bluuebunny/crossref_metadata_2025 huggingface dataset:
Simultaneous effect of macromixing and micromixing on growth processes
Authors: Fan L. T. , Tsai B. I. , Erickson L. E.
Published: June 2004

Interaction of macromixing and micromixing in microbiological flow reactors based on a kinetic model of the Michaelis‐Menten type has been treated by considering two general types of flow systems: the system of n continuous stirred‐tank reactors in series (n‐CSTR's in series) and the series combination of a plug‐flow reactor and a continuous stirred‐tank reactor. Systematic schemes to describe the micromixing conditions of a reactor system are presented. Additional micromixing states are considered besides those proposed by Kramers and those proposed by Zwietering if the systems are employed as empirical models of a flow system. When the number of stirred‐reactor units in the system of n‐CSTR's in series is small, micromixing has a significant effect on the growth processes. As the number of reactor units increases, the micromixing effect on the growth processes decreases. The effect of micromixing is also important for a system described by a series combination of a plug‐flow reactor and a continuous stirred reactor. In addition, the exit concentrations from the system having the same residence time distribution and the same degree of segregation may be different from each other. Information obtained in this study is pertinent in the design of biological flow reactors and sewage treatment systems.
Complex reactions in oscillating reactors
Authors: Dorawala T. G. , Douglas J. M.
Published: June 2004

Previous work has shown that perturbation methods are useful for estimating the difference between the time average conversion obtained from an oscillating reactor and the optimum steady state value. The present study extends this approach to complex kinetic mechanisms. Both forced and self‐generated oscillations are studied, and in the latter case both positive and negative feedback control systems are used to alter the shape of the oscillations. The results indicate that large improvements in yields sometimes can be observed for parallel reactions but that only small improvements are possible for consecutive reactions, in the range of system parameters considered.
Turbulent flow of dilute polymer solutions through an annulus
Authors: Rubin Hillel , Elata Chaim
Published: June 2004

A semiempirical analysis of the turbulent flow of dilute polymer solutions through an annulus between two coaxial tubes is presented. This analysis is based upon the assumption that the velocity profile is logarithmic in the turbulent region. The thickness of the laminar boundary sublayer is changed by adding polymers to the solvent; this change is different at each wall of the annulus. A series of experiments was conducted in an annular system. The experimental results fit the theoretical predictions quite well.
The dynamics of thin liquid films in the presence of surface‐tension gradients
Authors: Ludviksson V. , Lightfoot E. N.
Published: June 2004

The climbing of Marangoni films up vertical solid surfaces was investigated experimentally and theoretically. The system considered was a nonisothermal plate with its warm end partially immersed in a nonvolatile liquid. Observed film thicknesses and rates of climb were in agreement with an approximate hydrodynamic model obtained by assuming the supply capacity of the film to be rate limiting.

The results of this study confirm the hypothesis is that previously observed liquid films formed against gravitational forces above equilibrium menisci are produced by surface‐tension inequalities. It is pointed out that hydrodynamic processes cannot allow for the advancement of the leading edge of Marangoni films and a separate physicochemical process is required to explain spontaneous spreading of these films. Evidence is presented for the formation of much thinner primary films ahead of the secondary bulk films described by hydrodynamics. These primary films appear to be produced by a combination of multilayer adsorption and/or surface diffusion. The kinetics of these diffusional processes may limit spreading rates when surface‐tension gradients become sufficiently large.

Finally, the Marangoni films were found to be unstable in a manner hithertonot considered.
The coalescence of drops in liquid‐liquid fluidized beds
Authors: Maraschino Mario J. , Treybal Robert E.
Published: June 2004

The coalescence rates of equisized drops of organic liquids fluidized by water under conditions of mutual saturation were studied. A drop‐size separation technique permitted the direct count of the coalesced drops. Six organic liquids (benzene, cyclohexane, n‐butylacetate, methyl isobutyl ketone, diisobutyl carbinol, and tetrahydrobenzaldehyde) were used, and the coalescence was in all cases total, that is, without formation of small satellite drops.

A new hydrodynamic model is presented to calculate the parameters governing the drainage of liquid between two deformable drops in head‐on collision. A parameter from this model permits correlation of the coalescence rates with only two arbitrary constants, provided the ratio of dispersed to continuous liquid viscosities lies between 0.5 and 2. High viscosity ratios or the presence of trace quantities of surfactant greatly depress the coalescence rate, while continued reuse of the dispersed liquid leads to a statistically significant reduction. The presence of a fog of very small droplets increases the coalescence rate.
Accumulation and continuous removal of impurities in fuel cells: I. One‐dimensional model
Authors: Lyczkowski R. W. , Gidaspow Dimitri
Published: June 2004

A mode of operation and a design technique have been developed which permit the attainment of continuous purging of impurities directly from the gas compartments of a fuel cell—either anode, cathode, or both—with the realization of minimum reactant loss, most stable voltage and current output, and operating conditions with respect to reactant gas flow and electrolyte inventory. We have found a way to eliminate the complex periodic purge valves and attendant electronics by a fuel cell system which is both simple in structure and operation and which has a high degree of reliability. The technique was suggested by the observation that in dead‐ended fuel cell gas compartments, the inert impurities present in reactant gases tend to accumulate at the dead‐ended portion of the cell. Hence a small amount of bleed should be placed there. This observation has been made analytically by solving numerically a system of two partial differential equations simultaneously.
Pressure drop and holdup in horizontal slug flow
Authors: Greskovich E. J. , Shrier A. L.
Published: June 2004

The Dukler‐Hubbard slug‐flow model is used along with independent correlations for in situ holdup and slug frequency to predict pressure drops for two‐phase slug flow. The holdup and frequency correlations are for the most part based on data for air‐water flowing in a 1.50‐in. pipe. Predictions of pressure drop using this approach are compared with experimental data taken from studies utilizing various systems and pipes from 1.50 to 6.065 in. in diameter. Alternative correlations by Dukler and Hughmark for predicting two‐phase pressure drops and holdup, respectively, are included for comparison. In general, the present approach is at least equivalent to the Dukler‐Hughmark method, and for values of ΔP/L > 0.06 lb./sq. in./ft. appears to be slightly better.
Viscosity of gas mixtures at normal pressures: Binary polar‐nonpolar systems
Authors: Hattikudur U. R. , Thodos George
Published: June 2004

An interaction model is presented for the prediction of viscosities at normal pressures of gas mixtures containing a polar and a nonpolar constituent. This model is based on the principle of corresponding states and requires TR, the viscosity parameter ξ = T/M1/2P for each component, and the value of zc for the polar component.

Viscosity measurements available in the literature for several binary systems have been used to establish interaction coefficients which have been correlated to obtain relationships capable of predicting them. This method has been applied to 14 systems for temperatures ranging from 288° to 523°K. to produce an average deviation of 2.64% for 356 experimental values.
The PVT behavior of isopropyl alcohol at elevated temperatures and pressures
Authors: Tseng James K. , Stiel Leonard I.
Published: June 2004

Experimental PVT data have been obtained for isopropyl alcohol by the use of a constant‐volume apparatus. Smoothed values of the compressibility factor are presented for temperatures from 200° to 300°C. and pressures from 1,000 to 8,000 lb./sq. in. The experimental data are estimated to be accurate to within 0.4%. The compressibility factor of isopropyl alcohol is also analyzed by the fourth‐parameter approach. It is shown that the normal fluid relationship for the compressibility factor can be extended to polar fluids by the inclusion of linear and quadratic terms in the fourth parameter.
Interfacial shear viscosity at fluid‐fluid interfaces
Authors: Wasan D. T. , Gupta Lalit , Vora M. K.
Published: June 2004

Fluid‐fluid interfaces containing surface‐active agents or macromolecules exhibit interfacial shear viscosity phenomena. The purpose of this paper is to investigate theoretically the dynamics of liquid‐liquid and liquid‐gas interfaces containing surfactants, and to establish the validity of the proposed model from shear flow data at uncontaminated interfaces.

A theoretical analysis for the measurement of interfacial shear viscosity at liquid‐liquid interfaces with an improved viscous traction surface viscometer is presented. The analysis takes into account the finite depths of the two liquids and permits interpretation of the experimental results in terms of interfacial shear viscosities at the liquid‐gas interface in addition to the liquid‐liquid interface. Results of the present analysis clearly show a strong coupling of interfacial and bulk fluid flows.

Extensive measurements of the interfacial velocities at a xylene‐water interface were made. A cetane‐water interface was also studied. Interfacial flow data for uncontaminated systems were found to be in excellent agreement with theory.
Models for vapor‐phase and liquid‐phase mass transfer on distillation trays
Authors: Hughmark G. A.
Published: June 2004

Three mass transfer models are developed for the vapor phase. The first model assumes a rigid interface between the liquid and vapor and yields the Schmidt number as the correlating variable. The other two models represent a free interface with the penetration theory as the mechanism for one model and eddy diffusion as the mechanism for the other model. Both free interface models correlate experimental data within the error of the data. A liquid‐phase mass transfer model is developed for a free interface and the penetration theory as the mass transfer mechanism. Design equations are developed from this analysis.
Membranes which pump
Authors: Cussler E. L.
Published: June 2004

Carrier‐containing membranes which can pump a specific ion from a region of low concentration into a region of high concentration have been constructed. This pumping is a large effect, proportional to the amount of carrier present. The main requirement for this type of transport is that the carrier react competitively with two simultaneously diffusing solutes. One solute is pumped; the second supplies the energy for the pumping. A theory based on the assumption that the two carrier reactions are fast predicts that the amount pumped is proportional to the carrier concentration, that the pumping stops when the concentration gradient of the energy supplying solute reaches zero, and that the effect goes through a maximum when the solubility in the membrane of the solute being pumped decreases. These predictions are in agreement with experimental results for sodium transport across membranes containing a variety of carriers, including stearic acid, lecithin, and monensin.
Solutions for distillation processes treating petroleum fractions
Authors: Taylor D. L. , Edmister W. C.
Published: June 2004

The general solution for multicomponent distillation processes is used to obtain solutions for systems treating petroleum fractions. The integral technique is the basis for this adaptation. Example solutions are presented for a conventional distillation column, a distillation column with a side stream, and an absorber. The design capabilities of the general solution are illustrated by an absorber problem in which the composition of the lean vapor is specified. The amount of absorber oil, a petroleum fraction, required to accomplish this degree of separation is found.
Convective stability in the presence of a catalytic chemical reaction. Part I. Stationary instability
Authors: Wankat P. C. , Schowalter W. R.
Published: June 2004

A linear analysis of hydrodynamic stability has been applied to a problem in which a fluid mixture is contained between two horizontal planes. One species diffuses to the lower plane where it is destroyed by a rapid exothermic or endothermic catalytic reaction. Results show that important coupling takes place between thermal and concentration fields. This coupling gives rise to unusual stabilizing or destabilizing effects, depending upon the value of Lewis number. Several examples are discussed. It is also shown how the results can be applied to other problems involving heat and mass transfer.
Joule‐Thomson effects for mixtures of helium‐nitrogen‐methane and hydrogen‐nitrogen‐methane
Authors: Sabnis Suman T. , Wenzel Leonard A.
Published: June 2004

Experimental isenthalps and corresponding Joule‐Thomson coefficients are reported for nitrogen and equimolar ternary mixtures of helium‐nitrogen‐methane and hydrogen‐nitrogen‐methane. The estimated precision of the Joule‐Thomson coefficients was within 1.5% of recent literature values.

These Joule‐Thomson coefficients are compared with predictions from the virial equation and Beattie‐Bridgman, Benedict‐Webb‐Rubin, and Redlich‐Kwong equations of state. The predicted Joule‐Thomson coefficients are as accurate as predictions for the pure species. Standard mixing rules and methods of combining equations of state constants are satisfactory at higher temperatures. At low temperatures the predictions from the equations of state are poor.
Hydrodynamic stability of marangoni films:II. A Preliminary analysis of the effect of interphase mass transfer
Authors: Wang K. H. , Ludviksson V. , Lightfoot E. N.
Published: June 2004

The stability of vertical laminar falling films subjected to interphase mass transfer and surface‐tension gradients in the direction of flow is investigated by linear perturbation analysis. The perturbations considered are vertical waves or rivulets as described by Ludviksson and Lightfoot for nonisothermal films. Perturbations of this type are thought to lead to the maldistribution of flow observed in distillation and gas absorption by Zuiderweg and Harmens and by Francis and Berg.

Three unstable regions are predicted, one corresponding closely to that found by Ludviksson and Lightfoot, and two new ones, previously unreported, resulting from interphase mass transfer across the free surface.

These predictions confirm the conclusions of Zuiderweg and Harmens for situations in which surface tension increases upward, and they provide a means of estimating the range of unstable gradients. Experimental evidence for instability predicted when the surface tension increases downward is inconclusive. Further investigation of this region, which is of considerable importance, is recommended.
An experiment on turbulent diffusion in additive solutions
Authors: Wu Jin
Published: June 2004

Turbulent diffusion in high molecular weight additive solutions was measured and compared on a laboratory scale by observing the axisymmetric spreading of a cylindrical turbulent cloud in these solutions of various concentrations. Significant suppression of turbulence in additive solutions was observed. The trend of the results as a function of additive concentrations is similar to that of the additive reduction of turbulent frictional resistance.
Optimally sensitive and adaptive control systems
Authors: Weinrich S. D. , Lapidus Leon
Published: June 2004

The sensitivity of optimally controlled systems to parameter variations is examined in this paper. Two general approaches toward compensating for these variations are employed. The first, for open‐loop systems, involves augmenting the performance index with sensitivity terms and minimizing this combined index. The second approach, an adaptive‐type controller, involves estimating those parameter variations that have caused an observed state deviation, and adjusting the control policy in response to this measurement. Numerical examples applied to continuous, discrete‐time, and discrete‐staged systems demonstrate the effectiveness of these approaches in adapting the control policy to parameter variations.
Entrance region flow of polymer melts
Authors: Han Chang Dae
Published: June 2004

An experimental study has been made to investigate polymer melt flow in the entrance region of a circular tube. For the study, a capillary rheometer was used to measure wall normal stresses in polymer melts in the reservoir and along the axis of the capillary. In order to investigate the influence of reservoir diameter on the entrance pressure drops, reservoir‐to‐capillary diameter (DR/D) ratios of 3, 6, 9, and 12 were used, with the capillary length‐to‐diameter (L/D) ratio being 20 and the capillary diameter being 0.125 in. Analysis of the experimental data shows that the entrance pressure drop increases and then levels off as DR/D ratio is increased. A correlation between the dimensionless entrance pressure drop and Reynolds number has been obtained, which follows the creeping flow analysis by Weissberg over the range of the area contraction ratio studied, 0.00694 <β< 0.111.
Process optimization by the “complex” method
Authors: Adelman Alvin , Stevens William F.
Published: June 2004

The “complex” method of M. J. Box has been adapted and used to optimize the design of continuous chemical processes. Such a design involves the extremization of a nonlinear objective function subject of nonlinear equality and inequality constraints. The method consists of finding an original feasible “complex” of solutions, eliminating the worst of these by reflection through the controid of those remaining, and repeating until an optimum has been reached. An example of significant complexity has been solved and the results are reported. The method looks quite promising for use in the optimization of chemical process designs.
Drag reduction in dilute flowing gas‐solid suspensions
Authors: Rossetti Salvatore J. , Pfeffer Robert
Published: June 2004

The effect of solids loading ratio, particle size, and gas Reynolds number on the pressure drop and flow characteristics of a dilute gas‐solid suspension in turbulent pipe flow has been studied experimentally in both vertical and horizontal test sections. Glass beads of 10 to 60μ diameter were used at air Reynolds numbers of 10,000 to 25,000 and solids loading ratios of up to 2.5 Drag reduction was observed in the vertical test section for all of the particles studied, with the 30μ particles yielding a maximum drag reduction of about 75% at a loading ratio of 1.5. In the horizontal test section, drag reduction was observed only with the smallest sized particles, indicating a gravity effect. An explanation of these results based on the particles interacting with the turbulent structure of the gas near the wall has been proposed.
Surface diffusion of adsorbable gases through porous media
Authors: Roybal L. A. , Sandler S. I.
Published: June 2004

An activated diffusion, or site‐hopping, mechanism is used to describe surface diffusion of gases through porous media. This analysis provides a useful and accurate method for correlating data at submonolayer coverages on energetically heterogeneous surfaces. The data needed to use this correlation are surface area and pore structure of the adsorbent, adsorption isotherms at two or more temperatures, and the activation energy for migration. The former quantities are easily determined from Knudsen diffusion and adsorption measurements, while the activation energy can be found from a single permeability measurement. Predictions made in this way show excellent agreement with experimental data.
A new algorithm for the estimation of parameters in ordinary differential equations
Authors: Hwang M. , Seinfeld J. H.
Published: June 2004

A new computational algorithm for the estimation of parameters in ordinary differential equations from noisy data is presented. The algorithm is computationally faster than quasilinearization because of the reduction of the number of ordinary differential equations that must be solved at each iteration. A modification is also presented to remove ill‐posedness. The algorithm is illustrated on a simple example.
Direct contact heat transfer between immiscible fluid layers in laminar flow
Authors: Mukerjee Dipankar , Davis E. James
Published: June 2004

The problem of heat transfer (and, by analogy, mass transfer) between immiscible fluids in laminar parallel flow is analyzed as a conjugated boundary value problem. Exact solutions are developed in terms of known functions by solving for the temperature fields in the two phases separately for constant boundary conditions, then generalizing the results to obtain solutions for the interfacial temperature distribution and the complete temperature field for the conjugated system. The analysis and the results of calculations for heat transfer between two immiscible films flowing down an adiabatic inclined plane are presented. It is shown that axial conduction can be included, and the effects of axial conduction in one stream are examined. The predicted Nusselt numbers are plotted versus axial position for various parameters, and the interfacial temperatures and mixed mean fluid temperatures for the two phases are plotted to elucidate the heat transfer characteristics.
Hydrodynamic stability of viscoelastic fluids: Importance of fluid model, overstability, and form of disturbance
Authors: McIntire L. V. , Schowalter W. R.
Published: June 2004

A linearized stability analysis has been applied to a fluid flowing in a gravity field between horizontal planes in Couette flow under conditons such that the temperature of the bottom plane exceeds that of the top. It is shown that, under conditions likely to be encountered with polymer solutions, oscillatory instabilities will not be controlling. Criteria are offered for ascertaining when an analysis based upon a second‐order fluid model may be expected to yield physically meaningful results. It is also shown that for the fluid model considered, critical conditions for stability are not changed when disturbances which vary in the flow direction are substituted for those which are a function of the coordinate transverse to the flow.
Drop sizes in an agitated liquid‐liquid system
Authors: Mlynek Youval , Resnick William
Published: June 2004

The relationship between drop size and location in an agitated liquid‐liquid system was investigated, with a new sampling method in which the dispersion was sampled in a specially designed trap and immediately encapsulated by a polymer film. The liquid‐liquid system used was water and a mixture of isooctane and carbon tetrachloride with a density closed to that of the water. Dispersed phase holdup was varied from 0.025 to 0.34 volume fraction.

For this system, which has low mutual sulubility and high interfacial tension, there is almost no dependence of drop size on location for the mixing geometries studied. This was due to the fact that the coalescence rate is low compared to the circulation time. An increase in impeller speed and drop size decreased the coalescence rate while an increase in holdup increased it.

The mean drop diameter was related to the Weber number and holdup by an equation. By comparison of mean drop diameters obtained using different impellers, it was shown that the criterion of equal power per volume can be used for estimating drop size when going from one mixing geometry ot another, not too different, geometry at moderate impeller speeds.
Kinetics of slow thermal chlorination of hydrogen in nickel tubular flow reactors
Authors: Bernstein Leonard S. , Albright Lyle F.
Published: June 2004

The first reliable kinetic data and correlations yet reported were obtained for the thermal reaction of gaseous chlorine and hydrogen over a wide range of operationg conditions. Earlier data had been obtained in reactors that result in irreproducible data. The results of the present investigation clarify the reaction sequence that consists of both gas‐phase and surface reactions.
Some performance characteristics of spray columns
Authors: Vedaiyan S. , Degaleesan T. E. , Laddha G. S. , Hoelscher H. E.
Published: June 2004

Experimental data on the drop size distribution obtained from multiple nozzles in a spray column are presented and analyzed. For nozzles having a diameter above the critical size, the distribution pattern change from near normal monomodal to bimodal and back again to monomodal but skewed toward the larger size fraction. There is no change in the observed maximum drop size in the distribution with flow rate except near the critical velocity region. Drop breakup mechanisms appear to be different from the above pattern for nozzles below a critical size.

A model is proposed for prediction of the complete range of drop sizes observed.
Mass transport and reaction in sulfonic acid resin catalyst: The dehydration of t‐butyl alcohol
Authors: Heath H. W. , , Gates B. C.
Published: June 2004

Kinetics of the dehydration of t‐butyl alcohol to isobutylene were measured with a semibatch reactor containing liquid reactant and suspended particles of cation exchange resin catalyst [sulfonated copolymer of styrene and divinylbenzene (DVB)]. Effects on rate were determined for variations in temperature (58 to 76°C.), reactant water mole fraction (0.0005 to 0.10), and catalyst pacticle diameter (77 to 620 μ) and crosslinking (2 to 12% DVB).

Nearly anhydrous t‐butyl alcohol failed to penetrate the shrunken network of the polymer. Reaction ebgan only on particle peripheries, and product water penetrated the gel network and s welled it to allow penetration of the alcohol. Rate consequently increased to a maximum (about 0.5 moles/min. equivalent of catalyst SO3H groups at 76°C.) and then decreased as water competed with reactant fro catalytic sites. A spherical catalyst particle is modeled as a shrinking cetrol core, free of reactant and water, and a swollen shell in which concent rations are independent of position and time. The model fits reaction rate and separate particle swelling data for 80 μ particles of catalyst containing 12% DVB, but it is increasingly inadequate for larger particles and catalysts of lower DVB contents.
Separations via continuous parametric pumping
Authors: Chen H. T. , Rak J. L. , Stokes J. D. , Hill F. B.
Published: June 2004

A continuous pump in which the feed and product streams flow steadily both in upflow and downflow is experimentally investigated in the model system toluene‐n‐heptane on silica gel adsorbent. The experimental data compare reasonably well with analytical results based on an equilibrium theory. The operating conditions necessary to achieve high separation factors are shown to be dependent on the relative magnitudes of penetration distances and the height of the column.
Identification, hysteresis, and discrimination in enzyme kinetic models
Authors: Tanner Robert D.
Published: June 2004

Three kinetic rate constants and an initial enzyme concentration are estimated in Britton Chance's classical peroxidase model by applying both the Picard iteration‐orthogonal polynomial and stationary state methods to his transient experimental data. Since this model does not describe the hysteresis exhibited by the data, more complex models are examined in order to account for this behavior. From a study of this hysteresis phenomena which is inherent to the structure of consecutive reactions, it is found that in addition to discriminating between mechanisms much useful information about the history of enzyme induction can be observed from the direction, shape, and area of the hysteresis loop.
Secondary nucleation in a class II system: Ammonium sulfate‐water
Authors: Youngquist Gordon R. , Randolph Alan D.
Published: June 2004

Secondary nucleation at low supersaturation for the ammonium sulfate‐water system was studied using a seeded continuous crystallizer. Counter size distribution measurements in the subsieve size range indicated that nuclei are formed by microattrition of seed crystals and that the growth rate of the nuclei is very small. Nucleaion rate was correlated with the characteristics of the secondary environment. The results of this correlation, which shows strong dependence on stirring rate and essentially linear dependence on solids concentration, indicate that secondary nuclei are generated by collisions of the seed crystals with the impeller blades.
Application of modern control theory to distillation columns
Authors: Hu Y. C. , Ramirez W. Fred
Published: June 2004

Modern control theory for systems with load changes is applied to distillation column control. Both linear and nonlinear distillation models are developed and tested. Excellent control is achieved by using an optimal multi‐variable‐proportional‐integral (MPI) controller for systems with unmeasurable disturbances. When the disturbances are measurable an optimal multi‐variable proportional controller with error coordination (MPE) is desirable. Various structures for distillation control have also been investigated.
Multicomponent diffusion and vapor‐liquid equilibria of dilute organic components in aqueous sugar solutions
Authors: Chandrasekaran S. K. , King C. Judson
Published: June 2004

A technique for direct measurement of the differential diffusion coefficients in a ternary system of water, sugar, and a dilute organic species is described. The individual sugars were d‐fructose, d‐glucose, and sucrose; and ethyl alcohol, ethyl acetate, n‐butyl acetate, and n‐hexanal individually constituted the dilute organic species. The four ternary diffusivities were obtained over a range of sugar concentrations by the use of horizontal diaphragm cells, a differential interferometer, a flame‐ionization gas‐liquid chromatograph and postulation of the validity of the Onsager reciprocal relations. The equilibrium partial pressures of the dilute organic species over these solutions have also been measured, using a vapor head space chromatographic technique.
The interrelationship between bubble motion and solids mixing in a gas fluidized bed
Authors: Haines A. K. , King R. P. , Woodburn E. T.
Published: June 2004

The stochastic differential equations for particle motion in a homogeneous fluidized bed have been modified to incorporate a bubble‐particle interaction. In a freely bubbling bed this interaction causes an instantaneous random step upwards when a particle collides with a bubble. In addition the particles are subject to a Brownian Motion due to particle‐particle interactions and to a vertical drift velocity. The particle motion was modeled by the set of stochastic differential equations

where N and W are Poisson and Wiener processes respectively. U is the velocity vector, X the vertical coordinate, Y and Z the horizontal coordinates. This set of equations has been solved and the form of the probability density function p(x, t) has been obtained. Predictions are in terms of the mean bubble frequency at a point λ the average displacement associated with a particle‐bubble collision, and the dense phase diffusion coefficient.

The main result is that the effective diffusion coefficient in the vertical direction is given by

where E is the dense phase diffusion coefficient and 1/α is the average displacement suffered by a particle on collision with bubble.

The model was tested experimentally using random forcing function techniques. All parameters were evaluated independentely; λ by direct measurement and the other two inferred from available published data. The predictions of the theory agreed well with experimental observations of the solids dispersion.
The stress state of elastic fluids in viscometric flow
Authors: Miller M. J. , Christiansen E. B.
Published: June 2004

A new method of instrumentation for normal‐stress determinations was developed, making possible accurate unsteady state as well as steady state measurements, eliminating errors arising from fluid‐filled pressure‐tap holes, and permitting the determination of the complete stress state in a single cone‐and‐plate shearing‐geometry experiment. Sensitive, nonflow semiconductor pressure transducers mounted at several radial positions with their pressuresensing diaphragms flush with the plate surface provide data for the normal‐stress distribution. The normal‐stress distribution, together with the total normal force from the single‐geometry experiment, enables determination of the primary and secondary normal‐stress differences by two independent methods of analysis while the transmitted torque enables determination of the viscosity, each as a function of shear rate. Only the normal‐stress distribution is required if an independent check on the normal‐stress determination is not desired. Similar advantages arise in the application of the instrumentation to a parallel‐plate shearing geometry, The new instrumentation was used in the determination of the complete rheological stress state of three aqueous and two “Tetralin” solutions of polymers in a cone‐and‐plate shearing geometry shear rates of 0.02 to 450 s−1 on a Model R‐17 Weissenberg Rheogoniometer. The normalstress differences computed by means of two methods of analysis are in surprisingly good agreement. The ratio of the secondary to the primary normal‐stress difference was negative. The absolute values of this ratio decreased with increases in the shear rate, the maximum observed value being 0.4.
Finite element analysis of slow non‐newtonian channel flow
Authors: Palit Kalipada , Fenner Roger T.
Published: June 2004

A finite element method is applied to isothermal slow channel flow of power‐law fluids. The fully developed flow is normal to the channel cross section. The method and results are compared with a finite difference method for rectangular channels and with exact solutions for the Newtonian case. An advantage of finite element methods is the flexibility of the mesh of elements approximating the continuum, chosen to suit the particular problem. Arbitrary boundary shapes can be handled as illustrated by a rectangular channel with rounded corners.
Prediction of drop volumes in liquid–liquid systems
Authors: Izard John A.
Published: June 2004

A method is described for calculating drop sizes obtained in Newtonian immiscible liquid‐liquid systems when a dispersed fluid is continuously injected at uniform subjectting point velocities through a sharp‐edged nozzle that is preferentially wet by the continuous phase. This method is based on the calculation of the shape of a drop forming at the nozzle tip by means of a pressure balance over the drop interface and the use of a force balance to determine if any portion of the forming drop can break away. Calculated drop sizes are compared with experimental data for systems of different physical properties.
The florite‐water vapor sorption therm
Authors: Jury Stanley H. , Edwards Harold R.
Published: June 2004

The sorption isotherms for moist air and Florite were determined at a total pressure of one atmosphere and 75°, 100°, 125°, 150°, 175°, and 200°F. No hysteresis was evident.

An investigation of the sorption isotherms showed that a concentration‐temperature coordinate could be identified, which when plotted against amount sorbed, causes all sorption isotherms to collapse into a single sorption therm.

For purposes of sorption curve fitting the concentration‐temperature coordinate was incorporated into a version of BET theory. This relation produced an excellent fit of data without resorting to more complicated versions of BET theory.

The concentration‐temperature coordinate was also incorporated into a modified version of Langmuir‐Hey theory to show that this interpretation also leads to a very satisfactory fit of sorption data.

Some additional observations are made concerning the computerized curve fitting technique as applied to silica gel, the data for which were reported in an earlier publication.
Minimum realizations and system modeling. I. Fundamental theory and algorithms
Authors: Rossen R. H. , Lapidus L.
Published: June 2004

This review article surveys representative literature on minimum realizations and system modeling. This theory makes possible the construction of minimum size state‐space models directly from experimental input/output data. Theoretical developments, numerical algorithms, and the connection with other methods of identification of linear systems are covered. Partial minimum relaizations which are extensions of the concepts developed are also included. A numerical example illustrates many of the techniques.
Liquid counterdiffusion of selected aromatic and naphthenic hydrocarbons in type Y zeolites
Authors: Satterfield Charles N. , Cheng Chon S.
Published: June 2004

Rates of Counterdiffusion are markeldy affected not only by the critical molecular diameter of the diffusing molecules but also by other physicochemical properties of the liquids and the nature of the cation in the zeolite. The effective diffusivity in NaY or HY under counterdiffusion conditions is less by a factor of 10−1 to 10−3 than that for unidirectional diffusion into an initially empty pore structure.
HI‐H2 vapor etch for low temperature silicon epitaxial manufacturing
Authors: Dyer Lawrence D.
Published: June 2004

Etching of semiconductor silicon slices at 998°C with HI‐H2 mixtures was developed to the level that practical etch rates (≥ 0.1 μm/min) and smoothness of surfaces were obtained in a manufacturing type reactor without the addition of HF or He. Such a low temperature etch is expected to lead to improved device characteristics, mainly because of more sharply defined junction surfaces.

Using deposition at 998°C on very clean slices as a testing method, two sources of impurities that cause stacking faults in the deposition layers were identified and eliminated. These were the polypropylene vessel used in the slice cleanup procedure, and the hydrogen peroxide used in conjunction with sulfuric acid in the primary cleaning step.
Controller design for distributed systems via bass' technique
Authors: Baker Thomas E. , Brosilow Coleman B.
Published: June 2004

Bass' feedback controller design technique is extended to distributed parameter systems and its use is illustrated for a parabolic system with boundary control.

The development of the design technique rests on a conjecture concerning the necessary and sufficient conditions for the asymptotic stability of linear time invariant partial differential equations. It is shown through a study of the discretized analog of a distributed system that the most likely candidate for a Lyapunov functional general enough to yield the necessary and sufficient conditions for asymptotic stability is a double integral with a symmetric kernel.
Nearly optimal control of a pilot plant distillation column
Authors: Merluzzi P. , Brosilow C. B.
Published: June 2004

A nearly optimal on‐off control strategy, previously applied to a rectification column, has been successfully implemented on a full distillation column. The controller employs a linear combination of temperature measurements to adjust the reflux flow rate in order to maintain a desired overhead product composition. A simple relationship between the control coefficients is shown to be characteristic of countercurrent systems. This relationship allows the controller to be tuned on‐line by the adjustment of a single parameter, thereby eliminating the need for a dynamic model of the process and for lengthy design calculations.

The performance of the tuned on‐off controller is compared with that of a tuned proportional plus integral controller and a single measuremnt on‐off controller for feed flow disturbances and set point changes. Results show that the multi‐measurement on‐off control system is superior for both types of disturbances.
Kinetics and mechanism of the epoxidation of unsaturated fatty acids
Authors: Abraham M. E. , Benenati R. F.
Published: June 2004

A study was made of the epoxidation of octadecenoic acids with peroxybenzoic acid in benzene. Activation energies, frequency factors, enthalpies of activation, entropies of activation, and free energies of activation were obtained for the following fatty acids: cis‐9‐octadecenoic acid (oleic), trans‐9‐octadecenoic acid (elaidic), 12‐hydroxy‐cis‐9‐octadecenoic acid (ricinoleic), 12‐hydroxy‐trans‐9‐octadecenoic acid (ricinelaidic), cis‐11‐octadecenoic acid (vaccenic), and cis‐6‐octadecenoic acid (petroselinic). It was observed that the reaction rate was adversely affected by the proximity of the carboxyl group, that is, the closer the carboxyl to the reaction site the lower the rate. A shift from a trans to a cis configuration results in an approximate 50% increase in reaction rate with a corresponding decrease in free energy of activation of 260 cal/mol. The effects of isomerism and the replacement of substituent groups on the reaction rate were generally additive. A mechanism for the peroxydation of octadecenoic acids is proposed.
Investigation of the thermodynamic behavior of the system, acetone‐carbontetrachloride, by the equilibrium sedimentation technique
Authors: Sethy Anil , Cullinan Harry T.
Published: June 2004

The equilibrium sedimentation technique for the direct determination of the chemical potential composition derivatives of a liquid mixture is applied to the binary system acetone‐carbontetrachloride. Equilibrium concentration profiles obtained in an ultracentrifuge are used with the Wilson equation to quantitatively determine the composition variation of the activity coefficients over the entire range of composition. Results agree well with previous data and indicate the technique to be accurate and reliable.
Equilibrium, thermodynamic, and transport properties of polyatomic gases from molecular structure
Authors: Galloway T. R.
Published: June 2004

The possibility of predicting physical properties for polyatomic gases entirely from molecular structure has been explored. Intramolecular force constants for the bonds can be drawn from spectroscopically established tables and applied successfully to molecules involving a large variety of structures. A vibrational analysis of the molecule using these constants yields the thermodynamic functions of the ideal gas. The intermolecular pair potential parameters for the spherical core model of Kihara can be obtained quantitatively from molecular constants, and this potential can be used in obtaining the dilute gas transport properties. A linear relationship was found between the Kihara sphereical core size and Pitzer's acentric factor. Also from the Kihara model the critical constants are derived, which allows one to use Pitzer's compressibility tables for the dense gas corrections to the ideal gas law and the excess functions of the thermodynamic quantities. A complete package of computer programs which predict all important physical properties directly from input name alone has been written and tested. Suggestions are given for future work needed to improve many of the techniques presented.
Minimum realizations and system modeling: II. Theoretical and numerical extensions
Authors: Rossen R. H. , Lapidus L.
Published: June 2004

The ideas and techniques discussed in Part I of this Review

Part I of this paper was published in the July, 1972, AIChE Journal.

are extended to the modeling of nonlinear lumped and distributed systems. Troublesome numerical and computational difficulties are examined, and recommendations for the alleviation of these difficulties are made. Particular emphasis is placed on the stability of system models constructed with the Tether method. Highly successful modeling of realistic systems are presented numerically.
Losses of mercury from chlorine plants: A review of a pollution problem
Authors: Caban Reinaldo , Chapman Thomas W.
Published: June 2004

The problem of mercury losses from chlorine plants is reviewed. The mercury material balance is difficult to establish because mercury escapes from the process by a number of routes. Some of the reasons for the mercury emissions are explored, and some problems involved in the measurement of mercury in various effluents are discussed.

A number of mercury containment processes for specific streams have already been proposed, but the need for an integrated mercury recycle policy still exists.
The mixing of solid particles in a motionless mixer—a stochastic approach
Authors: Chen S. J. , Fan L. T. , Watson C. A.
Published: June 2004

A Markov chain model was used to model the axial mixing of solid particles in a motionless mixer having no moving parts. One step transition probabilities were determined experimentally for the model. Based on these transition probabilities, the model was able to predict spatial distribution of tracer particles up to seven steps of the Markov chain, which was equivalent to seven consecutive passes of the mixture through the mixer. Experimental results were in good agreement with those predicted from the Markov chain model.
Dissociation of oxygen in a radiofrequency electrical discharge
Authors: Bell Alexis T. , Kwong Kam
Published: June 2004

An experimental investigation was made of oxygen dissociation in a radiofrequency discharge. The conversion and yield were examined as a function of power, pressure, and gas flow rate. These measurements were supplemented by measurements taken with catalytic and noncatalytic thermocouple probes in order to determine the local gas temperature and atomic oxygen concentration. An interpretation of the results is given in terms ofa theoretical model of the reactor.
Measured enthalpy changes for a simulated natural gas mixture and their prediction using a modified BWR equation
Authors: Sood Sotander K. , Haselden Geoffrey G.
Published: June 2004

A new method of incorporating binary interaction data into the BWR equation is proposed. It is developed to predict phase equilibria and enthalpies for multicomponent mixtures using interaction data for 18 binaries.

A calorimeter is described, together with experiments made upon it, for a 6‐component simulated North Sea Gas mixture at three pressure levels from 18 to 36 bar, and over a temperature range from 373 to 188K. The experimental enthalpy results are claimed to have an accuracy of ± 0.9%. These results are compared with the predictions of the modified BWR equation. The average deviation is 1.1%, the values being negative at about 18 bar and generally positive for the higher pressures tested.
Interpretation of overall area tests for thermodynamic consistency: The effect of random error
Authors: Samuels Michael R. , Ulrichson Dean L. , Stevenson F. Dee
Published: June 2004

Methods are developed and illustrated for determining the amount of nonsatisfaction of the overall area (integrated Gibbs‐Duhem equation) test for vapor‐liquid equilibrium data that is to be expected on the basis of random experimental uncertainties. Data which satisfy the overall test within these limits, as well as the local area test, are said to be consistent within the bounds established by their experimental uncertainties, while data which do not are said to show significant systematic error and hence are termed inconsistent.
Gas separation through expansible tubing
Authors: Blaisdell Charles T. , Kammermeyer Karl
Published: June 2004

The basic difficulty in membrane separations has always been their inherent slowness, resulting in high area requirements. Thus fine‐bore tubing becomes of considerable interest. Studies showed that some materials will expand appreciably and reversibly and gas flow rates which are multiples of those in the unexpanded condition can be obtained.