saturated liquid solutions reflected strong positive deviations from ideality. The magnitudes were consistent with the results of independent vaporliquid equilibrium studies.
Stability of loop reactors
Authors: Luss Dan , Amundson Neal R.
Published: June 2004

A method of determining all the possible steady states of a tubular recycle reactor with plug flow is presented. The information needed to determine the steady states can be used to ascertain the asymptotic and global stability of the reactor without performing transient computations. The effects of changes in the recycle ratio and start‐up conditions are examined. Several numerical examples are included to demonstrate the use of the method for various types of recycle reactors.
The identification of nonlinear reaction systems with two‐level inputs
Authors: Harris G. H. , Lapidus Leon
Published: June 2004

The general problem of characterizing a nonlinear, physical process from its input‐output records is examined. A method of identifying the class of nonlinear, time‐invariant processes with switched two‐level inputs and finite memories is successfully applied to several nonlinear systems. The identification model consists of a finite, orthogonal series expansion for the output as a function of the past of the input. Of particular interest is the characterization and synthesis of a nonlinear, continuous stirred‐tank reactor. This system, as well as others that are investigated, is simulated on a digital computer and identified after an initial observation period. No specific knowledge of the unknown process is presumed; however, only moderately fast input switching is permitted. After synthesizing the identification model, the process and model outputs are compared.
Application of molecular corresponding states theory to highly nonideal liquid mixtures
Authors: Wheeler Joe D. , Smith Buford D.
Published: June 2004

There are four points of flexibility in present molecular formulations of the corresponding states idea. At these points the procedure followed or the numerical values can be tailored to achieve better agreement between predicted and experimental properties without violation of physical principles. These flexibilities are the exponent values used in the pair‐potential function, the averaging procedure used to obtain an effective mixture pair‐potential function, the combination rule for unlike‐pair parameters, and the selection of a reference substance. The first two flexibilities are used in this paper to show that the conformal‐parameter equations can correlate excess free energy and activity coefficient data of highly nonideal liquid mixtures. A pair‐type‐probability function is introduced in the averaging procedure used to obtain a mixture pair‐potential function. Any macroscopic or molecular property may be used in this weighting function to improve mixture‐property prediction.
An application of noninteracting control to a continuous flow stirred‐tank reactor
Authors: Foster Robert D. , Stevens William F.
Published: June 2004

A general method, given in a companion paper, by which an interacting linear multivariable system may be decoupled into independent subsystems, is applied to a continuous flow stirred‐tank reactor. The form of the compensating controllers required for the physical system is obtained. It is then verified numerically that noninteraction is achieved, as postulated, by simulation of the linear model with compensating control on the analog computer.