bluuebunny/crossref_metadata_2025 huggingface dataset:
Invariant imbedding, iterative linearization, and multistage countercurrent processes: III. Estimation and the overdetermined system
Authors: Lee E. S. , Noh J. C.
Published: June 2004

In the design of distillation processes, it is frequently necessary to obtain a specified purity of certain product from a given feed mixture by the use of an existing column. The only variable within the designer's control is the reflux ratio. This design problem cannot be solved easily by existing computational methods. In general a trial‐and‐error approach is used. To avoid this difficulty, this problem is solved as an estimation problem by the use of the quasilinerization approach. To show the effectiveness of this approach, several problems are solved. In general, a four‐digit accuracy is obtained in four iterations with very approximate initial approximations. Furthermore, this approach can treat the overdetermined system in a straightforward manner by the use of least squares criterion and minimization. Only the cases with constant total flow rates of the vapor and liquid streams within each section of the column are considered. The relative volatilities are also taken to be constant throughoutthe column.
Dispersed phase mass transfer during drop formation and coalescence in liquid‐liquid extraction
Authors: Skelland A. H. P. , Minhas Sardul S.
Published: June 2004

Rates of mass transfer during drop formation and coalescence were investigated for three dispersed phase‐controlled liquid systems, one binary (ethyl acetate‐water) and two ternary (acetic acid‐chlorobenzene‐water and acetic acid‐50% by volume mixture of carbon tetrachloride and nujol‐water). A calculation procedure was devised to isolate these end effects. The measured rates during drop formation were in general greater than predicted by various theoretical models, including those by Heertjes et al. and Ilkovic; and measurements during drop coalescence were in general lower than predicted by the simplified penetration theory model of Johnson and Hamielec. The results were statistically correlated with average absolute deviations of 26.2 and 25.4%, respectively, for drop formation and coalescence.
The suboptimal control of nonlinear systems using liapunov‐like functions
Authors: Schlossmacher E. J. , Lapidus Leon
Published: June 2004

A technique which calculates approximate solutions to optimal control problems is developed in this work. The technique, which uses an empirically found weighted quadratic Liapunov function to transform the original n‐dimensional optimization problem into a scalar optimization problem, is applied to a number of optimal control problems typical of those encountered in chemical engineering practice. The problems considered include both linear and nonlinear, lumped and distributed systems with minimum time, and quadratic and final value type performance indices. The solutions of these control problems show that the Liapunov‐like suboptimal method, in general, requires less computer time and storage than that required by iterative and noniterative optimal methods currently used to solve optimal control problems. The reduction in computer storage and time enables the Liapunov‐like technique to handle large dimensional control problems with relatively little effort.
A corresponding states correlation of saturated liquid volumes
Authors: Gunn R. D. , Yamada Tomoyoshi
Published: June 2004

A corresponding states correlation is presented for the prediction of saturated liquid volumes. Parameters required are the critical temperature, the acentric factor, and a scaling volume. The correlation is valid over the entire useful range of reduced temperatures from 0.2 to 1.0. The full temperature range has not been covered by previous corresponding states correlations. Average absolute deviations in predicted liquid volumes is one‐quarter of 1% for 26 compounds. The correlation is also useful for calculating critical temperatures, pressures, and volumes when experimental critical data are lacking. The proposed method also provides a convenient means for calculating rapidly and accurately the statistical mechanical parameters used in the cell model correlation developed by Renon, Eckert, and Prausnitz.
A single‐parameter equation for isothermal vapor‐liquid equilibrium correlations
Authors: Tassios Dimitrios
Published: June 2004

The Wilson equation is modified so that it contains only one adjustable constant per binary system. In describing binary behavior the new equation is inferior to the original Wilson but superior to the Van Laar equation. In developing ternary behavior from binary data, the new equation seems to be comparable to the original Wilson but definitely superior to the Van Laar equation.

Binary and ternary vapor‐liquid equilibrium behavior has been successfully predicted from one γ° value per binary only.
Hydrodynamic measurements for imperfect mixing processes: Newtonian Fluids
Authors: Hubbard Davis W. , Patel Harish
Published: June 2004

The response of a continuous flow mixing system to a step change in an input variable is discussed from the standpoint of dimensional analysis. This idea is presented as an alternative to using zone models for predicting residence time distributions in systems where imperfect mixing occurs.

Mixing experiments were performed in a cylindrical flat bottomed tank geometrically similar to tanks commonly used for industrial processes. The response of the system to a step change in feed concentration was observed. Initially the tank contained a salt solution. At the start of an experiment, a stream of salt‐free diluent was introduced at the top of the tank and a stream of the salt solution was drained from the bottom, keeping the liquid volume in the tank constant. The salt concentration in the output stream was measured continuously after the start of the experiment.

The experimental results are correlated in terms of dimensionless variables, and the variables affecting the mixing process most strongly are determined. The results show that variations in throughput rate or in impeller shape or rotational speed affect the mixing process much more than does impeller position. The data are also compared with models proposed by other authors, and the model constants are evaluated.
A generalized method for predicting vapor‐liquid equilibrium
Authors: Lee Byung‐Ik , Edmister Wayne C.
Published: June 2004

Vapor‐liquid equilibrium distribution ratios for hydrocarbons can be computed by the new equations presented in this work with higher accuracy than is possible by previous generalized methods. In this proposed new method, the three coefficients of the combination Viγi/ϕi are newly developed and generalized functions.

The vapor‐phase fugacity coefficient ϕi was formulated via a new generalized equation of state, and the liquid‐phase activity coefficient γi is predicted via a proposed new equation that contains three generalized binary interaction coefficients for each binary set in a mixture. These interaction coefficients were developed from experimental K value data. Two expressions are employed in predicting the liquid fugacity coefficient Vi, one for the real liquid state and one for the hypothetical liquid state, the latter being developed empirically from experimental K value data also. These two Vi equations are also generalized.

This new K value prediction method gave an average absolute deviation of 5.25% on a total of 3,504 data points on 19 hydrocarbons in binary and ternary mixtures, these data points being selected so that they cover the range of pure component Tr = 0.5 and up and pressures up to 0.9 of the true mixture critical pressure. Inclusion of nonhydrocarbon‐hydrocarbon systems in the evaluation gave an overall absolute deviation of 6.33% for 4,290 K value data points on 23 components.
Flow of viscoelastic fluids through a rectangular duct
Authors: Han Chang Dae
Published: June 2004

A study is carried out on the flow of polymer melts in a rectangular duct. As the theoretical study a three‐constant Oldroyd model is used to derive expressions which correlate the rheological properties of materials with the distributions of wall shear rates and wall normal stresses in the rectangular duct. As the experimental study, a die of rectangular cross section having an aspect ratio of 6 is designed, and then melt extrusion experiments are performed with high density polyethylene. In the experiments wall normal stresses are measured along two adjacent walls of the rectangular duct as a function of the axial position. The measurements permit one to obtain the normal stress differences at the duct exit, and then to calculate the distributions of shear rates at two adjacent walls of the rectangular duct, by use of the theoretically derived expressions. Also measured is the extrudate swell, showing trat more pronounced extrudate swell occurs at the long side of the rectangular duct than at the short side. This behavior of extrudate swell correlates with the exit pressure measurements at two adjacent walls of the rectangular duct.
Diffusion of inert and Hydrogen‐bonding solutes in aliphatic alcohols
Authors: Lusis M. A. , Ratcliff G. A.
Published: June 2004

The diffusion of various inert and of hydrogen‐bonding solutes into aliphatic alcohols was considered. The diffusivities of benzene, p‐dichlorobenzene, biphenyl, and triphenyl methane in methanol, ethanol, n‐propanol, n‐butanol, n‐pentanol, and n‐heptanol were measured at 25°C. for low solute concentrations. An equation was developed for the limiting values of the binary mutual diffusion coefficient in complex‐forming mixtures. This equation, used in conjunction with the Wilke‐Chang correlation, gave a considerable improvement over existing predictive methods for the diffusivity of inert solutes, mono‐ and polyhydroxy alcohols, and water in aliphatic alcohols.
The role of porosity in filtration VII effect of side‐wall friction in compression‐permeability cells
Authors: Tiller Frank M. , Haynes Stewart , Lu Wei‐Ming
Published: June 2004

The effect of side‐wall friction on the uniformity of packing of beds in compression‐permeability cells is examined. A large portion of pressure applied to the top of a compressible bad is absorbed in wall friction, resulting in a nonuniformly packed bed. A simplified analysis of wall friction and its effect on porosity and permeability is presented.

All experimenters involived in flow through porous media are urged to examine the effects of stress distribution on the structure and uniformity of the packing. In general, compressible beds of small particles will be strongly affected by the walls.
Flow attachment to solid surfaces: The Coanda effect
Authors: Panitz T. , Wasan D. T.
Published: June 2004

The phenomenon of flow attachment to solid surfaces, occurring with both liquids and gases, is the long‐known though inadequately understood Coanda effect.

A flow visualization study was made using a birefringent milling yellow dye solutions flowing over a deflection surface consisting of flat plates. A two‐dimensional flow channel with transparent side walls was used. Photographic observations of the development of the Coanda effect reveal the method of flow attachment and confirm a number of literature predictions. One of the most interesting of these phenomena is the existence of a well defined mixing region along the deflection surface.

A simplified model of the flow field has been proposed in order to described the mechanism governing the Coanda effect. The model is supported by experimental data consisting of pressure profiles obtained along the deflection surface and secondary flow entrainment measurements.
Predictive equations for self‐diffusion in liquids: A different approach
Authors: Dullien F. A. L.
Published: June 2004

Simple relationships have been obtained which can be used to predict self‐diffusion coefficients of liquids with an average error of ±4%. In addition to the customary parameters, one of these equations contains the critical volume

whereas the other uses Lennard‐Jones potential parameters

Both relations were derived by using a general relation between transport coefficients of pure fluids and a molecular‐kinetic‐model of liquids. No use has been made either of the Stokes‐Einstein relation or the absolute rate theory.

By applying the same relation between transport coefficients of pure fluids to gases, an equation has been obtained which can be used to calculate consistently molecular diameters in gases as a function of temperature, using Lennard‐Jones potential parameters.
Thermodynamics of nearly‐ideal systems
Authors: Ellis James A. , Chao Kwang‐Chu
Published: June 2004

The industrial importance of mixtures of closely similar substances is out of proportion to their relatively small numbers due to their frequent occurrence and the difficulty of their separations. A procedure specially designed for the general prediction of their properties, particularly relative volatility, over a wide range of state variables is needed.

Such a procedure is developed in this work for convenient application to multicomponent systems with the use of generalized functions. The relative volatility of a nearly ideal system is decomposed into ideal solution factors and nonideality factors. The first order perturbation thory of Longuet‐Higgins is adopted for the calculation of the nonideality factor. The validity of the procedure for the quantitative description of real mixtures is demonstrated with the system propane/propylene for which extensive data are available.

The required pure fluid properties for the general application of the procedure are reviewed. System parameters are evaluated for 15 binary systems of industrial interest.
On intrinsic errors in pressure‐hole measurements in flow of polymer melts
Authors: Han Chang Dae
Published: June 2004

In order to investigate the possibilities of pressure‐hole errors in the measurement of wall normal stresses in the flow of polymer melts, a 2.280‐in. long slit die has been designed, having a slot with a rectangular cross section, 0.050 in. by 1.000 in. Three transducers were mounted on each of the two long sides of the rectangular slot along the longitudinal center line of the die and located so that each transducer was directly opposite another in the opposite side. The three transducers on one side were flush mounted. Those on the other side were mounted through pressure‐holes with different diameters (0.017, 0.034, and 0.050 in.) Measurements of wall normal stresse were made with high density polyethylene and polypropylene melts at 200°C., following the experimental procedure described in the author's earlier papers. The present study indicates that pressure measurements made through pressureholes are essentially the same as those made flush‐mounted instruments, and that there are no pressure hole errors in the measurements of wall normal stresses, insofar as polymer melts are concerned.
Distributed‐Parameter dynamics by correlation analysis
Authors: Ledbetter James B. , Bruley Duane F.
Published: June 2004

The experimental dynamic response of a distributed‐parameter, simulaneous heat and mass transfer system was investigated using correlation analysis. The system was a wetted‐wall column operating as a nonadiabatic humidifier with both liquid and gas phase in turbulent flow.

The experimetnal frequency response results were compared to the values predicted by an existing mathematical model. The investigation also included a study of the effect of employing forcing functions having nonideal power spectra. Analog‐simulated, first‐order systems were tested to verify the computational procedure and to support the conclusions for the humidification system.

System dynamic identifications, acceptable for most engineering purposes, were obtained from forcing signals having power spectra which differed significantly from ideality. For the reduction technique employed, a time‐domain record of approximately 2,500 pairs of input‐output data points was found to suffice for a satisfactory analysis. The correlation technique yielded reliable results over approximately the same range of frequencies as reported for previous pulse test studies based on a comparable forcing procedure. However, the results showed an upper frequency limit below that previously achieved by direct frequency forcing of the same system.
Non‐Newtonian behavior of a suspension of liquid drops in tube flow
Authors: Hyman W. A. , Skalak Richard
Published: June 2004

This paper present an analysis and computed results of the flow of deformable droplets of one Newtonian flow suspended in another Newtonian fluid. Surface tension is assumed to act at the interface of the two fluids. Non‐Newtonian characteristics of the suspension are demonstrated and are qualitatively similar to flow characteristics of blood in capillaries.

The results show that the deformation of the drops may result in a significant reduction in the pressure gradient compared with that necessary for a suspension of rigid spheres or spherical (nondeformable) liquid drops. The decrease in the pressure gradient is velocity dependent. This constitutes a mechanism of non‐Newtonain behavior of the suspension as a whole, and is attributable to the flexibility of the suspended elements. The resultant shapes of the liquid drops are similar to the shapes of red blood cells that have been observed in narrow glass capillaries as well as in blood vessels.
The blending efficiencies of some impellers in batch mixing
Authors: Moo‐Young M. , Tichar K. , Dullien F. A. L.
Published: June 2004

Mixing times for the blending of viscous liquids with tracer materials have been measured in a mechanically agitated tank using two conventional agitutor types (turbine, helical ribbon) and a series of novel tubular‐type agitators. The range of conditions studied were: viscosity = 1 to 70,000 cP, agitator Reynolds number = 5 to 105, tank diameter = 11.5 in. It was found that in terms of agitator power requirement, the tubular agitators were generally more efficient for viscosities greater than 100cP than the others for the blending process.

The effects of pseudoplastic non‐Newtonian fluid behavior, of tank‐baffles, and of tank size on mixing times have also been examined in several of the above cases.
Corresponding states: I. Theoretical development for mixtures
Authors: Gunn Robert D.
Published: June 2004

Part I of this work develops a corresponding states theory for fluid mixtures. A greater predictive capability for the thermodynamic properties of mixtures is achieved through three developments: 1. The theretical validity of the pseudocritical method is established. 2. The theory is founded on well‐defined assumptions. 3. The composition dependence of the scaling parameters (pseudocritical constants) is developed from rigorus mixing rules. Implementation of the new method is discussed in Part II.
II. Prediction of component fugacities and related properties of mixtures
Authors: Leyendecker W. R. , Gunn R. D.
Published: June 2004

A computer program based on the theory of Part I is developed for calculating equilibrium ratios and related thermodynamic properties of mixtures, and a variety of data are used to test the method. For the carbon dioxide‐n‐butane system both liquid and gaseous compressibility factors are predicted with an average absolute deviation from experimental values of 1.3% for a wide range of conditions. A maximum deviation of 5.4% occurs in the critical region. Derivative properties such as component fugacities and equilibium ratios show somewhat larger deviations as expected. For the same system average deviations are 2.7% for carbon dioxide fugacities, 2.6% for n‐butane fugacities, and 3.3% for carbon dioxide and n‐butane equilibrium ratios. Average deviation for predicted equilibrium ratios for eight binary systems and 574 data points is 4.6%. Equilibrium ratios for two ternary systems are also predicted accurately. The major advantage of the method, however, is the small or negligible amount of experimental mixture data required. The method has not been tested below a mixture reduced temperature of 0.8, the lower limit of the Pitzer tables. Without density corrections to the scaling parameters best results are obtained if all binary pairs in a mixture fall within range 0.25 <VCj TCj/VCi TCi < 4.0.
Foam separation of complex anions: Silver thiosulfate
Authors: Bhattacharyya Dibakar , Grieves Robert B.
Published: June 2004

An experimental study is conducted of the ion flotation of Ag(S2O3)– and Ag(S2O3)23– from an aqueous solution at pH 4.5 with a cationic surfactant. For initial solutions 2.0 × 10−3 to 8.0 × 10−3 M in total silver, optimum silver flotation at foam cesssation is achieved at a molar thiosulfate to silver ratio (Th/Ag) of 0.75 and surfactant to silver ratio (EHDA/Ag) of 0.5, at Th/Ag = 1.0 and EHDA/Ag = 1.1, and at Th/Ag = 2.0 and EHDA/Ag = 2.2. The silver flotation is 99+, 98+, and 92+ % at the three sets of ratios, respectively. At Th/Ag > 2.0, highly efficient flotation cannot be achieved due to decreased particle size, and perhaps by competition with free S2O32− for the surfactant.

The stoichiometry of the ion flotation product is established from relative silver and surfactant flotation rates. The stoichiometry is independent of foaming time, but is a strong linear function of EHDA/Ag and Th/Ag, in contrast to the stoichiometry of flotation products of other simple and complex anions. Rate data can be fit reasonably by a first‐order reversible model. The rate constant is an inverse function of EHDA/Ag, indicating the desirability of pulsed surfactant addition. Results are discussed in terms of the average ligand number of silver, particle size, and surface potential measurements.
A theoreticol and experimental study of the centrifugal molecular still
Authors: Greenberg David B.
Published: June 2004

A mathematical model of the centrifugal molecular still has been derived based on a fully developed profile, but negligible normal and tangential velocity components. Thermal gradients, film thicknesses, and evaporation rates calculated from this mathematical expression correlate well with reported literative values as well as with the present data.

Mean distillation rates were measured for five pure liquids on a centrifugal still with an effective evaporating surface area of 100 sq. cm. These experimentally obtained rates for liquids exhibiting ideal behavior agreed quite well with theoretical values predicted on the basis of simple kinetic theory. In the case of an associated liquid, however, rate measurements were found to be only 53 to 90% of the theoretical value. Although these low values tend to support the concept of an evaporation coefficient as a true molecular property, there wasevidence that surface irregularities could have accounted for all or at least part of the discrepancy noted.
Activity coefficients of strong electrolytes in multicomponent aqueous solutions
Authors: Meissner H. P. , Kusik C. L.
Published: June 2004

The quantity T12 here called the reduced activity coefficient is related to Γ12 the mean activity coefficient of a strong electrolyte 12 as follows:

where z1 and z2 are the charge number on the ions. The value of Γ12 for electrolyte 12 in an aqueous solution containing the three ions 1, 2, and 3, such as Na+ Cl− and Ba++, is to be calculated as follows:

Here Γ°32 and Γ°12 are for the indicated electrolytes, namely NaCl and BaCl2 in this example, at the total ionic strength of the mixture. The term X3 represents the fraction m3z32/(m1z12 + m3z32) in which m represents the molality of the indicated ion. Fair success is usually attained with this equation in predicting γ, even at high electrolyte concentrations.

Similar equations are proposed for aqueous solutions containing four or more ions.
On the computation of complex equilibria
Authors: Ma Y. H. , Shipman C. W.
Published: June 2004

A method is described for solving the problem: given fixed pressure, temperature, the amounts of the chemical elements, and the chemical potentials of possible chemical species at the pressure and temperature specified, determine the equilibrium composition. The method requires a minimum of judgment on the part of the user.

A modification of Naphtali's method for direct minimization of Gibbs' function provides an estimate of the composition of sufficient accuracy to insure convergence of solution, by the Newton‐Raphson method, of the nonlinear equations describing the equilibrium.

Problems in treating multiple phaes of unknown stability and chemical species present in small amouts are handled by ignoring unstable phases and small quantitites in the direct minimization until the amounts of the major consitituents have been at least approximately determined. To accomplish this, species temporarily ignored are assigned a ficitious mol fraction so that their re‐entry into the calculation can be established. Truncation errors in the direct minimziation can be tolerated because of the two‐step method.

Examples of some of the problems solved are given.
The peak pool boiling heat flux from a sphere
Authors: Ded Jagjit S. , Lienhard John H.
Published: June 2004

A hydrodynamic prediction is formulated for the peak nucleate boiling heat flux on spheres. It employs no empirical constants but it is justified by an experimental correlation of the vapor blanket thickness at the equator of the sphere. The prediction compares very favorably with 27 original data obtained by the transient calorimeter method in both water and N2 on spheres of different sizes. It also compares well with the data of prior investigators for a large range of size, gravity, and boiled liquids. Assumptions as to the vapor removeal configuration are supported with photographic observations of the boiling procss.
Forced convection heat transfer correlations for flow in pipes, past flat plates, single cylinders, single spheres, and for flow in packed beds and tube bundles
Authors: Whitaker Stephen
Published: June 2004

Previously obtained experimental heat transfer data have been collected and are illustrated along with minor variations of the standard correlations. Analysis of data for heat transfer in randomly packed beds and compact (void fraction less than 0.65) staggered tube bundles indicates that the Nusselt number for a wide range of packing materials and tube arrangements is given by

provided NRe ≥ 50. The correlations presented in this paper are not necessarily the most accurate available; however, they have wide application, are easy to use, and are quite satisfactory for most design calculations.
Laminar tube flow through an abrupt contraction
Authors: Christiansen E. B. , Kelsey S. J. , Carter T. R.
Published: June 2004

The general equations of motion were solved numerically for the laminar isothermal flow of Newtonian fluids from a large tube of circular cross section through an abrupt contraction into a coaxial tube of smaller diameter and through the flow‐development region of the smaller tube. The ratio of the diameter of the large tube to that of the smaller tube was varied from one to eight (the latter in one case). Solutions were obtained for the case where the larger tube is real, with no slip at the wall, and for the case where it is a frictionless “stream” tube. The results are presented as charts giving excess pressure losses attributable to contracted and developing flow in terms of equivalent smaller‐tube diameters as functions of the tube‐contraction ratio and the Reynolds number, which was varied from 0.01 to as high as 500 in one case. Both radial‐ and axial‐velocity profiles are presented. The computed results are shown to be in satisfactory agreement with some experimental data. The results are presented in a manner convenient for use in the design of equipment in which contracted Newtonian flow occurs, such as fiber spinnerettes and heat exchangers, and in the analysis of experimental data for contracted flow.
Prediction of breakthrough curves in packed beds: II. Experimental evidence for axial dispersion and intraparticle effects
Authors: Jeffreson C. P.
Published: June 2004

The effects of axial fluids dispersion on breakthrough curves in packed beds is considered and formulae are derived for ‘F‐factors’, which allow heat transfer coefficients obtained by step testing to be corrected for axial fluids dispersion. A comparison of steady state and unsteady correlations for heat transfer in packed beds suggests that axial dispersion effects are incorporated in certain steady state heat transfer correlaions. Further correction would thus lead to errors in breakthrough curve prediction. Experimental data for breakthrough curves in packed beds of highly conductive and poorly conductive spheres is examined and Biot number correction factor 1 + Bi/5 shown to be valid for Biot numbers up to about 4.
Residence time and fluid mixing on commercial scale sieve trays
Authors: Bell Richard L.
Published: June 2004

A fiber optic technique was used to obtain point residence time distributions at several points on an 8 ft. diam. sieve tray in hydrocarbon service. Residence time patterns were obtained over a wide range of vapor and liquid loadings with the isopropyl alcohol–water system and at both ends of the cyclohexane toluene system. The data reveal severe flow nonuniformities on the tray including nonuniform velocity distribution and retrograde flow near the column walls. The reasons for this behavior are discussed.
Kinetics of reduction of nickel oxide with CO
Authors: Krasuk J. H. , Smith J. M.
Published: June 2004

Initial rates were measured for the reduction of single pellets of nickel oxide with carbon monoxide at atmospheric pressure and temperatures from 566 to 796°C. The nickel oxide pellets were porous (ϵ0 = 0.032 − 0.35) and intrapellet diffusion retarded the rate so that the shrinking core model was not applicable. Effective diffusivities for the lower porosity pellets were very small, corresponding to tortuosity factors of about 180 for ϵ0 = 0.032 and 92 for ϵ0 = 0.062.

The reaction appeared to be first order in carbon monoxide. Rate constants, based upon the intraparticle area, indicated an activation energy of 47 kcal/g.‐mole over the temperature range 566 to 682°C. At higher temperatures the rate was constant. These results, while not conclusive, are in agreement with a reaction sequence consisting of formation of nuclei of nickel atoms in the nickel oxide surface, rapid adsorption of carbon monoxide at the nickel‐nickel oxide interface, migration of the adsorbed carbon monoxide to the adjacent lattice, and a slow reaction to extract oxygen from the lattice.
Volatiles retention during drying of food liquids
Authors: Chandrasekaran Santosh K. , King C. Judson
Published: June 2004

The retention of trace volatile components in food liquids during low temperature drying processes is analyzed through a ternary diffusion model. Flux equations for both water and trace organic components are solved numerically for typical drying situations. Several effects are found with the ternary analysis which are not evident from a simpler binary model. The sugar‐water composition gradient which develops during drying causes an appreciable transport of the trace volatile species. This transport can occur in the same direction as the transport resulting from the concentration gradient of the volatile species, or in the opposite direction, and can result in a local accumulation of the volatile species. Concentration profiles for both water and dilute volatile components were experimentally measured during nearly isothermal drying of gelled slabs of synthetic sugar solutions and natural fruit juice concentrates. The predicted internal maximum in volatiles concentration is borne out by the experiment, and a satisfactory agreement of observed with predicted volatiles retention is found, within the limits of the experiment.
An efficient algorithm for optimum decomposition of recycle systems
Authors: Upadhye Ravindra S. , Grens Edward A.
Published: June 2004

A method is developed for decomposition of a recycle process so as to minimize the summation of weighting factors for variables torn. This procedure is based on application of dynamic programming to a state space representing combinations of cycles opened. The resulting algorithm is well suited to machine implementation and is more efficient for large problems than alternative procedures that also guarantee decomposition.
Penetration characteristics of a submerged steam jet
Authors: Kerney P. J. , Faeth G. M. , Olson D. R.
Published: June 2004

An experimental investigation was made of the lenght of the turbulent vapor cavity formed by a steam jet discharging into a subcooled liquid water both. The experiments considered both constant area and convergent‐divergent steam injectors of various external geometries. The tests were conducted with the bath at atmospheric pressure, bath temperatures in the range 301–358K, injector exit diameters in the range 0.00040–0.0112 m, for choked injector flows having mass velocities in the range 332–2050 kg/m2.s. These conditions yielded injector exit Reynolds numbers from 2 to 150 × 104. Over this range a correlation was developed to yield the length of the vapor cavity as a function of the injector diameter, exit mass velocity, and a driving potential for the condensation process. The heat transfer coefficients for this condensation process were found to be significantly greater than those encountered in turbulent film condensation processes in the vicinity of tubes and walls.
The role of porosity in filtration VIII: Cake nonuniformity in compression–permeability cells
Authors: Tiller Frank M. , Lu Wei‐Ming
Published: June 2004

Compression‐permeability cells are utilized for measurement of porosity and permeability of compressible cakes. Shortcomings of the cells have tended to be minimized in the literature. Data are presented which show that the stress distribution in typical C‐P cells is highly nonuniform because of wall friction. For compressible materials, the porosity and permeability would also be nonuniform. Use of large L/D ratios and minimizing wall friction are essential to proper use of C‐P cells.
The effect of gibbs adsorption on marangoni instability in penetration mass transfer
Authors: Brian P. L. T. , Ross J. R.
Published: June 2004

A theoretical analysis of Marangoni convection in gas‐liquid mass transfer shows the stabilizing effect of surface convection in the Gibbs adsorption layer. Results are obtained for various ratios of liquid layer thickness to mass transfer penetration depth. For deep liquid layers, complete stabilization results when the inventory in the Gibbs layer equals the solute deficiency in the liquid phase boundary layer, irrespective of the shape of the unperturbed concentration profile.

This new theory agrees much better with experimental results than did previous theories. For example, for triethylamine desorption from water, the discrepancy is reduced from a factor of 8,000 to a factor of 8. Speculations are offered concerning this residual discrepancy.
A study of inversion curves
Authors: Juris Kenneth , Wenzel L. A.
Published: June 2004

A comparative study has been made on the predictive capabilities of a number of the more popular equations of state in use today. The equations were compared in their ability to predict the locus of points for which the Joule‐Thomson coefficient is zero, the inversion curve.

The prediction of an inversion curve is an extremely severe test of an equation of state. To date inversion curves have been calculated only for the Van der Waals, Dieterici, Lennard‐Jones and Devonshire, and DeBoer‐Michels equations of state. This study covers the Van der Waals and Dieterici equations as well as the Virial, Berthelot, Redlich‐Kwong, Beattie‐Bridgeman, Benedict‐Webb‐Rubin, and Martin‐Hou equations of state.

The results of the investigation show, among other things, that the Redlich‐Kwong equation is quite unusual in that it predicts the inversion locus with more accuracy than any of the much more complex equations of state. Its predictive capabilities extend into the liquid region.
Gas‐liqud slug flow with drag‐reducing polymer solutions
Authors: Rosehart R. G. , Scott D. S. , Rhodes E.
Published: June 2004

The two‐phase slug flow regime in horizontal cocurrent gas‐liquid flow was studied for the case of the liquid phase containing small amounts of polyacrylamide, a drag‐reducing long chain polymer. The experimental work was performed in a 2.54 cm I.D. horizontal test section 10.7 m long.

Results indicated that two‐phase drag reduction was greater than in single phase flow at the same superficial liquid velocities. By the use of pressure drop results with and without polymer additive, and a knowledge of slug geometry, frequency, and velocity, it was possible to separate approximately the contribution to the pressure drop of liquid wall friction and slug intertial effects. In all cases, the acceleration term was important and is the major energy term at most flow conditions. The technique may be of general usefulness in determining accelerational effects in two phase flows.

When drag reducing agents have been added to a horizontal slug flow, the pressure loss can be correlated successfully both by the Lockhart‐Martinelli type of relationship or by a universal drag reduction curve of the type proposed by Virk.
Thermodynamics of multi‐solute adsorption from dilute liquid solutions
Authors: Radke C. J. , Prausnitz J. M.
Published: June 2004

The thermodynamics of ideal dilute solutions is applied toward establishing a method for predicting multi‐solute adsorption using only data for single‐solute adsorption from dilute liquid solution. The method is similar to that proposed by Myers and Prausnitz for adsorption of gas mixtures.

Experimental adsorption data for activated carbon at 25°C are reported for dilute aqueous solutions containing acetone and propionitrile, and p‐chlorophenol and p‐cresol. Calculated and experimental results are in excellent agreement for the first system and in fair agreement for the second system. It appears that the ideal dilute‐solution theory for predicting multisolute adsorption is most reliable for those systems where solute adsorption loading is moderate. When solute adsorption loading is large, the simplifying assumptions in the theory must be relaxed to allow for solute‐solute interactions on the surface. The method presented here is simple to use and provides good approximations for engineering design.
The retention of large particles in fibrous filters
Authors: Freshwater D. C. , Stenhouse J. I. T.
Published: June 2004

The inertial interception mechanism of particle‐fiber collision in fibrous filters is described. The main mechanisms by which particles are retained in filters together with the effect of a number of operating parameters are discussed. The effect of particle size, gas velocity, relative humidity, and filter loading on the retention efficiency of large particles (> 5μ) is investigated experimentally.
Counterdiffusion of liquid hydrocarbons in type Y zeolite: Effect of molecular size, molecular type, and direction of diffusion
Authors: Moore Rebecca M. , Katzer James R.
Published: June 2004

This paper presents experimental results on the counterdiffusion of liquid hydrocarbons in the Y zeolite as determined by an unsteady state technique using the zeolite powder. The critical diameter of aromatic molecules counterdiffusing with respect to cyclohexane into NaY zeolite has a marked effect upon the counterdiffusion rate. For a given molecular type, the single parameter of critical molecular diameter correlates the size effect well. Molecular type, for example, toluene vs. phenol, also has a pronounced effect on the counterdiffusion rate. Those molecules showing stronger interactions with the zeolite have lower counterdiffusion rates. In both NaY and SK‐500, the diffusion coefficients for adsorptive counterdiffusion are an order of magnitude greater than the diffusion coefficients for desorptive counter‐diffusion indicating that factors other than simple intracrystalline diffusion as such are also important in zeolite counterdiffusion. Simple diffusion models do not account for the differences observed indicating that a more sophisticated approach is necessary.
Calculation of multicomponent liquid‐liquid equilibrium with Renon's and Black's activity equations
Authors: Guffey Charles G. , Wehe Albert H.
Published: June 2004

The combination of optimization theory and thermodynamics was used to develop a fast, reliable computerized procedure for predicting or representing multicomponent liquid‐liquid phase equilibrium. Both the Renon and Black activity coefficient equations were compared with experimental data using the procedure. Experimental data for three quarternary systems from the literature were examined. Prediction of ternary data from binary data is not very reliable, although ternary data can nearly always be represented by adjustment of the predicted binary constants. Quarternary data can be predicted from accurate ternary representations of similar species provided the additional compound is from the same family group. The Renon equation is recommended rather than the Black equation.
Protein ultrafiltration: A general example of boundary layer filtration
Authors: Kozinski A. A. , Lightfoot E. N.
Published: June 2004

A rotating disk membrane was developed to investigate experimentally concentration polarization during the ultrafiltration of bovine serum albumin solutions. The experimental data supported analytical and numerical predictions which were developed as part of this study. Osmotic pressure and concentration dependent viscosity and diffusivity were demonstrated to be important tactors. The results were also extended to predict ultrafiltration in porous walled ducts. Finally, a formal description of protein ultrafiltration in terms of the Stephan‐Maxwell flux equations was shown to provide a unifying description of all filtration processes from mechanical filtration to reverse osmosis.
A general expression for the correlation of rates of transfer and other phenomena
Authors: Churchill S. W. , Usagi R.
Published: June 2004

The expression Y = (1 + Zn)1/n where Y and Z are expressed in terms of the solutions for asymptotically large and small values of the independent variable is shown to be remarkably successful in correlating rates of transfer for processes which vary uniformly between these limiting cases. The arbitrary exponent n can be evaluated simply from plots of Y versus Z and Y/Z versus 1/Z. The expression is quite insensitive to the choice of n and the closest integral value can be chosen for simplicity. The process of correlation can be repeated for additional variables in series. Illustrative applications are presented only for flow, conduction, forced convection, and free convection, but the expression and procedure are applicable to any phenomenon which varies uniformly between known, limiting solutions.
A self‐adapting time‐optimal control algorithm for second‐order processes
Authors: Hsu E. H. , Bacher S. , Kaufman A.
Published: June 2004

A method for performing time‐optimal control with only limited prior knowledge of specific process dynamics is described. The time constants of the process are identified during the transient period accompanying the desired set point change, and the valve switching times of the control algorithm are calculated based on these time constants. The adaptive features of this method make its use independent of process or operating variation. The effectiveness of the proposed control method was evaluated using digital simulation and experimental techniques. The experimental phase which involved random changes to the temperature set point of a batch reactor was carried out with the aid of an on‐line digital computer.
Diffusion studies of CO2, NO, NO2, and SO2 on molecular sieve zeolites by gas chromatography
Authors: Ma Yi Hua , Mancel Claude
Published: June 2004

Gas chromatographic techniques were used to measure the diffusion coefficients and the isosteric heats of adsorption of CO2, NO, NO2, and SO2 on 5A and 13X molecular sieves, natural mordenites, and synthetic Na‐ and H‐mordenites in the temperature range of 133 to 325°C. Diffusional resistances for all gases studied decrease in the following order: natural mordenites > Na‐mordenites > H‐mordenites > (13X, 5A) indicating the increased ease of flow in the 3‐dimensional network. Isosteric heats of adsorption (range from 3 kcal/mole to 12 kcal/mole) and activation energies (range from 3 kcal/mole to 19 kcal/mole) decrease in the same order. The variations of diffusion coefficients, heats of adsorption, and activation energies are discussed in terms of the interaction between the surface and gas molecules as well as the openings of the pores relative to the size of the diffusing molecules.
Effects of surface active agents on mass transfer during droplet formation, fall, and coalescence
Authors: Skelland A. H. P. , Caenepeel C. L.
Published: June 2004

This experimental study shows effects of anionic and cationic surface active agents on mass transfer during drop formation, fall, and coalescence for both continuous and disperse phase‐controlled systems. Three dispersion nozzles, mounted with 1.906 cm equilateral pitch, and a 5.08 cm I.D. extraction column were used to simulate certain conditions in commercial liquid‐liquid extraction units.

The surfactant effects on extraction were pronounced, frequently reducing transfer to 10% of that in uncontaminated systems, with marked minima at intermediate concentrations of surfactant. In contrast, the continuous phase coefficient during coalescence was substantially increased by surfactants, with maxima in some cases.
Generalized multicomponent equation for activity coefficient calculation
Authors: Chien Henry H. Y. , Null Harold R.
Published: June 2004

A new model for the prediction of liquid phase activity coefficients used for predicting multicomponent phase equilibria is presented and compared with presently available methods for making these calculations. In its binary form, the new model includes Margules, van Laar, NRTL, Scatchard‐Hamer, and Fariss models as special cases. In its multicomponent form the van Laar, Margules, and Scatchard‐Hamer forms are different from and superior to the Wohl expansion. It is also possible with the new model to use different special case models for each of the binary pairs.
Use of Monte Carlo in calculating the thermodynamic properties of water clathrates
Authors: Tester Jefferson W. , Bivins Robert L. , Herrick C. C.
Published: June 2004

Equilibrium dissociation pressures for monovariant three‐phase (icesolid clathrate‐gas) systems were predicted for water clathrates with Ar, Kr, Xe, N2, O2, CO2, and CH4as the guest molecules. A Monte Carlo approach of statistically sampling the states available to the guest molecule inside the host water cage was used to evaluate the configurational properties including the free volume integral. The Lennard‐Jones 6–12 potential adequately described the guest‐host interaction for monatomic species, for example, Ar, Kr, and Xe, while the nonspherically symmetric Kihara potential with a fixed hard‐core geometry was required for polyatomic guests. The simulated motion of the guest within the cell was consistent with the geometrical features of the host lattice.
Correspondling states correlations for liquid compressibility and partial molal volumes of gases at infinite dilution in liquids
Authors: Brelvi S. W. , O'Connell J. P.
Published: June 2004

A statistical mechanical solution theory is used as the basis for corresponding states formulations. Universal functions relate the compressibility to the reduced density and the partial molar volume to reduced solvent density only. Correlations are in good agreement with data for all types of nonelectrolytes over wide ranges of temperatures including saturated and compressed systems. The correlations provide simple methods for describing the isothermal pressure dependence of liquid volumes and the pressure dependence of the ideal‐solution solubility of gases in liquids.