bluuebunny/crossref_metadata_2025 huggingface dataset:
Heat transfer and binary diffusion with thermodynamic coupling in variable‐property forced convection on a flat plate
Authors: Zeh Dale W. , Gill William N.
Published: June 2004

The variable‐property, laminar, boundary‐layer equations, which describe simultaneous momentum, heat, and binary mass transfer with thermodynamic coupling,

Thermodynamic coupling refers to the Soret (or thermaldiffusion)effect, which is the flow of mass caused hy a temperaturegradient, and the Dufour (or diffusion thermo) effect, which is theflow of heat caused by a concentration gradient.

are analyzed for air flows over a flat plate with the injection of foreign gases through the solid surface. A simplified general treatment of thermodynamic coupling is developed and applied to yield approximate but accurate expressions for evaluating heat transfer rates and adiabatic wall temperatures for injection of hydrogen, helium, and carbon dioxide. This method explains why the driving force based on (Tω − Tω) can be used to correlate heat transfer results for situations where diffusion thermo is important. Furthermore, and perhaps most significant, the method provides a simple error estimate for the correlation obtained by using the adiabatic wall temperature.

It is shown that the injection of lightweight gases can significantly reduce viscous dissipation in flows over slender bodies and that diffusion thermo and dissipation effects can be otion in flows over slender bodies and that diffusion thermo and dissipation effects can be of the same order of magnitude even for reasonably high‐velocity flows. These effects are discussed in terms of convenient quantities, called σ functions.
Numerical solution of the Navier‐Stokes equation for flow past spheres: Part II. Viscous flow around circulating spheres of low viscosity
Authors: Hamielec A. E. , Johnson A. I. , Houghton W. T.
Published: June 2004

Steady state solutions of the Navier‐Stokes equations for Reynolds numbers of 0.1, 1, 50, 100, and 200 have been obtained by using finite‐difference methods. The effects of radial and angular step size and wall proximity have been investigated. Results were found in the form of stream function and vorticity distributions with pressure distributions and drag coefficients calculated from them. The results compare favorably with experimental data and show a steady trend from Hadamard‐Rybczynski flow to boundary‐layer flow after Levich‐Chao‐Moore. For a circulating sphere of low viscosity there is no flow separation indicated at Reynolds numbers equal to or less than 200.
The forgotten effect in thermal diffusion
Authors: Korchinsky Walter J. , Emery Alden H.
Published: June 2004

The basic equations that describe the thermal diffusion column, including the forgotten effect, were solved numerically. When the density of the liquid in the column varies with concentration, the effect is important in transient batch operation of columns, increasingly so as the wall spacing decreases, but it has no influence at the steady state. Experimental work corroborated the theoretical results.

According to the theory, the instances of concentration reversal reported in the literature cannot be the result of the forgotten effect; the fluids involved could not have had the necessary properties. Attempted duplications of these instances in careful experiments yielded normal behavior. However, theoretical and experimental work on a column with a deliberately nonconstant wall spacing indicated that concentration reversals could occur in the complete absence of any forgotten effect contribution.
Partial control of linear inventory systems
Authors: Wilde Douglass J. , Passy Ury
Published: June 2004

Feedback and feedforward inventory control systems are derived which give improved probability of holding all inventories between predetermined limits, even when there are fewer controllers than controlled variables. The concept of partial controllability is developed to describe systems with uncontrollable states. An example shows that four tank levels can be held within limits with high probability, with only one manipulated flow rate used.
The prediction of bubble terminal velocities from wave theory
Authors: Mendelson Harvey D.
Published: June 2004

The terminal velocity of bubbles in low viscosity liquids of infinite extent is known to undergo a marked transition in behavior at an equivalent radius in the order of 0.07 cm. This transition is apparently due to a change from viscous to inviscid flow. It is also known that the inviscid flow regime can be further subdivided into surface tension‐ (Weber number) and buoyancy‐ (Froude number) dominated regimes. This behavior of rising bubbles is strikingly similar to the behavior of surface waves propagated over deep water. The analogy is found to be in quantitative agreement when the wavelength is suitably interpreted in terms of bubble dimensions. The inference of this analogy is that bubbles may be thought of as interfacial disturbances whose rate of propagation is governed by the well‐known laws of wave motion.
Flow of viscoelastic fluids past a flat plate
Authors: Hermes R. A. , Fredrickson A. G.
Published: June 2004

The flow of viscoelastic fluids past a flat plate has been investigated. Experimental studies were performed with aqueous solutions of sodium carboxymethylcellulose used as viscoelastic fluids and corn syrup as a viscous Newtonian fluid. It was observed that the flow patterns of elastic and inelastic fluids are markedly different. Tracer particles placed in the approaching viscoelastic fluids to follow their motion were seen to first decelerate and then to accelerate until a nearly constant velocity was reached. On the other hand tracer particles in the Newtonian fluid were observed merely to decelerate smoothly to the constant velocity.

The drag force measured for the viscoelastic fluids was found to be roughly twice that predicted by inelastic models of fluid behavior. Predicted and measured values of the drag force for the Newtonian fluid agreed well.

A discussion of mathematical solutions to the problem of flow of viscoelastic fluids past a flat plate is given. Solutions are obtained for a prototype of flow past a flat plate, the suddenly accelerated flat plate (Stokes' problem) with linear viscoelastic models used. The results from Stokes' problem qualitatively explain the anomalous kinematical behavior and the large drag force.
Electrokinetic‐potential fluctuations produced by pipe flow turbulence
Authors: Chuang Hsing , Cermak J. E.
Published: June 2004

The distribution across a pipe of turbulent intensities, shearing stress, and energy spectra are inferred from measured electrokinetic‐potential fluctuations in a fully developed flow of distilled water in a 2.54‐cm. diameter glass pipe. These quantities are shown to be in good agreement with those obtained by Laufer and Sandborn with hot‐wire anemometers for air flows at the same mean Reynolds number. A tentative analytical model of the phenomenon is constructed and analyzed by Maxwell's electrodynamic field equations for a nonmagnetized medium moving with a velocity which is much smaller than the velocity of light. A set of equations governing the interrelation between the electrokinetic‐potential fluctuations and the turbulent velocity‐fluctuation components of the flow field in fully developed pipe flow is deduced. Fourier transforms are then introduced and simple relations between the electrokinetic‐potential fluctuations and velocity fluctuations are obtained.
Two‐phase flow in Hele‐Shaw models
Authors: Greenkorn R. A. , Matar J. E. , Smith R. C.
Published: June 2004

A study of the motion of the interface in two‐phase flow in two dimensions with gravity force parallel to the plane of motion is described. The experiments were run in a porous medium analog, the Hele‐Shaw model. A modification of the Saffman‐Taylor solution is compared with the experimental results. The arbitrary parameter in the solution, measured in the experiments, does not approach an asymptote but is a function of the ratio of plate spacing to channel height. In the course of the air‐water experiments three forms of the interface were observed before turbulence, which indicate regime changes in the flow. Finally, the effects of heterogeneities (change in plate spacing) on the interface were observed.
Development of the Scatchard‐Hildebrand and Wohl equations in terms of pair and triplet weighting functions
Authors: Wheeler Joe D. , Smith Buford D.
Published: June 2004

A previous paper introduced the pair‐type‐probability (PTP) function for use in molecular corresponding states theory. The present paper develops the predictive equations of Scatchard and Hildebrand and the correlation equations of Wohl from particular pair and triplet weighting functions for clusters of two and three molecules in a liquid mixture. The cluster‐weighting idea therefore unifies the major prediction and correlation schemes now in engineering use.
Penetration theory for diffusion accompanied by a reversible chemical reaction with generalized kinetics
Authors: Secor R. M. , Beutler J. A.
Published: June 2004

The penetration theory equations representing diffusion with a generalized, reversible chemical reaction of the form γAA + γBB ⇌ γMM + γNN are solved by a finite‐difference method. Many solutions are presented in graphical form. Approximate solutions to several limiting cases are obtained analytically by means of a steady state representation and are useful for estimating results of the solution to the penetration theory equations.
The frequency domain evaluation of mathematical models for dynamic systems
Authors: Hays James R. , Clements William C. , Harris Thomas R.
Published: June 2004

An important problem in the mathematical modeling of dynamic systems is the testing of model applicability and the determination of the best model parameters through the minimization of the squared difference of the observed and predicted responses. This paper discusses the advantages of the transformation of the expression for the integral of the squared deviations ϕ to the frequency domain by the use of parseval's theorem. Two important advantages of the minimization of ϕ in the frequency domain are the ease with which the transform of the predicted response can be obtained and the algebraic nature of frequency domain operations. Other advantages are discussed and techniques for the numerical transformation and inversion of the observed and predicted responses are given.
Mass transfer with chemical reaction from single gas bubbles
Authors: Johnson A. I. , Hamielec A. E. , Houghton W. T.
Published: June 2004

Numerical solutions of the equations that describe steady state, forced‐convection mass transfer around single circulating or noncirculating gas bubbles have been obtained for both first‐ and second‐order chemical reaction conditions. For the noncirculating bubbles, solutions have been obtained up to Reynolds numbers of 200 with Kawaguti velocity profiles used to describe the flow. In the case of circulating gas bubbles, Kawaguti profiles have been utilized up to Reynolds numbers of 80, while the potential flow velocity profiles have been used for higher Reynolds numbers. The numerical results for circulating gas bubbles have been compared with penetration theory for both first‐ and second‐order chemical reactions. For the case of noncirculating gas bubbles the solutions for physical mass transfer have been compared with the Ranz and Marshall correlation as well as with the results of Griffith and the more recent work of Tsubouchi and Masuda.
The relationship between transport properties and rates of freeze‐drying of poultry meat
Authors: Sandall Orville C. , King C. Judson , Wilke C. R.
Published: June 2004

Controlled studies have been made of unidirectional freeze‐drying of turkey meat. The results provide a test of the model of a uniformly retreating ice front. Comparisons are made with independent measurements of thermal conductivity and with the predicted effect of pressure level upon diffusivity. Variables explored include the pressure and humidity of the drying chamber, the meat surface temperature, and the grain orientation. Drying rates were measured in the presence of water vapor alone and also in the presence of 0 to 760 mm. Hg of nitrogen or helium. Nitrogen and helium runs were made both with a stagnant gas phase and with a circulating gas stream. The rates show quantitative agreement with the uniformly retreating ice front model during the removal of most of the moisture.
Effect of the resonance parameter on a chemical reaction subjected to ultrasonic waves
Authors: Aerstin Franklyn G. P. , Timmerhaus Klaus D. , Fogler H. Scott
Published: June 2004

Experimental results are presented which indicate that the application of a fixed intensity of ultrasonic waves to a water‐tetrachloride solution containing dissolved air provides yields of chlorine varying from zero to maximum simply as a function of the liquid height in the capillary above the transducer. The difference in heights of the liquid between zero and maximum yields is found to be equal to one‐quarter the wavelength of the ultrasonic wave in the liquid. A mathematical model to explain this phenomenon is presented.
A generalized model for the dynamic behavior of a distillation column
Authors: Tetlow N. J. , Groves D. M. , Holland C. D.
Published: June 2004

The generalized model accounts for the effects of channeling, transfer lag, mixing, and mass transfer that occur on each plate of a column in the process of separating a multi‐component mixture at unsteady state operation. The equations required to describe the model were tested by solving a wide variety of numerical examples. Selected numerical results are presented to demonstrate certain characteristics and uses of the generalized model.
Model‐reference adaptive control system
Authors: Casciano Robert M. , Staffin H. Kenneth
Published: June 2004

An adaptive process control scheme—which uses a differential equation model, requires no differentiations in the adaptive circuitry, and no identification of the varying process parameter—was analyzed mathematically and studied on an analog computer. The adaptive loop is operative only during a transient and corrects only in the direction of mismatch between the process and model. Linear analysis of the system differential equations when the correction signal is not introduced into the controller provides a means of designing the adaptive circuitry and approximating the effect when the signal is introduced. The effects on system stability with a pure delay, measurement lag, or an additional pole in the process are presented. Computer results show that when large differences exist between the actual process time constant and the original controller setting, the adaptive feature reduces the overshoot to essentially zero.
Friction factors and pressure drop for sinusoidal laminar flow of water and blood in rigid tubes
Authors: Hershey Daniel , Song Geasoon
Published: June 2004

From the Navier‐Stokes equations and a modified Fanning equation, a theoretical equation was derived for computing friction factors and pressure drop for sinusoidal flow in rigid pipes. The friction factor equation was f = (π/16S) (16/NRe), which is analogous to the usual laminar flow equation. The factor S is dependent on the frequency and kinematic viscosity and is easily computed. Friction factors were calculated from experimental data and it was found that the theoretical friction factors predicted the experimental values to within less than 5%.
An investigation of solids distribution, mixing, and contacting characteristics of gas‐solid fluidized beds
Authors: Halwagi M. M. El , Gomezplata Albert
Published: June 2004

This two‐part series describes an integrated experimental investigation. The first part is concerned with the determination of axial and radial solids concentration profiles at different superficial gas velocities for three columns having I.D. of 2.5, 6.5, and 9.5 in. respectively. The second part is concerned with steady state point source gas tracer experiments carried out in the 9.5‐in. column and in which the tracer concentration was measured at different radial positions above and below the injection source at various gas velocities Both parts are complimentary to each other for describing the internal flow behavior of the gas‐solid fluidized system.
Constant total pressure evaporation with heat reuse by a built‐in engine
Authors: Cheng Chen‐Yen , Cheng Sing‐Wang
Published: June 2004

A new way of promoting a nonspontaneous process, namely, a built‐in engine, is introduced showing that a process with a large temperature coefficient of free energy change [that is, d(ΔG)T,P/dT] can be utilized to promote a nonspontaneous process which has a small temperature coefficient of free energy change. When such a built‐in engine is incorporated into an evaporating system, heat reuse in the system can be obtained under a constant total pressure condition.

An auxiliary system consisting of two organic substances which are partially miscible in a certain temperature range and have a critical solution temperature can be used to serve as a built‐in engine. One substance is added to the boiling mass of an evaporator to lower its boiling temperature, and the other is added to the condensing side to raise the temperature of the condensing mass. Heat of condensation can be effectively utilized in evaporating the boiling mass. Regeneration of the auxiliary system is achieved by taking advantage of the solubility gap.
Concentrated polymer solution: Part II. Dependence of viscosity and relaxation time on concentration and molecular weight
Authors: Williams Michael C.
Published: June 2004

A previouly presented molecular theory for non‐Newtonian viscosity in moderately concentrated polymer solutions is extended here to a specific consideration of the influence of solute concentration c and molecular weight M on the limiting viscosity ηo and the relaxation time λ. Estimates of the M,c dependence of several intermediate functions are necessary including that of Kirkwood's friction coefficient. The prediction ηo ∼ (cM0.625)2 is in good agreement with the empirical observation that ηo is a function of the parameter cM0.68, but is inadequate for extremes of M and c. Plausibility arguments are advanced to suggest λ ∼ ηoc−2 rather than λdil. ∼ Mηoc−1 predicted by dilute solution theory and widely accepted. This would explain the utility of the factor c2 used in recent rheological correlations, and would reconcile some conflicting reports of λ(M) measurements.
External flows of viscoelastic materials: Fluid property restrictions on the use of velocity‐sensitive probes
Authors: Metzner A. B. , Astarita Gianni
Published: June 2004

The more pronounced macroscopic features of flows of viscoelastic materials around submerged objects are considered in the light of restriction imposed on the flow by the Deborah number, a dimensionless group representing a ratio of time scales of the fluid and the flow process. It is seen that one major effect is to thicken the boundary layer appreciably in the region of the leading edge or stagnation point of the object in the fluid; depending on the shape of the object this thickening of the boundary layer may be felt for appreciable distances into the velocity field.

The influence of these and other effects on the use of probes for determination of point values of the velocity of viscoelastic fluids is considered in some detail. The general effect is to impose strong restrictions on the use of such probes and on the interpretation of measurements made with them. These predicted limitations are supported, in a general way, by recent experimental measurements; thus the present macroscopic analysis appears to define several major effects to be considered in subsquent, more detailed investigations.
Liquid‐vapor equilibrium in the system helium‐methane
Authors: Heck C. K. , Hiza M. J.
Published: June 2004

Liquid and gas phase compositions for the system helium‐methane have been measured at 15° intervals from 95° to 185°K. up to 200 atm. pressure. Data for these seven isotherms were taken in a gas phase recirculation apparatus with chromatographic analysis. In most regions the phase compositions obtained are thought to be within ± 3% of the mole fraction of the minor component. The maximum deviation from the enhancement factor curve at the lowest concentration levels was 16%. These data are in excellent agreement with most of the very recent data but are in poor agreement with the older data for this system.
Generalized solution of the tomotika stability analysis for a cylindrical jet
Authors: Meister Bernard J. , Scheele George F.
Published: June 2004

The stability of cylindrical jets in immiscible liquid systems is analyzed with the low velocity theory of Tomotika. For the first time the several limiting solutions in the literature are obtained from a general equation, so approximate restrictions on their applicability can be presented. These restrictions show that for many systems none of the limiting solutions is valid. Correlations applicable to all Newtonian liquid‐liquid systems are presented for predicting the growth rate and wavelength of the most unstable disturbance.
A study of interstitial liquid flow in foam part III. Test of theory
Authors: Shih Fang‐Shung , Lemlich Robert
Published: June 2004

The theory for foam drainage and overflow recently proposed by the authors' group is tested with extensive experimental data gathered from foam fractionation columns and also from stationary foams at steady state. The experimental results support the theory.
Process control by digital compensation
Authors: Mosler H. A. , Koppel L. B. , Coughanowr D. R.
Published: June 2004

Discrete control algorithms, suitable for programming in a direct digital control computer, are presented. For processes whose dynamics can be adequately modeled as first order with delay, digital compensation algorithms are derived to yield theoretically a response with finite settling time, when the system is step forced in either set point or load. The utility of the proposed designs is experimentally verified by application to a higher order physical process whose dynamics are not fully described by the model. The results demonstrate that sampling frequencies may be reduced considerably below presently accepted values while still maintaining transient response characteristics of the system comparable with those obtainable from conventional continuous control.
Flow characteristics of horizontally moving stable aqueous foams
Authors: Weissman Eugene Y. , Calvert Seymour
Published: June 2004

An empirical study was made of the flow characteristics of a stable aqueous foam (based on dilute solutions of saponin) moving horizontally inside a duct. Characteristic foam data have been determined experimentally, namely, drainage, interfacial areas, and related dimensions such as lamella thickness and foam cell size, fractional liquid holdups, foam velocities, and extent of gas channeling through the foam. Simple correlatability of drainage, interfacial area, and fractional liquid holdup in terms of basic parameters such as the liquid flow rate entering the apparatus, and the longitudinal position in the duct has been demonstrated. The sometimes simple dependence on the geometry of the perforated gas‐liquid contactor and on the physical properties of the foaming solutions (surface tension and bulk viscosity) has also been described.
Mass transfer in rectangular cavities
Authors: Jarrett E. L. , Sweeney T. L.
Published: June 2004

The captured vortex system produced by the flow of a fluid along a plate containing a transverse rectangular cavity was investigated by measuring the local mass transfer coefficient kg on the cavity walls. Both transverse and peripheral kg profiles are presented for cavity depth‐to‐length ratios of 0.5, 1.0, and 2.0 at free‐stream velocities of 6.8, 13.5, and 27 ft./sec. for water evaporating into air. These profiles reflect the three‐dimensional nature of the flow in the cavity.
Estimation of dispersion and hydrogen bonding energies in liquids
Authors: Wiehe I. A. , Bagley E. B.
Published: June 2004

It is proposed that the product of the molar volume and the internal pressure is a measure of the dispersion interaction energy in liquids regardless of the presence of other intermolecular forces. If this is true, then the energy of interaction due to hydrogen bonding may be estimated for hydrogen bonding liquids by the difference between the energy of vaporization and the product of the molar volume and the internal pressure. It is also shown that Small's group contribution technique provides a good estimate of internal pressure of hydrogen bonding liquids.
A dynamic method for the study of heterogeneous catalytic kinetics
Authors: Bennett Carroll O.
Published: June 2004

For a trial multistep mechanism for a heterogeneous catalytic reaction, it is suggested that dynamic experiments can be used to calculate the forward and reverse rate constants of individual steps. The experiments consist of the measurement of the composition of the effluent from a continuous stirred‐tank catalytic reactor as a function of time as the input composition to the reactor is perturbed. The method of moments is used to obtain the kinetic constants for a trial mechanism from the experimental data.
Unsteady diffusion in ternary gas mixtures
Authors: Arnold K. R. , Toor H. L.
Published: June 2004

Unsteady diffusion in the system methane‐argon‐hydrogen was studied in a Loschmidt apparatus with large changes in concentration. The mean concentration‐time history was predicted within experimental error by the linearized equations of multicomponent mass transfer. In the calculations the Stefan‐Maxwell equations were used to obtain the diffusivity matrix which was evaluated at the equilibrium concentration.

Digital computer solutions to the nonlinear differential equations were also obtained for various systems and boundary conditions. The fluxes predicted by the linearized equations with the diffusivity matrix evaluated at the arithmetic average of the initial and boundary concentrations were in all cases within 5% of the numerical predictions.
Linear, steady, two‐dimensional flows of viscoelastic liquids
Authors: Marrucci Giuseppe , Astarita Gianni
Published: June 2004

The general form of the equations describing a steady, two‐dimensional flow of an incompressible liquid is reduced to a form containing only two parameters. The histories of stress and of deformation of a material element are written explicitly. A second‐order, slow‐flow approximation and a Maxwell type of constitutive equation are used to infer properties of the rheological behavior of viscoelastic liquids in such flows.
Drop size distribution in agitated liquid‐liquid systems
Authors: Chen Hsiao Tsung , Middleman Stanley
Published: June 2004

The drop size distributions resulting from the agitation of immiscible liquids were measured over a wide range of parameters. The average drop size is correlated by \documentclass{article}\pagestyle{empty}\begin{document}$ \overline D _{32}/L $\end{document} = 0.053 NWe−0.60. The distribution function for volume fraction is normal and depends only upon \documentclass{article}\pagestyle{empty}\begin{document}$ \overline D _{32} $\end{document}. The results are valid for very dilute solutions wherein coalescence of droplets plays no role in the dispersion mechanism.
Drop size distributions in strongly coalescing agitated liquid‐liquid systems
Authors: Sprow F. B.
Published: June 2004

Emulsion drop size distributions have been measured at various locations in a turbine mixer for the methyl isobutyl ketone‐salt water system. The drop sizes are strongly dependent on the sampling position, being smallest near the impeller tip and largest at the bottom of the mixing tank. The variation of drop diameter with impeller speed has been studied and indicates that droplet breakup predominates near the impeller, whereas the coalescence of emulsion droplets can be controlling in other locations.
Polymer reactors and molecular weight distribution: Part II. Free radical polymerization in a batch reactor
Authors: Hamielec A. E. , Hodgins J. W. , Tebbens K.
Published: June 2004

The free radical polymerization of styrene in benzene was studied theoretically and experimentally over ranges of monomer and catalyst (AIBN) concentrations and temperature in an isothermal, stirred batch reactor. Molecular weight distributions were measured with a gel permeation chromatograph. Tung's hermite polynomial method was used to correct for imperfect resolution.

The differential rate equations have been solved to predict the conversion of monomer and molecular weight distribution of the polymer as a function of time. These solutions were used to interpret the experimental rate data.

Good agreement between theory and experiment was found for narrow and broad distribution, provided the variation of the termination constant with solvent concentration was accounted for.

The agreement between the experimental and calculated molecular weight distribution suggests the utility of gel pemeation chromatography in the investigation of polymer reaction kinetics.
Nonlinear convective diffusion: A hyperfiltration application
Authors: Nakano Yoshisuke , Tien Chi , Gill William N.
Published: June 2004

A nonlinear unsteady state convective diffusion problem that describes the performance of a constant pressure cell is studied. The cell can be used to either determine membrane constants or to carry out batch filtration operations. It consists of a cylinder closed by a semipermeable membrane at one end and a piston at the other.

The nonlinear partial differential equation governing the system was solved by both integral methods and the use of a similarity transformation. The similarity approach formulates the solution in the form of an infinite series and reduces the problem to finding the solution of an infinite system of ordinary differential equations. The series solution can be considered to be exact but its convergence is questionable for large values of time in the event B ≠ 0; when B = 0, the convergence is substantially better.

Approximate solutions obtained by integral methods were examined in detail. It was found that the results obtained by these methods can involve serious errors, under certain circumstances, and these errors seem unpredictable a priori. Consequently, it is concluded that considerable care should be taken in the use of integral methods for solving mass transfer problems in which the velocity field is coupled with the convective diffusion equation and its boundary conditions.

The numerical results obtained in this work are sufficiently comprehensive to be used, in conjunction with experimental data, to determine membrane constants which are required for the design of both continuous and batch membrane separation systems.
Vapor‐liquid equilibria at high pressures: Calculation of partial molar volumes in nonpolar liquid mixtures
Authors: Chueh P. L. , Prausnitz J. M.
Published: June 2004

Thermodynamic analysis of high‐pressure vapor‐liquid equilibria requires information on the effect of pressure on liquid phase fugacities; this information is given by partial molar volumes in the liquid mixture. A method for predicting these partial molar volumes is presented here. First, molar volumes of saturated liquid mixtures are computed by extending to mixtures the corresponding states correlation of Lyckman and Eckert. These mixture volumes are then used to calculate partial molar volumes with an expression based on a modification of the Redlich‐Kwong equation. At high pressures partial molar volumes are strong functions of the composition and in the critical region, may be positive or negative. Calculations are sensitive to the characteristic energy between dissimilar molecules; this energy is generally lower than that given by the geometric‐mean rule. Calculated results are in good agreement with experimental data for seven systems containing paraffinic and aromatic hydrocarbons, carbon dioxide, and hydrogen sulfide.
Some experiments on the Marangoni effect
Authors: Suciu D. G. , Smigelschi Octavian , Ruckenstein Eli
Published: June 2004

An experimental study of the spreading and dissolving of thin liquid films under the action of surface forces is presented. The method consists of the continuous feeding of a liquid over the surface of another liquid into which it dissolves; the steady film thus obtained covers only a part of the supporting liquid surface, dependent on the flow rate of the liquid fed. The dependence of the radius of the film contour on flow rate and concentration driving force is obtained for various film forming liquids dissolving into water. By using a Schlieren technique the film contour and the flow pattern outside the film contour are studied, several structures being evidenced.
Slug flow heat transfer with mass injection and linearly varying wall temperature
Authors: Yu W. S. , Chen John C.
Published: June 2004

The purpose of this study was to determine the two‐dimensional temperature field for a fluid in slug flow through tubes with uniform mass injection and linearly decreasing wall temperature. A series solution was obtained, the first ten eigenvalues for which were determined from the characteristic equation by the method of Runge‐Kutta. Expressions for local conductive heat flux at the tube wall and local Nusselt number were obtained as a function of inlet Peclet number, injection Peclet number, tube radius, temperature boundary conditions, and fluid properties. Sample results are presented for several injection rates at different wall temperature conditions. In general, mass injection was found to decrease the local heat flux and increase temperature driving force causing a decrease in the Nusselt number.
Performance of packed columns: Part VIII. Liquid flow patterns and velocities in packed beds
Authors: Shulman H. L. , Mellish W. G.
Published: June 2004

To develop a basis for a better understanding of the behavior of the liquid phase in packed columns, liquid velocities and flow patterns were studied at several typical points in a column packed with 1.0‐in. porcelain Raschig rings with a high‐speed photographic technique. Liquid velocities were found to fluctuate rapidly with time. Laminar flow predominates, but mixing occurs at junctions between pieces of packing. A complex model is required to describe the behavior of the liquid phase in packed columns.
Pressure drop in geometrically ordered packed beds of spheres
Authors: Susskind Herbert , Becker Walter
Published: June 2004

The pressure drop of water was measured when water flowed through a bed of stainless steel ball bearings packed in an ordered rhombohedral geometry. Experiments were carried out with eleven different packed beds, encompassing the entire range of the square‐base array, in the same 10.85 by 10.85 by 30‐in. rectangular test column in a forced circulation loop at modified Reynolds numbers up to 17,000. The test variables included water velocity, bed voidage, spacing between adjacent balls, ball diameter, and bed height. Curves of friction factor vs. Reynolds number are presented. An increase in the relative horizontal spacing between balls was found to have a more important effect than an increase in voidage in decreasing the pressure drop. A general correlation relating the mutual effects of bed voidage and ball spacing on pressure drop that would bring all the data points together, especially in the transition flow region, could not be found. As a result, the system appears to consist of two distinct parts separated at the minimum packing density. A correlation was found only for the first, but from a practical point of view more important, region. Data may be corrected for bed voidage, but only for small variations in ball spacing, by the ratios of (1 − ε)/ε3 at the two voidages. No entrance and exit effects could be measured beyond the first seven ball layers.
Continuous, dissolved‐air ion flotation of hexavalent chromium
Authors: Grieves Robert B. , Ettelt Gregory A.
Published: June 2004

An experimental investigation is presented of the ion flotation of dichromate from aqueous solution with a cationic surfactant and using a non‐ionic polymer as a flocculant aid. A dissolved‐air, continuous flow unit is used (with a surfactant‐dichromate premix period of 1 hr.) with a feed rate of 120 liters/hr. of a stream containing from 25 to 100 mg./liter of dichromate. Within the ranges of the variables studied, optimum results are obtained with a molar surfactant to dichromate feed ratio of about 2, a feed polymer dosage of about 3% of the dichromate feed concentration, a recycle rate 200% of the feed rate, and a column detention time of 35 min. With an air requirement of 0.043 liters of air (at STP)/liter of feed delivered at 40 lb./sq. in. gauge, feed streams containing from 25 to 100 mg./liter of dichromate can be readily reduced to 10 mg./liter of dichromate and 30 mg./liter of surfactant. The primary advantage of the process lies in the concentration of dichromate, surfactant, and polymer in a small liquid volume of collapsed foam, less than 1% of the total feed throughput. Foam concentrations are of the order of 10,000 to 20,000 mg./liter of dichromate.
Discrete dynamic optimization applied to on‐line optimal control
Authors: Rafal Marshall D. , Stevens William F.
Published: June 2004

A general method has been developed for controlling deterministic systems described by linear or linearized dynamics. The discrete problem has been treated in detail. Step‐by‐step optimal controls for a quadratic performance index have been derived. The method accommodates upper and lower limits on the components of the control vector.

A small binary distillation unit was considered as a typical application of the method. The control vector was made up of feed rate, reflux ratio, and reboiler heat load. Control to a desired state and about a load upset was effected.

Calculations are performed quite rapidly and only grow significantly with an increase in the dimension of the control vector. Extension to much larger distillation units with the same controls thus seems practical.
Crystal size distributions in continuous crystallizers when growth rate is size dependent
Authors: Abegg C. F. , Stevens J. D. , Larson M. A.
Published: June 2004

Empirical size‐dependent growth rate models are studied for their effect on the population density distributions from a continuous, mixed suspension, mixed product removal (CMSMPR) crystallizer. The growth rate models and/or their corresponding population density distributions are examined for continuity, convergence of moments, versatility, and their ability to fit experimental data.

A new empirical size‐dependent growth rate model is proposed which has properties superior to those of previous models. Experimental steady state data are presented to illustrate the application of the model to actual CMSMPR crystallization systems.
Local compositions in thermodynamic excess functions for liquid mixtures
Authors: Renon Henri , Prausnitz J. M.
Published: June 2004

A critical discussion is given of the use of local compositions for representation of excess Gibbs energies of liquid mixtures. A new equation is derived, based on Scott's two‐liquid model and on an assumption of nonrandomness similar to that used by Wilson. For the same activity coefficients at infinite dilution, the Gibbs energy of mixing is calculated with the new equation as well as the equations of van Laar, Wilson, and Heil; these four equations give similar results for mixtures of moderate nonideality but they differ appreciably for strongly nonideal systems, especially for those with limited miscibility. The new equation contains a nonrandomness parameter α12 which makes it applicable to a large variety of mixtures. By proper selection of α12, the new equation gives an excellent representation of many types of liquid mixtures while other local composition equations appear to be limited to specific types. Consideration is given to prediction of ternary vapor‐liquid and ternary liquid‐liquid equilibria based on binary data alone.
Mathematical modeling and numerical integration of multicomponent batch distillation equations
Authors: Distefano G. P.
Published: June 2004

A mathematical model for multicomponent batch distillation was derived, and a FORTRAN IV program was written for solution on a digital computer. The program has been used in the simulation of several commercial batch distillation columns.

A calculation procedure for the numerical solution of batch distillation equations starting from total reflux steady state conditions was developed, and the step‐by‐step procedure is presented here. Also included is a discussion of the stability and relative computational effectiveness of various numerical integration techniques when applied to transient distillation calculations. The discussion applies equally well to both batch distillation and unsteady state continuous distillation.
Stability of batch catalytic fluidized beds
Authors: Luss Dan , Amundson Neal R.
Published: June 2004

This work is a study of the stability of a batch fluidized bed with a simple model. It is shown that multiple steady states can occur with all catalyst particles at the same temperature, some of these states being unstable. If the initial temperature of all the particles is not the same, a special kind of steady state, in which particles of different temperatures can coexist in the bed, might be obtained. The number of these pathological steady states is not finite, and the conversion obtained may be very different from that obtained by a uniform steady state.

The analysis has demonstrated that the initial temperature of the catalyst particles may be a predominate factor in determining the kind of steady state obtained. For the case of uniform catalyst particles, a simple stability analysis has been developed. Several numerical solutions of the transient equations were performed to investigate the possible responses of the system to disturbances of various steady states.
Measurement of the velocity of gases with variable fluid properties
Authors: Wasan D. T. , Davis R. M. , Wilke C. R.
Published: June 2004

This paper describes the experimental measurements of the time‐averaged velocities of gases in a field of variable composition and temperature. The conventional theory of hot‐wire anemometry is extended to include the effects of both natural and forced convection to gases having variable fluid properties. Observations of the fully developed turbulent velocity fields in the presence of moderate mass transfer rates revealed no significant effect of mass transfer on the velocity distribution.
Kinetics of reaction and crystallization in condensed phases: The aqueous potassium dipicrylamine system
Authors: Savage H. R. , Butt John B. , Tallmadge John A.
Published: June 2004

An apparatus and experimental technique were developed for the study of the kinetics of relatively rapid reaction and subsequent crystallization in condensed phases. The method employs batch experiments to establish the integral of crystallization rate over ranges of pertinent external variables.

The crystallization of potassium dipicrylamine from aqueous solution, a system of potential interest in application to potassium recovery from brines, was studied experimentally. It is shown that both reaction and crystallization rate parameters may be determined from the data on the basis of the consecutive rate model developed; application of the Burton‐Cabrera‐Frank theory of crystal growth to this system is demonstrated.
An investigation of absorption‐reaction of carbon dioxide in liquid diethanolamine by the direct chromatographic perturbation method
Authors: Barrere C. A. , Deans H. A.
Published: June 2004

Physical and chemical equilibrium in the carbon dioxide‐diethanolamine system was studied by the direct chromatographic method. The amine was present as a coating on the inside of a capillary tube. Carbon dioxide‐helium mixtures were passed through the capillary until equilibrium was attained, at which time a sample of C14O2 was injected into the carrier stream. The retention volumes (carrier volume flowed at peak appearance) of concentration and radioactive perturbations were measured at four temperatures and five carrier gas compositions. Static equilibrium solubility of carbon dioxide in the amine was also measured to verify the dynamic results.

The theory of reactive chromatographic flow was extended to this system. The concentration and isotope retention volumes, which theory predicts to be different functions of carrier composition, were shown to be self‐consistent. The static solubility data was also seen to be consistent with theory and with the direct chromatographic data. The liquid phase of the system appeared to be ideal except at infinite dilution of carbon dioxide. The apparent departure from ideality could be explained in terms of weak ionization of reaction products. Electrical conductivity measurements tend to confirm this hypothesis.

Both physical and chemical equilibrium constants for carbon dioxide were obtained at the four temperatures. Gross heat of reaction and apparent ionization heat were also obtained.
Laminar liquid jet diffusion studies
Authors: Duda J. L. , Vrentas J. S.
Published: June 2004

A rigorous analysis of jet hydrodynamics is used to develop a technique for determining diffusion coefficients from laminar liquid jet absorption experiments, and the influence of the jet fluid mechanics on the absorption process is clarified. The new technique is used to determine the diffusivities of carbon dioxide, oxygen, argon, nitrous oxide, ethylene, and propylene in water within the temperature range 25° to 40°C.

A critical analysis of available diffusivity data for these gases indicates that there is no conclusive evidence that demonstrates the existence of a significant interfacial resistance in uncontaminated laminar jet experiments. In addition, comparison of existing data shows that the commonly accepted diffusivities for the oxygen‐water system may be significantly higher than the actual values. It is concluded that the laminar jet experiment is a rapid, accurate method of obtaining diffusion coefficients of dissolved gases in liquids.
The mechanism of heat transfer in a spray column heat exchanger
Authors: Letan Ruth , Kehat Ephraim
Published: June 2004

Temperature profiles of dispersed kerosene and water were measured in a spray column heat exchanger, 15 cm. in diameter and 160 cm. long. Dispersed packing of drops and narrow temperature ranges were used. The flow rates used were 0 to 50 liters/min. of water and 5 to 40 liters/min. of kerosene. The physical picture that emerges from the temperature profiles is that heat is transferred from fully mixed drops to fully mixed wakes while the wakes are formed, by shedding and renewal of elements of wakes in most of the column and by complete mixing of all streams at the water inlet at the top of the column. Mathematical equations were developed from the physical model. The volume of the wakes and the rate of shedding of wake elements were estimated from the temperature profiles and were used to calculate the temperature profiles for this and for other studies. The agreement of the calculated profiles with the experimental data is very good.
Turbulent heat transfer in drag reducing fluids
Authors: Wells C. Sinclair
Published: June 2004

An analysis is presented which extends the analogy between energy and momentum transport for turbulent pipe flow of purely viscous fluids to include drag reducing, non‐Newtonian fluids. The correlation by Meyer is used to predict friction factor and sublayer thickness for the drag reducing fluids. The use of the friction factor correlation with the heat transfer analogy makes it possible to predict heat transfer rates from simple measurements of pressure drop and flow rate for the drag reducing fluids. Some recent experimental data for two effective drag reducing fluids and for water are compared with the predicted heat transfer rates, and the mean deviation in Nusselt number is found to be +8.5% for all of the data. The heat transfer analysis predicts a reduction in Nusselt number accompanying a reduction in friction factor for a given Reynolds number and for Prandtl numbers greater than 1.