Summary of papers published in this month’s research quarterly, 1@EC Fundamentals
PLASTIC FLOW BEHAVIOR OF FLOCCULATED KAOLIN SUSPENSIONS
Data on shear stress us. shear rate were obtained for aqueous, flocculated kaolin suspensions, using concentric cylinder viscometers. Equations which predict the effects of kaolin concentration, shear rate, and chemical content of the ambient fluid were derived, based on a structural model which assumes that in a flocculated suspension, the basic flow units are small clusters of particles (plus enclosed water) called flocs. At low shear rates, the flocs group into clusters, or aggregates, which may form networks extending to the walls of the container and giving the suspension a finite yield stress. At high shear rates, the aggregates are broken down into individual flocs, and the model predicts a straight-line relationship between shear stress and shear rate.
A . S. Michaels and J. C. Bolger, Massachusetts Instifute of Technology, Cambridge, Mass.
BOUNDARY LAYER MASS TRANSPORT WITH HETEROGENEOUS CATALYSIS
A theoretical study was made of gas diffusion rates in particle beds with heterogeneous catalysis. The free surface model (spherical particle surrounded by a spherical envelope) is used with boundary layer theory. In considering the density variation in the boundary layer it is generally necessary to solve two integral equations. By neglecting second-order effects, the integral equations are solved to predict dissolution rates in a particle bed for a chemically dilute solution for void volumes of 0.3 to 1.0. These integral equations are also used to analyze the effects of a molar velocity perpendicular to the surface of the particle. The effect of this normal velocity is essentially the same for spherical surfaces as for flat plates, and good agreement is obtained with simple film theory.
C. Lembit Kusik and John Hajjel, New York Uniuersity, University Heeghts, New York, N . Y.
PROPELLER PUMPING A N D SOLIDS FLUIDIZATION IN STIRRED TANKS
Data characterizing propeller pumping, fluid entrainment, and solids fluidization in stirred tanks are presented. It is shown that propeller pumping is given by the product ND13, independent of Reynolds number and tank geometry in the turbulent range of operation, but that entrainment flow is a function of tank geometry. Particle fluidization is correlated in terms of the settling velocity for a single particle and the total circulation rate of the tank fluid. Joseph V. Porcelli, Jr., and Georgs R. Marr, Jr., Columbia Uniuerrity, h’ew York, N . Y.
THEORETICAL A N D EXPERIMENTAL STUDY OF FULLY DEVELOPED FLOW IN SCREW EXTRUDERS
Differential equations are presented for the thermally and hydrodynamically fully developed flow of gn incompressible fluid in a metering screw. A method of numerical integration and some
results therefrom are described for a “power law” fluid. The numerical results are shown to agree with experimental data obtained for comparison.
R. M . Gri2th, American Cyanamid Co., Stamford, Conn.
THERMAL CONDUCTIVITY OF HETEROGENEOUS TWO-COMPONENT SYSTEMS
The influence of included particle shape, composition, and pure component conductivity upon the thermal conductivity of heterogeneous two-component mixtures consisting of a continuous and a discontinuous phase was studied. Thermal conductivities were measured for mixtures of balsa wood and aluminum particles as several shapes in rubber at selected compositions. Thermal conductivities for widely different heterogeneous two-component systems can be calculated accurately using an equation in which the empirical shape factor n depends on thermal conductivities of the phases and the included particle shape. The influence of particle shape on n can be accounted for using the sphericity of the particle.
R. L . Hamilton, Celanese Cor#. of America, Summit, N . J., 0. K. Crosser, University of Oklahoma, hlorman, Okla.
MULTICOMPONENT VISCOSITIES OF GASEOUS MIXTURES AT HIGH TEMPERATURES
Binary diffusion and pure viscosity data are used to compute binary viscosities according to an expression derived from rigorous kinetic theory for monatomic gases. The rigorous expression is based on the assumption of central forces. An approximate but simpler formula proposed earlier by Wilke is also considered. A scheme is proposed for computing multicomponent viscosities from the known pure and related binary mixture viscosities at two compositions, and is tested for several ternary mixtures. This procedure permits calculation of the multicomponent viscosities for mixtures permuting out of the nine binary systems considered here with much less computation than for the rigorous method. The constants required for such a calculation are tabulated. S. C. Saxena and T. K. S. Naravanan, Atomic Energy Establishment
Trombay, Bombay, India
RATE EQUATIONS FOR CONSECUTIVE HETEROGENEOUS PROCESSES
A genzral discussion of the forms of rate equations for consecutive, heterogcneous processes is given. The complexity of the derivation of these rate equations depends on whether or not the process has parallel steps combined with the consecutive ones. The procedures that can be used for cases with only consecutive steps are outlined. The particular case of a heterogeneous catalytic reaction with more than one rate-controlling step is covered in detail. It may be extremely difficult to determine if more than one step is controlling. However, kinetic constants derived from experimental data on the basis of only one step controlling may be greatly in error.
K. B. Bischoff and G. F. Froment, Rijksuniversiteit te Gent, Gent, Belgium VOL 54
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BRIEFS THE STABILITY OF ADIABATIC PACKED BED REACTORS A N ELEMENTARY TREATMENT
COMMUNICATION.
The problem of stability of a packed bed adiabatic catalytic reactor is considered for a simple model in which mass and heat transfer resistances are lumped at the particle surface and the only intraparticle effect is that of chemical reaction. As has been shown, such a catalytic particle may exist in more than one state. A fixed bed reactor may contain particles whose states are determined by their past histories. The transient equations for the reactor are written and solved by the method of characteristics. The solutions show that under certain conditions, amenable to a priori prediction, there will be nonunique temperature and concentration profiles. In fact, there may be an infinite set of profiles, depending upon the initial state of the reactor. Calculations are made for a series of initial temperatures.
Shean-lin Liu and Neal R. Amundson, University of Minnesota, Minneapolis 74, Minn.
TOTAL PRESSURE METHOD OF KINETIC ANALYSIS
A general method of expressing the partial pressure of the selected reactant in terms of the total pressure, p i , or total pressure difference, A p t , is presented. It is based on the stoichiometry of reaction, initial pressures, and measurements of the total pressure with time. Its application, however, is limited to the kinetic analysis of simple gas phase reactions at constant T and V when the number of moles of reactants is different than that of products.
Leon S. Kowalczyk, University of Detroit, Detroit, Mich.
CORRESPONDENCE
Comments on an article by George T. Tsao, “Thermal Conductivity of Two-Phase Materials” [IND.ENG.CHEM. 53, 395 (1961)], and a reply by the author.
Jo.ce#h E. Warren and Joseph H . Messmer, Gulf Research C8 Development Co., Pittsburgh, Pa. George Tsu-Ning Tsao, 4261/2North Cyfiress Sf.,Florence, Ala.
THE SIMULTANEOUS ABSORPTION OF CARBON DIOXIDE A N D A M M O N I A I N WATER
The process of gas absorption accompanied by chemical reaction has been studied using the system COS-NH,-water. The two gases were mixed and contacted with a smooth laminar jet of water; after dissolution they reacted with each other by a bimolecular reaction. Rates of absorption were determined by chemical analysis of the liquid leaving the jet absorption device. The rate of absorption of COZ, significantly influenced by reaction with an excess of NH3 in the liquid, agreed with the prediction based on the penetration theory for absorption of two gases followed by secondorder, irreversible reaction. The high solubility of NH, in water, resulting in a large gas-side resistance to its absorption, made it impossible to determine the effect of the rate of reaction on its rate of absorption; this was because of the difficulty in knowing the NH, concentration at the gas-liquid interface. The confirmation of the diffusion-reaction theory was therefore limited to the observations on COz absorption, its validity depending on the accuracy of the NH, gas-phase resistance measurements.
T. F. Hatch, Jr., and R. L. Pigford, University of Delaware, Newark, Del.
CANONICAL FORMS FOR NONLINEAR KINETIC DIFFERENTIAL EQUATIONS
The evaluation of relative rate constants is difficult for complex chemical reactions because of the nonlinearity of the describing system of differential equations. A useful “matrix” method is described for the development of a canonical form for the kinetic differential equations. Three examples are drawn from the literature. The advantages of the procedure are simplification of the system of equations; automatic determination and elimination of redundancies; applicability to relative rate constant determination; and reduction of computation complexity.
W. F. Ames, University of Delaware, Newark, Del.
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COMMUNICATION. GENERAL RELATIONSHIP FOR EFFECT OF ENTRAINMENT O N DISTILLATION COLUMN PLATE EFFICIENCY
Many users of Colburn’s equation for correcting distillation column plate efficiencies for the cffect of entrainment are unaware that it is strictly valid only when the enrichment per plate is essentially constant. .4 general expression for E, is presented here, which removes this restriction.
CORRESPONDENCE
Comments on an article by J. 0. Hirschfelder, R. J. Buehler,
H. A. McGee, Jr., and J. R. Sutton, “Generalized Thermodynamic Excess Functions for Gases and Liquids” [IND.ENG.CHEM.50, 368 (1958)l. J . 0. Hirschfelder, Theoretical Chemistry Laboratory, University of
Wisconsin, Madison, Wis.
I& EC’S ANNUAL REVIEW SUPPLEMENT AVAILABLE OCTOBER 1ST FOR $3.50 A special service to I&EC’s reader makes available the complete package of Unit Operations and Materials of Construction reviews published from January through September PLUS nine Unit Processes reviews and five Chemical Engineering Fundamentals reviews, which are not available in any other form. Unit Operations reviews include: Size Reduction; Materials Handling; Crystallization; Liquid Ion Exchange; and Mixing. Extraction; Distillation; Titanium; Materials o f Construction reviews include: Lead; Protective Coatings; Stainless Steels; Elastomers; Fibers; Plastics; and Less Common Metals. Unit Processes reviews will cover: Halogenation; Nuclear Technology; Polymerization; Oxidation-Liquid Phase; Hydrogenation and Dehydrogenation; Pyrolysis of Coal and Shale; Alkylation; Sulfonation and Sulfation; and Fermentation. Chemical Engineering Fundamentals cover Fluid Mechanics; Process Control, Computers, and Automation; Mathematics, Statistics, and Operations Research; Thermodynamics; and Heat Transfer. And, complete bibliographies will be made available through the American Documentation Institute (ADI) for; Alkylation; Process Control, Computers, and Automation; and Thermodynamics. Only a limited number of copies of this special supplement will be mode available. Plan now to order yours from: Reprint Department ACS Applied Publications I 7 55 7 6th 2t. N.W. Washingfon 6, D. C.
C. E. Danly, The G‘hemsfrandCor#., Prnsacola, Fla. VOL. 5 4
NO. 8
AUGUST 1962
81
