bluuebunny/crossref_metadata_2025 huggingface dataset:
Stability analysis of a continuous flow stirred tank reactor with consecutive reactions
Authors: Sabo David S. , Dranoff Joshua S.
Published: June 2004

The stability of a continuous flow stirred tank reactor with consecutive chemical reactions A→B→C was investigated here for the first time. The system equations were integrated numerically, and parts of the three‐dimensional phase space were generated for systems having one and three steady states, respectively.

The surface separatrix was determined by trajectory plotting after extensive computation. The system was also analyzed by Liapunov's second method. Krasovskii's form was used to generate Liapunov functions which proved to be satisfactory but extremely conservative in the estimation of the largest possible regions of asymptotic stability.
A probabilistic time delay description of flow in packed beds
Authors: Buffham B. A. , Gibilaro L. G. , Rathor M. N.
Published: June 2004

A simple model for describing residence time distributions (RTD) in packed beds is derived and applied to a trickle flow system. It is based on the concept of fluid elements being randomly delayed in time on their passage through the bed and leads to a simple and flexible mathematical description.
Wiener‐Hopf methods for unstable, nonminimum phase processes
Authors: Lim H. C. , Bankoff S. G.
Published: June 2004

It is shown that existing methods for design of optimal regulators by the Wiener‐Hopf procedure must be modified in order to be applicable to unstable and/or nonminimum phase plant or disturbance transfer functions, such as are frequently encountered in the chemical industry. Solutions are developed for three cases: I. stable, but possibly nonminimum phase, plant and disturbance transfer functions; II. minimum phase, but possibly unstable, plant with no restrictions on the disturbance transfer functions; and III. prestabilized, with a proper modification to retain the original control effort inequality constraints, but possibly nonminimum phase plant and disturbance transfer functions. Case III gives the general solution for regulation of linear, time‐invariant, lumped‐parameter systems. When prestabilization is not necessary, it reduces to case I. Where applicable, solutions by the method of case II frequently involve less algebra than in case III.
Wiener‐Hopf methods for unstable, nonminimum phase processes. Part II. Application to a Stirred Tank Reactor
Authors: Lim H. C. , Bankoff S. G.
Published: June 2004

The Wiener‐Hopf procedure for synthesis of optimum constrained linear feedback regulators has been extended in part I to all linear time‐invariant lumped parameter systems. The solution is here applied to the control of the output concentration of an exothermic, stirred tank reactor operating close to an unstable steady state, by constrained manipulation of a cooling water flow rate, in the presence of a randomly fluctuating inlet concentration.

When the spectral density of disturbance is given (for example, white noise through a first‐order time delay, or a series of randomly alternating steps), the optimum controller has three modes: proportional, derivative, and integral with minor feedback. The responses of the nonlinear reactor and the linearized reactor control systems to a series of alternating deterministic step inputs and Gaussian distributed inputs are simulated, and a sensitivity study of the linearized system with respect to variations in process, controller, and disturbance parameters is made in order to demonstrate the feasibility of the method.
Simultaneous heat and mass transfer in free convection boundary layers
Authors: Saville D. A. , Churchill S. W.
Published: June 2004

Expressions are derived for the heat and mass transfer coefficients for laminar free convection driven by simultaneous differences in temperature and composition for the asymptotic cases of equal Schmidt and Prandtl numbers approaching zero, equal Schmidt and Prandtl numbers approaching infinity, Schmidt number approaching infinity and Prandtl number approaching zero, and Schmidt number larger than Prandtl number and Prandtl number approaching infinity.

The results are applicable for horizontal cylinders or vertical axisymmetric bodies with arbitrary body contours insofar as the approximations of boundary‐layer theory are valid. The results compare favorably with existing solutions and experimental results for particular conditions.
An experimental study of unstable states in a loop reactor
Authors: Root R. B. , Schmitz R. A.
Published: June 2004

An adiabatic loop reactor was operated at naturally unstable steady states in experiments employing the reaction between sodium thiosulfate and hydrogen peroxide in aqueous solution. The unstable states, the intermediate states in a multiple state regime, were stabilized by manual manipulation of the recycle ratio. Resulting temperature data agreed well with those predicted from a plug‐flow model. Observations of the transient response to small disturbances from the intermediate states verified that they were indeed unstable as had previously been predicted theoretically. Cursory attempts to stabilize the system by means of automatic feedback control employing a three‐mode controller were unsuccessful.
Characteristics of inclusions in the dispersed phase of liquid‐liquid suspensions
Authors: Kessler D. P. , York J. L.
Published: June 2004

The classical emulsion is made up of drops of one liquid dispersed in a containing liquid. Under certain circumstances, however, some of the containing phase may form drops within the drops of the dispersed liquid, giving rise to a structure known as a double‐multiple emulsion. This study was an investigation of the hydrodynamic formation of these structures.

Double‐multiple emulsions were produced by using both transient and steady state liquid injection, with a cylindrical jet configuration. Analysis of the spray was by means of high‐speed photography.

The distribution of the large drops and that of the included drops were both found to be represented satisfactorily by a log‐normal probability function. A simplified model based on the use of nozzle parameters satisfactorily correlated percent included area and volume as a function of Reynolds number and Weber number. Large dispersed phase drops contained proportionally many more inclusions than did the smaller sizes.

The mechanism of inclusion formation was found to involve the drawing out of a ligament or sheet from the flowing jet, followed by the recoalescence of the free end of this ligament or sheet with the main jet body, entraining in the process a portion of the containing phase. Thus, the inclusions predate the formation of the drops of the dispersed phase from the jet disruption.
Liquid‐phase dispersion in packed beds with two‐phase flow
Authors: Furzer I. A. , Michell R. W.
Published: June 2004

Liquid‐phase Peclet numbers have been measured for 1/4 in. Raschig rings with countercurrent air flow in a 2 in I.D. column. The response curve has been analyzed by a computer program, since the output data was collected directly on paper tape. The Peclet number calculated from a moments analysis is considered unreliable, and the diffusion model can be rejected for the liquid phase. If the Peclet number is calculated by a least‐squares fit, and if the result is forced through the peak in the response curve, then a correlation for over one hundred runs with gas flows from 0 to 99% of flooding is given by Equations (7) and (8).
Venturi and other atomizing scrubbers efficiency and pressure drop
Authors: Calvert Seymour
Published: June 2004

Particle collection efficiency and gas pressure drop for venturi and other atomizing scrubbers can be predicted by means of equations developed in this paper. The significance of the details of the liquid atomization process, the collection of particles on single drops, and the uncertainty regarding them are discussed. The role of drop holdup in the scrubber throat is also important.
Kinetics of catalytic cracking selectivity in fixed, moving, and fluid bed reactors
Authors: Weekman Vern W. , Nace Donald M.
Published: June 2004

A kinetic mathematical model of catalytic cracking is described which accounts for conversion and gasoline yield in isothermal fixed, moving, and fluid bed reactors. The model has been tested and verified by using laboratory moving bed data with a commercial gas oil and catalyst. It is shown that under certain conditions, the selectivity behavior and maximum gasoline yield of fixed, fluid, and moving bed reactors will be identical. Maximum gasoline yield is defined in terms of both the kinetic parameters and the process variables for fixed, moving, and fluid bed reactors.
An experimental study of steady state multiplicity and stability in an adiabatic stirred reactor
Authors: Vejtasa S. A. , Schmitz R. A.
Published: June 2004

Steady state and transient characteristics of an adiabatic, continuous flow, stirred reactor were studied in experiments employing the exothermic reaction between sodium thiosulfate and hydrogen peroxide in aqueous solution. Results illustrate the multiplicity of steady states in this system over a range of residence times. Temperatures of unstable states were attained experimentally by observing the effect of perturbations from stable temperatures. The observed steady states of the reactor under various mixing conditions are shown to be in good agreement with the predictions of a mathematical model which is based on the assumptions that mixing is perfect and that a single independent chemical reaction occurs. Less exact quantitative agreement between theoretical and experimental unsteady performance is accounted for in terms of the sensitivity of the unsteady state to small errors in the system parameters and the existence of appreciable extraneous heat capacities of the experimental equipment.
Heat transfer from boundary layers undergoing an acceleration induced reverse transition
Authors: Talmor Eliyahu , Weber Norman
Published: June 2004

An experimental and analytical investigation of heat transfer in an acceleration induced transitional flow regime is presented. A previously developed criterion for the onset of reverse transition of turbulent boundary layers is combined with a theory of forward transition to derive the effect of free‐stream turbulence intensity on the critical value of an acceleration parameter for two initial velocity profiles within the turbulent boundary layer. The results are consistent with experimental observations.

Local heat transfer measurements were obtained along converging walls of rectangular flow channels having convergence angles of 45, 60, and 70 deg. Free‐stream turbulence (1.6 to 11%) was induced by grids upstream of the start of convergence, and the local Reynolds number were varied by variation in channel size and stagnation pressures (200 to 500 lb./sq.in. abs.) at a gas stagnation temperature of 1,500°R.

The results indicate a two‐stage reverse transition process along the converging wall with a forward transition between the two stages of reverse transition. The local Nusselt numbers obtained over a wide range of an acceleration parameter are correlated with the local Reynolds number, the acceleration parameter at the start of convergence, and the local flow area contraction ratio. The corrlation is in the form of laminarization paths having negative slopes for (NNu)r/(NPr)0.4 vs. (NRe)r at common area ratios. Local values of free‐stream turbulence intensity are required for proper application of the reverse transition criterion in conjunction with the heat transfer correlation presented.
Viscous incompressible non‐Newtonian flow around fluid sphere at intermediate Reynolds number
Authors: Nakano Yoshisuke , Tien Chi
Published: June 2004

Approximate expressions of velocity profile and drag coefficients have been obtained for viscous incompressible non‐Newtonian flow over a fluid sphere in the intermediate Reynolds number range.

The equations of motion of both external and internal fluids are satisfied by using Galerkin's method. The internal fluid is assumed to be Newtonian, while the external is assumed to be non‐Newtonian and can be described by the power law model. Furthermore, the condition that the tangential stress is transmitted across the fluid‐fluid interface without diminution is also satisfied with Galerkin's condition.

Comparisons are also made between the predicted results and the experimental data available in the literature. The possible reasons for the discrepancy are also discussed.
The effect of surface active agents on liquid‐liquid mass transfer rates
Authors: Mudge Lyle K. , Heideger William J.
Published: June 2004

An interferometric investigation of the transfer of n‐ and iso‐butyl alcohols from water to carbon tetrachloride revealed the existence of large interfacial resistances (500 to 2,500 sec./cm.) attributable to the presence of surface active agents. Evidence of a solute‐surfactant interaction has been obtained with sodium dodecyl sulfate and sodium tetradecyl sulfate, but the effect appears to be much less pronounced with the shorter chain length surfactant or with the branched chain alcohol.
Iterative techniques in optimization: II. The linearity difficulty in dynamic programming and quasilinearization
Authors: McDermott Colin , Lee E. S. , Erickson L. E.
Published: June 2004

The quasilinearization technique is used to overcome the dimensionality difficulty in dynamic programming. The advantage of this approach is that not only the dimensionality or the fast memory requirement can be reduced, but the computation time required can also be reduced considerably. A technique is also devised to overcome the linearity difficulty encountered in this reduction in dimensionality. To illustrate the approach, the three dimensional crosscurrent extraction problem is solved as a one‐ and a two‐dimensional problem in the dynamic programming algorithm. Only approximately 1 min. is required to solve this one‐dimensional problem. However, if this problem were solved as a three‐dimensional problem, computation time of the order of hours would be required.
Determination of the mechanisms causing and limiting separations by column crystallization
Authors: Gates W. C. , Powers J. E.
Published: June 2004

The process of column crystallization at total reflux and steady state was analyzed mathematically and experimentally in order to determine the mechanisms by which separations are achieved and limited. The results of the study indicate that separation is produced by the formation of crystals in the freezing section and by interphase mass‐transfer in the adjacent purification section. The separation is mainly limited by axial eddy diffusion in the liquid phase.

Data from three binary chemical systems were used in the study. The first system, m‐chloronitrobenzene‐m‐bromonitrobenzene, forms a solid solution with a small phase separation (less than 6 wt. %) and was the primary subject of this study. The second system, azobenzenestilbene, forms a solid solution with a phase separation which exceeds 20 wt. %. The third system, benzene‐cyclohexane, has essentially no solid solubility in the range of compositions for which data on separation have been reported (½ to 3 wt. % cyclohexane).

Four mathematical models of column crystallization were developed and compared with experimental data. These models were based on different sets of assumptions as to the mechanisms which control the overall separation. The model which is consistent with experimental data was used to evaluate mass transfer coefficients and effective liquid‐phase diffusivities. Diffusivities varied between 1.3 and 4.6 sq. cm./sec., and mass transfer coefficients varied between 0.07 and 0.64 cm./sec. in reasonable agreement with results obtained in studies of liquid‐liquid extraction in pulsed columns.
A macroscopic condition for stability
Authors: Denn Morton M.
Published: June 2004

A basic inequality which is necessary and sufficient for macroscopic stability of lumped dynamical systems is applied to obtain further insight into the construction of stability regions, development of stability and control criteria, and meaning and simplified derivation of some conventional results.
Invariant imbedding, iterative linearization, and multistage countercurrent processes
Authors: Lee E. Stanley
Published: June 2004

The equations for multistage countercurrent operations are difference equations of the boundary‐value type, which are generally solved by trial and error or iterative procedures. The invariant imbedding concept is used to solve these boundary‐value problems as initial‐value problems. It is shown that by the combined use of invariant imbedding and iterative linearization, a sequence of estimator equations for the missing terminal conditions is obtained. These estimator equations can be used to obtain the desired terminal conditions and the number of stages required to perform a specified separation.
Natural convection distorted non‐Newtonian flow in a vertical pipe
Authors: DeYoung Scott H. , Scheele George F.
Published: June 2004

The equations of motion and energy are solved numerically for fully developed laminar flow of a power law fluid in a vertical pipe with constant heat flux at the wall. Density is assumed to be the only temperature dependent physical property of the fluid. Temperature profiles, velocity profiles, and Nusselt numbers are presented as functions of the power law exponent and the ratio of the Grashof number divided by the Reynolds number.
Adsorption of multicomponent mixtures by solid adsorbents
Authors: Gonzalez Agustin J. , Holland C. D.
Published: June 2004

A procedure based on kinetic principles is presented for the development of models for the adsorption of mixtures of gases in any number of layers by solid adsorbents. Equations of state for two‐dimensional gas mixtures which are thermodynamically consistent with the adsorption models are also presented. The constants in the adsorption models for mixtures are obtained from the isotherms for the pure components. Good accuracy for the predicted adsorption of mixtures for the data available was obtained by use of a model for the adsorption of mixtures in bimolecular layers.
A correlation for the prediction of interaction energy parameters for mixtures of small molecules
Authors: Hiza M. J. , Duncan A. G.
Published: June 2004

Low temperature, phase‐equilibria data for binary systems containing hydrogen, helium, and neon were used to develop a correlation relating deviations from the geometric mean combining rule for the characteristic energy parameter to the ionization potentials of the component species. With the exception of oxygen systems, this relatively simple relationship correctly predicts published deviations, determined by different methods, for a number of systems within expected uncertainties. It is shown that consideration of attractive forces only, as done by Hudson and McCoubrey, is inadequate for such predictions.
Calculation of solubility parameters of polar compounds
Authors: Konstam Aaron H. , Feairheller William R.
Published: June 2004

A graphical method is presented for calculating solubility parameters and molar volumes of functional groups, as well as for calculating solubility parameters of high molecular weight members of a homologous series from data on low molecular weight members. These functional group solubility parameters and molar volumes have been used to extend the values of \documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt {EV} $\end{document} presented earlier by Small. Finally, it is shown that the use of group contributions to calculate cohesive energy is limited by the lack of information available on the intramolecular energies of interaction of functional groups on the same molecule.
Optimal control of a continuous flow stirred tank chemical reactor
Authors: Javinsky Martin A. , Kadlec Robert H.
Published: June 2004

The time optimal control problem for jacket cooled continuous flow stirred tank reactor (CSTR) with an exothermic, irreversible, second‐order, homogeneous, liquid‐phase reaction (the saponification of ethyl acetate) was solved with the maximum principle and phase plane analysis. Both experimental studies and analogue computer simulation studies were conducted.

The overall performance of the experimental system agreed very well with the performance of the corresponding system simulated on an analogue computer. However, there were enough differences in the observed and predicted operating states and switching curves to warrant the conclusion that the experimental performance can be significantly improved if experimental results are used to modify the results predicted with computer analysis. These differences were attributed to uncertainties in the model and the values of the model parameters as well as nonrandom (and unforeseen) measurement errors.
The purification of Helium Gas by physical adsorption at 76°K
Authors: Kidnay A. J. , Hiza M. J.
Published: June 2004

The physical adsorption isotherms for three methane‐helium mixtures, two nitrogen‐helium mixtures, and one methane‐nitrogen‐helium mixture were measured at 76°K. and pressures of 2 to 65 atm. on a coconut shell charcoal. The adsorption isotherms of the pure components (nitrogen, methane, and helium) were also determined over the appropriate pressure ranges.

Methods for predicting the mixture adsorption isotherms by using only the pure component isotherms are discussed and are shown to be adequate for these systems.

The concentration vs. time or breakthrough curves were also measured for both the binary and ternary mixtures at a number of different flow rates. Mass transfer coefficients for both the gas phase and the absorbed phase were obtained from these breakthrough curves.
Numerical treatment of fully developed laminar flow in helically coiled tubes
Authors: Truesdell L. C. , Adler R. J.
Published: June 2004

Laminar flow in helically coiled tubes is treated numerically. Fully developed axial and secondary velocities are calculated for both circular and elliptical cross sections. Only closely wrapped helices, that is, helices with modest pitch, are considered. Ten solutions with Deans numbers up to 200 have good accuracy. Two additional solutions with Deans numbers up to 280 are approximate.
Optimal stochastic control of nonlinear systems
Authors: Seinfeld John H.
Published: June 2004

An algorithm is proposed for the feedback control of nonlinear systems, the observations of which are corrupted with noise of unknown statistics. The feedback loop contains a nonlinear Kalman filter, which produces sequential least‐square estimates of the state of the system, and a controller designed to minimize an instantaneous performance criterion based on the state estimates. The scheme requires the on‐line integration of n(n + 3)/2 differential equations, where n is the number of unknown states and parameters. The scheme is applied to the feedback control of a CSTR with a first‐order exothermic reaction the temperature measurements of which are corrupted with random noise.
Unsteady state behavior of multicomponent distillation columns: Part II: Experimental results and comparison with simulation during start‐up at total reflux
Authors: Howard G. Michael
Published: June 2004

Experimental concentration profiles throughout a fourteen plate column approaching steady state at total reflux were obtained for mixtures of benzene, toluene, and ethylbenzene. The concentration profiles are characterized by a large movement of the middle component, toluene, through the column so that its maximum concentration shifts from plate to plate until steady state is reached.

Computer runs were made in which the column variables were specified to be, as nearly as possible, those observed or calculated for the experimental runs. The computer results indicated the same behavior as the experimental runs, and the concentration profiles were in fair agreement. Thus, the computer model and calculation procedure used could replace the real column for many purposes. Inaccuracies in the computer simulation are due more to inadequate information about the characteristics of the real column than to deficiencies of the computer model.
Chromatography of nonadsorbable gases
Authors: Cerro Ramon L. , Smith J. M.
Published: June 2004

Chromatographic techniques are used with nonadsorbable and slightly adsorbable tracers to evaluate mass transfer parameters in packed beds. If accurate values of intraparticle diffusivities are to be obtained, it appears that long beds of relatively large particles must be used. Otherwise the moments of the chromatographic peaks are too small for accurate analysis. With adsorbable gases, such precautions are not necessary, and, in addition, the adsorption rate constant can be estimated. However, the intraparticle diffusivity determined for adsorbable gases can include a contribution due to surface migration. The method is applicable to all types of porous particles used as catalysts or catalyst carriers.

A combination of measurements of slightly adsorbable and nonabsorbable tracers can be used to approximate the adsorption rate constant for a slightly adsorbable gas such as nitrogen.
Experimental and theoretical investigation of continuous flow column crystallization
Authors: Henry Joseph D. , Powers John E.
Published: June 2004

A theoretical and experimental investigation of the separation achieved in a column crystallizer which utilizes a spiral conveyor was conducted to determine the effect of variables associated with continuous flow operation. A system that exhibits negligible solid solubility was used. Several feed mixtures containing less than 31,000 p.p.m. weight cyclohexane in benzene were employed. The principal variables evaluated in this study in a column of constant length were the feed position, internal crystal rate, and flow rates of terminal streams. A mathematical model is developed which considers axial dispersion and mass transfer between the liquid adhering to the crystals and the bulk liquid. The model satisfactorily explains the effect of the variables associated with continuous flow operation and shows that axial dispersion is more dominant in continuous flow than in total reflux operation. It is shown that multiple pass or cascade operation is necessary to produce material of purity higher than a critical level which is related to the feed composition. This occurs because of impurities in the crystal phase which are likely caused by volumetric inclusions.
Errata
Authors: Clamen Allen , Gauvin W. H. , Luss Dan , Amundson N. R. , Tierney John W. , Sage B. H. , Shih F. S. , Gordon R. J. , Weekman Vern W. , Patterson G. K. , Finlayson Bruce A.
Published: June 2004

No Absract.
Fog formation in boundary value problems
Authors: Toor H. L.
Published: June 2004

For a Lewis number one gas, the equations of energy and diffusion state that if local equilibrium exists in a fog region, fog may form in a continuous manner, but it may be vaporized only discontinuously at the boundary between fog and nonfog regions. The local rate of formation of fog is proportional to the square of the local gradient of temperature or concentration. A class of solutions to the transport equations has been obtained for problems in which no vaporization occurs at the fog boundary. Under these conditions, the temperature and concentration at the boundary of the fog region are both shown to be constant at values that depend only upon the initial and/or boundary values of temperature and concentration and upon the equilibrium curve.
Optimal operation of a variable‐volume stirred tank reactor
Authors: Lund Monty M. , Seagrave Richard C.
Published: June 2004

For certain classes of chemical reactions, it is possible to increase the yield of the desired products by choosing appropriate variable‐volume operating policies. An analysis of the steady state and semibatch operation of a stirred tank reactor demonstrates operating policies for both the isothermal and adiabatic case to maximize the steady state yield and to produce an improved semibatch yield. Computations carried out by using an analogue computer with a digital logic expansion system demonstrate further relationships between yield increase and operating policy.
Vapor‐liquid equilibrium in alcohol‐water systems containing dissolved acetate salts
Authors: Meranda David , Furter William F.
Published: June 2004

Isobaric vapor‐liquid equilibrium data at atmospheric pressure are reported for seven systems, each consisting of water, an alcohol (methanol or ethanol), and an anhydrous acetate salt (of sodium, potassium, barium, or calcium) dissolved to saturation in the boiling liquid phase. These systems are intended to complete a matrix about the single system ethanol‐water‐potassium acetate for which data were reported previously.

Solubility data are reported in terms of saturation salt concentration as a function of alcohol‐water proportionality in the liquid. Sodium acetate as well as potassium acetate was found capable of eliminating completely the ethanol‐water azeotrope.

Major differences in the effects of these salts as compared to those reproted for other salts in the salt‐effect literature were observed. Systems were discovered in which the salt appeared to cause both salting out and salting in of the alcohol in differing composition regions of the same system, the predominating effect depending on the relative proportions of alcohol and water. Systems were also discovered in which the salt salted‐in the component in which it was less soluble. Both observed effects are in contradiction with previously accepted theories of salt effect in vapor‐liquid equilibrium.
Steady state technique for measuring fluxes and diffusivities in binary liquid systems
Authors: Rao S. S. , Bennett C. O.
Published: June 2004

A steady state experimental technique for measuring fluxes of the components and diffusivities in binary liquid systems has been developed. Steady state diffusion is established through a sintered glass diaphragm of ultrafine porosity with a known concentration difference across the diaphragm. The concentrations are maintained by a flow of solution on one side of the diaphragm and an infinite sink on the other side. The fluxes and diffusivities are calculated from the measured flows and compositions. A syringe pump capable of delivering extremely small flow rates with good reproducibility is used to pump the solution past the sintered glass diaphragm. The diffusion cell design permits an accurate control of pressure drop across the diaphragm so that fluxes can be measured both with and without pressure gradients. The diffusion cell was calibrated by using the hydrochloric acid‐water system.

Three binary systems, ethanol‐benzene, aniline‐benzene, and aniline‐carbon tetrachloride were chosen for diffusion studies. Diffusivity‐composition data for these systems at 25°C. were used to test the existing correlations for the concentration dependence of binary diffusivity. Of these, the empirical correlation of Vignes (11) represents the data satisfactorily. In addition, experimental molar diffusion flux ratio data for the above systems at 25°C. with no pressure gradients are reported and found to be essentially equal to the ratio of molar volumes of the components.
Surface renewal and penetration models in the transient state
Authors: Chung Benjamin T. F. , Fan L. T. , Hwang C. L.
Published: June 2004

The transient models for some interphase transport processes have been developed based on the transient age distributions derived from the population balance. These models appear to represent physical reality more accurately than do the steady state models during the start‐up period of the transport processes.
Conformal solution correlation for the nitrogen‐oxygen‐argon system
Authors: Calvin William J. , Smith Buford D.
Published: June 2004

A correlation based on conformal solution theory has been developed for the excess properties of the nitrogen‐oxygen‐argon systems. A better method for calculating the conformal parameters makes possible the simulataneous correlation of the three excess properties FE, HE, and VE. Each binary is characterized by a k12, c12 set which represents corrections to the geometric and arithmetic mean combination rules. These binary constants predict the ternary data. Also, the correlation based on data at one atm. (77° and 84°K.) predicts the FE data accurately up to the critical points (110° to 120°K.).
Drop formation mass transfer
Authors: Rajan S. M. , Heideger W. J.
Published: June 2004

The mass transfer occurring between a liquid drop during its formation and the surrounding liquid phase was directly evaluated by a photographic technique. Slightly soluble organic drops containing no additional solute were formed in a continuous aqueous phase so that only the continuous phase resistance existed. Effects of nozzle diameter and both phase flow rates were evaluated and the possible influence of surfactant was investigated.

Mass transfer coefficients were observed to decrease sharply with time early in the formation period. This, together with the parameteric study of dispersed phase feed rate, indicates the strong effect of internal drop convection for this high Schmidt number system. The measured coefficients are substantially higher than would be expected for free drops.
Diffusion and chemical reaction in a tubular reactor with non‐Newtonian laminar flow
Authors: Homsy R. V. , Strohman R. D.
Published: June 2004

The problem treating an irreversible, first‐order chemical reaction in an isothermal, tubular reactor operating under steady, non‐Newtonian, laminar flow is studied. Numerical results for the eigenvalues, eigenfunctions, expansion coefficients and bulk concentration are reported for Ostwald‐de Waele and Prandtl‐Eyring fluids. Results show that chemical conversion in a tubular reactor may be significantly influenced by the non‐Newtonian characteristics of a fluid.
Prediction of vapor‐liquid equilibria of petroleum fractions
Authors: Mikolaj Paul G. , Dev Lachhman
Published: June 2004

The thermodynamic treatment of phase equilibria proposed by Chueh and Prausnitz has been modified to extend their method to systems of petroleum fractions. These modifications, which include the use of a symmetric convention for normalizing activity coefficients and replacement of the dilated van Laar model with a regular solution model, were required because existing data were insufficient to establish the needed binary interaction parameters. The resulting correlation was compared with experimental data on a naphtha‐furnace oil mixture at conditions up to 660°F. and 517 lb./sq.in.abs. The computed K values showed an average absolute deviation of 9.1%, while K values predicted by the Chao‐Seader correlation deviated by 12.4%.
Diffusion and reaction in ideal multicomponent systems: I. Tubular reactor near equilibrium
Authors: Solomon R. L. , Hudson J. L.
Published: June 2004

Diffusion and either surface or gas‐phase reaction in a ternary ideal gas mixture in steady fully developed laminar flow in a tube is considered. The linearized equations valid near equilibrium and under isothermal conditions are solved. Concentration profiles predicted using a multicomponent diffusivity matrix are compared to those predicted using more approximate diffusivities. Local overshoots past equilibrium occur, but oscillations (with axial position) are not possible. A simplified diffusivity expression is found which predicts cup‐mixing mole fractions in good agreement with those predicted using the multicomponent diffusivities.
Effects of molecular characteristics of polymers on drag reduction
Authors: Liaw Gin‐Chain , Zakin Jacques L. , Patterson Gary K.
Published: June 2004

Turbulent measurements in capillary tubes and in pipes were made on nonpolar solutions of seven polymer species, three at more than one molecular weight, over wide concentration ranges.

A critical concentration, Cc, was taken as the minimum concentration for disappearance of the turbulence transition region. Above this concentration, friction factor‐generalized Reynolds number data show only a gradual deviation from extension of the laminar line. Cc increases with tube diameter and decreases with molecular weight. The critical dimensionless volume friction Cc [η] is less dependent on molecular weight.

The levels of Cc [η] for different polymer species in a given tube show marked differences which are related to β, the molecular rigidity parameter. Low β values, or high flexibility, are associated with low Cc [η] values. Available data for Cc [η] in good and in poor solvents show little solvency effect.

Polymer samples of low m′, the ratio of the polymer molecular weight to the critical tanglement molecular weight of the polymer, give solutions with little or no drag‐reducing capacity, even those with low β values. Samples must have m′ values of 50 or more to show significant drag reduction. This allows prediction of the minimum useful molecular weights for drag reduction for any polymer species.

For solutions above Cc, all of these data and literature data (for aqueous and nonaqueous systems with a wide range of n′ values) fit a single f/fpv versus generalized Reynolds number relationship.
Pressure drag measurements for turbulent air flow through a packed bed
Authors: Van Der Merwe D. F. , Gauvin W. H.
Published: June 2004

Pressure drag coefficients of spheres in a cubic packing of equal spheres have been determined at Reynolds numbers of 27,000, 10,000, 5,000 and 2,500, where NRe is based on superficial air velocity and a sphere diameter of 7 cm. Two cubic arrangements were used: in the regular arrangement, the mean flow was parallel to one of the principal axes, while in the skewed arrangement, the mean flow made equal angles with the three principal axes of the packing.

The pressure drag coefficient of the central sphere has been measured for each of the 12 banks in the regular arrangement, and the effect of bed length has been determined for lengths varying between 1 and 12 banks. The pressure drag coefficient for the central sphere and the overall pressure drop in the skewed arrangement were found to be lower than for the regular arrangement at the same Reynolds number. From the distribution of local pressure measurements, the separation and reattachment points on the central sphere in each bank were determined, indicating that the boundary‐layer behavior on a sphere in a packing is similar to that over a single sphere, when allowing for the effects of turbulence and of pressure gradient.
Parameter sensitivity of systems described by nonlinear ordinary differential equations
Authors: Rayzak R. J. , Luus Rein
Published: June 2004

An approximate analytical method is developed to estimate the parameter sensitivity of the solution of a set of nonlinear ordinary differential equations describing a system which exhibits periodic behavior. An approximate solution is constructed in terms of both the approximate periodic solution determined from Galerkin equations and the envelope and phase of the oscillation away from such a periodic solution. Parameter sensitivity information is then obtained by examining the parameter variation effect on the approximate solution.

Examples of two‐ and three‐dimensional nonlinear systems illustrate this procedure and show that the effect of parameter change on the solution is predicted with sufficient accuracy to make this method useful for nonlinear analysis.
On suspended particles in tube flow
Authors: Schreiner Kristian E.
Published: June 2004

The paper considers the effect on fluid flow in a tube when rotationally symmetric particles follow the flow on the tube axis. It is found that a region of disturbed flow, similar to inlet flow, adheres to the particle. A model describing this disturbed flow is suggested, and an expression for the change in the apparent viscosity of the flow is developed. It is found that the accompanying disturbance may have an appreciable effect on the flow. The model should be applicable when the tube Reynolds number is larger than 10.
Adsorption equilibria of the light hydrocarbon gases on the activated carbon and silica gel
Authors: Gonzalez A. J. , Holland C. D.
Published: June 2004

A new method is presented for the determination of adsorption equilibria for pure components and mixtures both at high and low pressures. Isotherms for carbon dioxide, methane, ethane, propane, i‐butane, n‐butane, i‐pentane, and n‐pentane on activated carbon (Columbia grade NXC 8/10) and on silica gel (Mobil Sorbead H) at 75°, 125°, 200°, and 300°F. are given for pressures ranging from below atmospheric to 1,000 lb./sq. in. Also, adsorption equilibria data are presented for several multicomponent mixtures of the light hydrocarbon gases.

The data collected were correlated with good accuracy by use of the two‐layer kinetic model developed previously by Gonzalez.
Multivariate control of a phase separation process
Authors: Kleinpeter Joseph A. , Weaver Robert E. C.
Published: June 2004

This paper presents a nonequilibrium mathematical model of a vapor‐liquid separator. The model is used as the focus of a computer simulation control study conducted to provide the foundation for applying recent multivariate control developments to distillation systems.

Greenfield and Ward's structural analysis was found to provide reasonably good feedforward and decoupling control of pressure, liquid temperature, and liquid pressure. Because of implicit relationships between product composition variables and their manipulative inputs, structural analysis was inapplicable when these composition variables were among the controlled variables.

A method is presented which provides feedforward and some decoupling control for linear multivariable systems despite the existence of implicit relationships between controlled variables and their manipulative inputs. It is seen however that genuinely decoupled servo action on isolated state variables requires control through derivatives and thus an expansion of state space.
Velocity and turbulence measurements of air flow through a packed bed
Authors: Van Der Merwe D. F. , Gauvin W. H.
Published: June 2004

Mean velocity and turbulence measurements in the void spaces of a cubic packing of equal spheres have been made at Reynolds numbers of 27,000, 10,000, 5,000 and 2,500, where NRe is based on superficial air velocity and a sphere diameter of 7 cm. Two cubic arrangements were used: in the regular arrangement, the mean flow was parallel to one of the principal axes, while in the skewed arrangement, the mean flow made equal angles with the three principal axes of the packing.

Transverse mean velocity and turbulence intensity profiles across the center line of a central pore have been measured behind every bank and behind the bed for the regular arrangement of ten banks of spheres. The power spectrum and probability distribution of the fluctuating velocity have also been determined.
Convective dispersion of blood gases in curved channel exchangers
Authors: Chang Hsin‐Kang , Mockros Lyle F.
Published: June 2004

The rates of hemoglobin saturation and carbon dioxide reduction in blood flowing in a curved channel membrane exchanger were studied theoretically by considering the fluid‐limited process and the wall‐limited process. The fluid‐limited process was studied for laminar flows with and without secondary circulations. The relatively nontraumatic centrifugally induced circulations in the curved channel can reduce the required channel length to less than 1/500 that required for unperturbed flow. Such improvement, however, is practical only if very permeable membranes are available. If thePO2= 715 mm. Hg andPCO2= 0 mm. Hg at the walls, the fluid‐limited analyses show oxygenation to be the slower process and the wall‐limited analyses indicate CO2removal to be the limiting process. If the best available silicone rubber membranes are used, the process will be fluid limited for the unperturbed flow and wall limited for the flow with secondary circulations.
Theoretical analysis of the turbulent flow of non‐newtonian slurries in pipes
Authors: Hanks Richard W. , Dadia Bharat H.
Published: June 2004

A theoretical model is derived which permits the analytical calculation of the friction factor‐Reynolds number curves for non‐Newtonian slurries flowing isothermally in smooth pipes. This model is based upon the Bingham plastic rheological equation of state.

A change of mechanism in the transition phenomenon is observed to occur for NHe = 5 (105), where NHe is the familiar Hedstrom number. Below this value turbulence is suppressed relative to Newtonian flow, while above this value the transition is delayed but turbulence is enhanced relative to Newtonian flow.

A set of theoretical design curves of friction factor versus Reynolds number covering laminar, transitional, and turbulent flows is calculated and presented for a range of NHe values from 103 to 109.
Waves on a thin film of viscous liquid
Authors: Byatt‐Smith John G. B.
Published: June 2004

In this paper we consider the problem of the flow of a viscous incompressible fluid down an inclined wall. A solution is obtained by assuming that the free surface is a wave of low frequency. The solution is numerical and the results are compared with existing theories and available experimental results.
Drop‐size distributions from pneumatic atomizers
Authors: Kim K. Y. , Marshall W. R.
Published: June 2004

A study was made of the atomizing characteristics of convergent‐type pneumatic nozzles. Drop‐size correlations were obtained for the following ranges: drop size, 6 to 350 μ, mass median diameter; mass flow ratio, 0.06 to 40; relative velocity, 250 ft./sec. to sonic velocity; and viscosity. 1 to 50 cp. The technique employed was to spray cool a molten wax, and melts of wax‐polyethylene mixtures. The most important operating variables in pneumatic atomization are the dynamic force of the atomizing gas, and the mass flow ratio of air to liquid. The cumulative volume drop‐size distribution of spray from a pneumatic nozzle was fitted by a modified logistic equation. Empirical correlations developed in the study can be used to design nozzles or to predict drop size for sprays produced by the types of nozzles studied. In particular, this study provides new experimental data on the performance of pneumatic atomizers in producing relatively large drops.
Simultaneous computation of heat transfer and dispersion coefficients and thermal conductivity value in a packed bed of spheres: II. Technique of computing numerical values
Authors: Goss M. J. , Turner G. A.
Published: June 2004

The method of computing the numerical values is given. It is illustrated with a simulated example to show the high accuracy that is possible, the unknowns being found to four significant figures. The only quantities required are ones that can be measured accurately: the radius of the spherical packing, its volumetric specific heat, and values of the amplitude attenuation and phase angle lag at a minimum of four finite values of the frequency.
Statistical analysis of growth of microorganisms
Authors: Aiba Shuichi , Endo Isao
Published: June 2004

A mathematical model is derived in the form of a functional equation to describe a population dynamics of microorganisms (bacteria). The individual cells are due to experience a cycle of growth and division during the proliferation period.

The interdivision growth rate of bacterial cells (Azotobacter vinelandii) in a continuous and steady state culture is assessed by introducing a probability of division and by using the cell size distributions which are measured with the Coulter counter.

Sigmoid patterns, the single‐cell volume versus time, agree incidentally with the previous data which have been published by Harvey et al. from an approach devoid of a particular model. A mutual relationship between the microbial activities from the macroscopic scale of cell mass concentration and those from a statistical analysis is discussed briefly.