Summary of papers published in this month's research quarterly, I@EC Fundamentals
ESTIMATION OF THE HEAT CAPACITY OF LIQUIDS
THE SECOND LAW ACCORDING TO KELVIN
T h e heat capacity of liquids composed of small molecules as well as of polymer melts has been divided into computable components. T h e contribution of internal degrees of freedom, Ci, was taken as identical with that of the ideal gas. For all monomeric molecules, a translational contribution Ct,X, is assumed nearly equal to that of liquid argon at the same reduced temperature. The contribution of hindered external rotation of the molecule, Ch,x, is calculated in an a przorz fashion for small molecules ( N s < 5), but for large rigid molecules is amplified by an empirical correction for cooperative motion which is proportional to ( E o / R T ) 2 . I n liquids composed of flexible molecules and polymers, the different external degrees of freedom cannot be separated, and C,X is represented as a function of E o / R T . Where strongly polar molecules are involved, the barrier to external rotation is expressed as a function of the orientation energy, r2/dW3.
A recent axiomatic analysis by Arens has put the classical approach to the foundations of thermodynamics, via the second law formulations of Kelvin and Planck, on as sound a mathematical footing as the approach of Caratheodory based on adiabatic inaccessibility. The present paper gives an engineering exposition of the central portion of Arens's work, with particular attention to the question, often overlooked, of the existence of adiabatic surfaces in complex systems.
A . Bondi, Shell Develofiment Go., Emeryville, Calif. IND.ENG.CHEM.FUNDAMENTALS 5 , 442-449 (1966)
THERMODYNAMICS OF TERNARY, LIQUID-SUPERCRITICAL GAS SYSTEMS WITH APPLICATIONS FOR HIGH-PRESSURE VAPOR EXTRACTION
The phase behavior of a ternary system consisting of two liquids and a supercritical gas is predicted by thermodynamic considerations employing only binary data. T h e thermodynamic properties of the liquid phases are described by two-suffix Margules equations with activity coefficients normalized by the unsymmetric convention. T h e vapor phase is treated as a nonideal gas consisting only of the supercritical component. An iterative numerical technique is used to solve the resulting equations of phase equilibria. This approach yields good qualitative results for a variety of ternary phase diagrams, some of which appear to have applicability for extractive separation processes wherein a supercritical gas is the selective solvent. Finally, criteria are developed for choosing a suitable supercritical gas for efficient separation.
J . R. Balder and J . M . Prausnitt, University of California, Berkeley, Calif. IND.ENG.CHEM.FUNDAMENTALS 5 , 449-455 11966)
FUGACITY COEFFICIENTS IN GAS MIXTURES CONTAINING LIGHT HYDROCARBONS AND CARBON DIOXIDE
Mixtures of carbon dioxide with light hydrocarbons, such as ethane and ethylene, exhibit unusual P-V-T behavior which can be attributed to interaction effects between the carbon dioxide and hydrocarbon molecules. Conventional methods for calculating fugacity coefficients do not yield satisfactory results when applied to these gas mixtures. After reviewing methods for taking interaction effects into account, a method was developed for introducing interaction coefficients into the constants of the Redlich-Kwong equation. T h e interaction coefficients of this equation may be derived from those of the virial equation. Fugacity coefficient values derived from the Redlich-Kwong equation with modified mixture parameters are at least as reliable as those obtained by the method of Pitzer and Hultgren and are valid over a much wider pressure range than values obtained from the virial equation. The procedure, based on the Redlich-Kwong equation, is more convenient for computer applications than the method of Pitzer and Hultgren. The proposed method has been applied to the calculation of vapor-liquid equilibria in a carbon dioxide-hydrocarbon system.
Joseph Joffe and David Zudkevitch, Esso Research and Engineering Co., Florham Park, N .J . IND.ENG.CHEM.FUNDAMENTALS 5,455-462 (1966)
Stanley K a t z , Czty University of N e w York, N e w York, N . Y . IND.ENG.CHEM.FUNDAMENTALS 5 , 462-465 (1966) PREDICTION OF DISSOCIATION PRESSURES OF MIXED GAS HYDRATES FROM DATA FOR HYDRATES OF PURE GASES WITH WATER
The dissociation pressures of ternary gas hydrates predicted using only data for binary hydrates are compared with experimental values. The methane-propane-hydrate crystallizes in structure I1 for the pressure range studied here, while the methane and propane hydrates crystallize in structures I and 11, respectively. Predicted results are in close agreement with experimental data. The methane-ethane hydrates both crystallize in structure I. The predicted hydrate pressures are higher than the observed data for the methane-rich concentration regions.
Isamu Nagata and R i k i Kobayashi, W i l l i a m M a r s h Rice University, Houston, Tex.
IND.END.CHEM.FUNDAMENTALS 5 , 466-469 (1966) AQUEOUS OXIDATION OF ELEMENTAL SULFUR
+
The reaction S f 11/2 0 2 HzO -+ HzS04 is greatly dependent on temperature and oxygen partial pressure. Below the melting point of sulfur it is extremely slow, and above this temperature the rate is appreciable and increases rapidly with temperature. The reaction is chemically controlled, and the activation energy is 11.75 kcal. per mole. The rate is proportional to p 0 2 / ~ ,thus l l / g 0 2 -+ SO3 and suggesting that it takes place in two steps: S SO3 HzO -+ HzSOa, the first being the rate-determining step. Sulfur dioxide is not an intermediate reaction product. The rate is affected by the presence of some foreign ions.
+
+
Fathi Habashi and E. L. Bauer, Montana College of Mineral Science and Technology, Butte, M o n t .
IND.ENG.CHEM.FUNDAMENTALS 5 , 469-471 (1966) SYNTHESIS OF NITROGEN FLUORIDES IN A PLASMA JET
A nitrogen plasma jet was intermixed with gaseous fluorides (CF4 or SFB)and subsequently quenched. Small yields of NF3, NzF4, and CFaNFr were produced, together with trace quantities of other products. A reaction sequence involving the formation of the labile intermediate, FCN, and its subsequent stepwise fluorination by addition at the triple bond, accounts for the observed products. The yield of fixed-nitrogen products is about 1 yo of inlet nitrogen for typical conditions. Yield increases with increased power input and increased F/N ratio in the plasma, in qualitative agreement with thermochemical calculations of the equilibrium composition of the high-temperature plasma.
B. R. Bronfin and R. N. Hazlett, U. S. Naval Research Laboratory, Washington, D. C. IND.ENG.CHEM.FUNDAMENTALS 5 , 472-478 (1966)
(Continued on page 778) VOL. 5 8
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1966
117
BRIEFS
RATIONALE FOR OPTIMAL REACTOR DESIGN
Using a general homogeneous reaction rate law as an example, the effect on the rate of deviating from the optimal temperature is calculated. Large errors in the estimates of the kinetic constants can sometimes give a maximum reaction rate within a few per cent of the true value. Graphs enable the designer to decide on the accuracy with which the constants must b e determined and the quality of temperature control that the reactor needs.
W. H. Ray and Rutherford Aris, Uniaersity of Minnesota, Minneapolis, Minn. IND.ENG.CHEM.FUNDAMENTALS 5, 478-483 (1966)
of closely sized uniform spheres or of binary mixtures of these. Sphere diameters ranged from 125 to 305 microns. Superficial air velocities ranged up to 10 cm. per second. A general viscosity correlation for uniform beds of this particle density has been obtained. The measurements tend to indicate Newtonian behavior, in which case the observations would be of a true kinematic viscosity. Evidence that fluidized beds can assume certain crystal-like structures has been found.
Thomas Hagyard and Albert M . Sacerdote, University o j Canterbury, Christchurch, .$Tew Zealand IND.END.CHEM.FUNDAMENTALS 5, 500-508 (1966)
NECESSARY AND SUFFICIENT CONDITIONS FOR INEQUALITY CONSTRAINED EXTREME VALUES
EFFECT OF INTERPARTICLE ADHESIVE FORCES O N FLUIDIZATION OF FINE PARTICLES
The second Kuhn-Tucker theorem furnishes sufficient conditions for a global extreme value of a function subject to inequality constraints. This theorem is useful particularly for convex functions and constraints. Sacrificing the global properties, a new theorem is proved which does not require the convexity property. It is sufficient that the Hessian matrix of the Lagrangian be definite on the hyperplane tangent to the constraints having nonzero Lagrange multipliers at the extreme value. Existing quadratically convergent unconstrained search routines are modified by the introduction of Lagrange multipliers for the inequality constraints. An example is solved in detail using the hTewton-Raphson method suitably modified to handle the inequalities and to ensure convergence. This example illustrates the usefulness of the sufficient conditions derived in this paper.
The feasibility of gaseous fluidization of particles in the size range of less than 50 microns was investigatcd. The ratio of the incipient fluidization velocity, calculated by a conventional relationship without accounting for interparticle forces, and the incipient fluidization velocity, determined by pressure drop and heat transfer measurements, was used as an index, FI, describing the fluidizability of a particulate material. The results indicate that FI is closely related to the interparticle adhesive force. T h e limitations of the feasibility of fluidization depend on the ratio of the weight of a particle to the sum of its weight and adhesive force; no fluidization could be obtained when this ratio was less than
Manfred Baerns, Argonne National Laboratory, Argonne, Ill. IND.ENG.CHEXFUNDAMENTALS 5 , 508-516 (1966)
R. P. King, University of Witwatersrand, .Johannesburg, South Africa IND. ENG.CHEM. FUNDAMENTALS 5 , 484-489 (1966) MERCURY PENETRATION INTO AGGREGATES OF SPHERES ADSORPTION OF BINARY HYDROCARBON GAS MIXTURES ON ACTIVATED CARBON
The Polanyi adsorption potential theory is extended to predict the adsorption of binary gas mixtures on activated carbon. The calculation method assumes that the adsorbate behaves as an ideal liquid mixture and that the total adsorbate volume determines the adsorption potential of each pure component and hence its adsorption pressure as a pure gas. The method in principle applies to a wide variety of binary mixtures and can be extended to multicomponent systems. It is here successfully applied to new data on mixtures of methane with propane, butane, and hexane at 25' C . and total pressures u p to 1000 p.s.i.g., as well as to literature data at atmospheric pressure.
At high pressures, mercury is excluded from the points of contact in an aggregate of spheres and also from the region between spheres which are nearly in contact. At any given pressure there is a maximum separation above which mercury will completely fill the space between the spheres. T o take into account the distribution of near neighbors as well as those which are in contact, the total excluded volume (divided by the volume of the spheres) is calculated as half the excluded volume between a pair of spheres (divided by the volume of a sphere) times the number of neighboring spheres summed over all possible separations. Results are in moderately good agreement with experiment.
Raymond P . Iczkowski, Allis-Chalmers, Mtlwaukee, W i s . IND.
ENG.CHEX FUNDAMENTALS 5 , 516-519 (1966)
R. J . Grant and M i l t o n Manes, Mellon Institute, Pittsburgh, Pa. IND.ENG.CHEX FUNDAMENTALS 5, 490-498 (1966) EFFECT OF D.C. ELECTRIC FIELDS ON LIQUID-LIQUID SETTLING DIFFUSION APPROXIMATION TO COUNTERCURRENT DISTRIBUTION THEORY
Expressions have been derived for the distribution of solute in a separating train of cells. These expressions are sufficient for the calculation of any required properties of a countercurrent process.
N. E. Day, University of Aberdeen, Aberdeen, Scotland IND. ENG.CHEM. FUNDAMENTALS 5,499-500 (1966)
VISCOSITY OF SUSPENSIONS OF GAS-FLUIDIZED SPHERES
The apparent viscosity of air-fluidized beds of spherical particles has been measured with a torsion pendulum viscometer especially designed to minimize disturbance of the bed. Beds were made 118
INDUSTRIAL AND ENGINEERING
CHEMISTRY
The results of an experimental study on the effectiveness of electric fields in separating water in oil dispersions are reported. The dispersions are made by flowing the liquids through mixing tubes and the average drop diameter is correlated with the mixing velocity using transmitted light measurements. The variables studied are the degree of mixing-Le., drop size-dispersed phase volume fraction, residence time in the settler, depth of the oil layer, and strength of the imposed electric field. Electric fields are effective in reducing the water carryover by a factor of 3 to 200, depending on the mixing conditions and residence time. T h e contamination is correlated as a function of two variables, ( da2Apg0/ 18pH) and (eeaEZ/ApgdA). The behavior of the drops in the electric field is described.
Glen L. Sjoblom and Simon L. Goren, University of C a l ~ o r n i a ,Berkeley, CalSf. IND. END.CHEhl. FUNDAMENTALS 5 , 519-525 (1966)
BRIEFS
.\\-
EFFECT OF IONIC MIGRATION O N LIMITING CURRENTS
The effect of migration on limiting currents is calculated for four hydrodynamic situations : the rotating disk, the growing mercury drop, the semi-infinite stagnant fluid, and the Nernst diffusion layer, and for several electrolytic systems. John Newman, Uniuersity of California, Berkeley, Calif.
NO VALVES
IND.ENG.CHEM.FIJNDAMENIALS 5,525-529 (1966)
NO CONTAMINATION
NO CORROSION
NO CLEANING
I n Sigmamotor AL Pumps a loop of plastic tubing i s placed i n back of plate ”X”. A rotating eccentric shaft tilts this plate i n a nutating manner compressing the tubing and forcing liquid or slurry around the loop. Speed of DC Motor is varied by a solid state converter operating o n regular 115 Volt AC. Flow rate can be recorded and repeated exactly. Set-up and calibration i s quick and easy.
DIFFUSION OF GASES ACROSS POROUS MEDIA
Basic laws of gaseous diffusion in porous media are derived directly from a n extension of the “friction model,” without recourse to detailed kinetic theory.
K. S. Spiegler, University of California, Berkeley, Calif. IND. END. CHEM.FUNDAMENTALS 5, 529-532 (1966)
Column Chromotograph 0 Feeding-Sampling e Drug Infusion
BREAKAGE AND COALESCENCE IN DISPERSED PHASE SYSTEMS
A mathematical model is developed to relate the breakage and coalescence of droplets in a two-phase system to the steady-state distribution of droplet sizes in a continuous system. The analysis is extended to include transients in continuous and batch systems. The resulting integral and integrodifferential equations are solved numerically to indicate the effects of some physical parameters. Existence of an equilibrium size distribution in a batch system is established analytically for a special case.
CAPACITIES:
K . J . Valentas and N . R. Amundson, University of Minnesota, M i n neajolis, M i n n . IND.ENG.CHEM.FUNDAMENVALS 5, 533-542 (1966) ANALYSIS OF OPERATION OF POROUS GAS ELECTRODES WITH TWO SUPERIMPOSED SCALES OF PORE STRUCTURE
Many of the types of porous gas electrodes used in fuel cells have a double porosity structure : a system of gas-filled macropores superimposed on one of liquid-filled micropores. A model for the operation of such an electrode is formulated by considering the macroand micropore systems as parallel one-dimensional continua, appropriately joined by a series of “linking pores” which represent the micropore structure immediately surrounding each macropore. Transport of dissolved gas reactant, ionic species, and current to/from reaction sites in the linking and micropores is analyzed, together with local electrode kinetic relationships, to characterize the reaction distribution and exterior behavior for the electrode. The calculated behavior for an oxygen cathode operating in 6.9N KOH illustrates the high activity and almost linear overpotential-current relationship predicted by this model. There are significant differences in electrode behavior from that predicted by available treatments based on a single PO e or uniform pore structure.
Edward A . Grens II, Unzuersity of California, Berkeley,
‘d [-z$
Circle No. 38 on Readers’ Service Card
SELECTIVE OXIDATION PROCESSES Do oxidation processes, products, and mechanisms interest you? “Selective Oxidation Processes’’ ADVANCES IN CHEMISTRY SERIES No. 51 surveys a number of processes and details research on improving the range, selectivity, and mechanisms of such processes.
Gal$
IND.ENG.CHEM.FUNDAMENTALS 5, 542-547 (1966) SPHERICAL GAS BUBBLE MOTION THROUGH MAXWELL LIQUIDS
An order-of-magnitude dimensional analysis of the problem of the motion of a spherical gas bubble through a viscoelastic Maxwelltype liquid is carried out. The form of asymptotic approximations for high and low Reynolds numbers, and high values of an elastic dimensionless group, is inferred from the analysis. T h e merits of an approximate evaluation of viscoelastic flow phenomena over more formal ways of attack are discussed in general, on the basis of the results obtained for the specific problem which has been Considered. The physical interpretation of dimensionless groups which are to be considered in the analysis of viscoelastic flow is discussed in general.
Gianni Astarita, University of Delaware, Newark, Del.
IND.ENG.CI-IEM.FUNDAMENTALS 5, 548-553 (1966) (Continued on page 720)
I N C O R P O R A T E D 67 North Main St. * Middleport, N. Y.
The book includes discussions of hydroxylating selected aromatics and olefins, pyrolysis o f isobutylene -all of these by vapor phase processes. Among liquid phase processes are three general methods for oxidizing aromatics, sulfur dioxide as oxidant for a number of products, use of nitrogen dioxide catalyzed selenium dioxide, and ozone as a selective oxidant. The last chapter is a broad survey of carbanion oxidation. The book is based on a symposium sponsored by the ACS Division of Petroleum Chemistry. 177 pages with index
Cloth bound
(1965)
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NO. 1 1
NOVEMBER 1 9 6 6
119
DlFFUSlVlTlES IN THE SYSTEM: NITROGEN-ARGON
BRIEFS
CARBON DIOXIDE-
Binary diffusivities are presented for the systems CO2-Ar and COg-Nz at 1 atm. and 1081" to 1810' K. Tracer diffusivities of 14COzthrough ternary mixtures are also given. The binary data, together with prior, low-temperature data, are corrclated empirically (mean deviations of 2 to 37,) with the Lcnnard-Jones (12-6) potential. The resulting potential is related to that obtained from prior measurements of viscosity by means of a rigid, spherocylinder model, thus providing means for prediction of one transport property from measurements of the other. Ternary measurements agree satisfactorily with values computed from binary diffusivities. Concentration effects on binary diffusix-ities are small and just beyond the observable range.
Thomas A . Pakurar and John R. Ferron, Department of Chemical Engineering, Universit)' of Delaware, Newark, Del.
only measurements necessary are of temperature, pressure, and mass. Sample data taken with a prototype balance are presented by way of illustration.
S. F. D i Zio,LW.M . Abbott, Daniel Zibello, and H. C. V a n Yess, Rensselaer Polytechnic Institute, Troy: N . Y . IND.ENG.CHEX FUNDAMENTALS 5, 569-571 (1966) COMMUNICATION. VARIATIONS
Sufficiency conditions for an optimum of a continuous diffcrcntiable function to exist are derived for the case when equality or inequality restrictions are present.
R. S. Schechter and G. S. G. Beceiidge, Unmrsity burgh, Scotland
IND.ENG.CHEM.FUNDAMENTALS 5, 553-557 (1966)
IND.
LAMINAR-TURBULENT TRANSITION I N DUCTS OF RECTANGULAR CROSS SECTION
The lower critical Reynolds number for the laminar-turbulent transition has been calculated theoretically as a function of the duct aspect ratio (ratio of width to height) for the steady, isothermal flow of Newtonian fluids in straight ducts with constant, rectangular cross sections. T h e theoretical calculations are compared with data reported by seven independent investigators in ten systems and found to be in agreement to within experimental precision. The theoretical curve is recommended for practical calculations, and a simple "rule of thumb" for ducts of large aspect ratio is given.
R . W . Hanks and H.-C. Ruo, Brigham Young Unwersity, Prouo, U t a h I N D .END.CHEM.FUNDAMENTALS 5, 558-561 (1966) FILM BOILING OF SPHEROIDAL DROPLETS. PHENOMENON
THE LEIDENFROST
of
Edinburgh, Eddin-
ENG.CHEM. FUNDAMENTALS 5,571-573 (1966)
COMMUNICATION.
RADIAL EFFECTS IN A STEFAN DIFFUSION TUBE
A steady-state analysis of the Stefan experiment for gases has shown that the measured binary diffusivity will be affected by radial variations in velocity and concentration only for the diffusion of highly volatile solvents.
S. S. Rao and C. 0. Bennett, University of Connecticut, Storrs, Conn. IND.EXG.CHEWFUNDAMENTALS 5, 573-575 (1966) COMMUNICATION. MECHANISMS FOR ELBOW- AND DRUM-TYPE MIXERS IN MIXING OF SOLIDS
Elbow- and horizontal drum-type mixers were designed with comparable geometry, making possible direct comparison of mixing mechanisms.
J . B. Gayle, Bureau
o j Mines, Tuscaloosa, Ala.
IND.ENG.CHEM.FUNDAMENTALS 5 , 575-576 (1966)
Theoretical and experimental studies were made on the vaporization of spheroidal drops undergoing film boiling (the Leidenfrost phenomenon). An analytical model is developed which considers a droplet to be suspended by its own vapor while slowly evaporating because of heat conduction across the \-apor cushion, thermal radiation from the heating surface, and molecular diffusion over the top surface of the drop. Predicted drop vaporization times, obtained by numerical integration, are compared w-ith corresponding experimental data for four fluids over a wide range of plate temperatures. T h e agreement between theory and experiment is reasonable and consistent. An analytical solution, neglecting radiation and diffusion, is presented, but is shown to be invalid. The measured vaporization times are well correlated, and the Leidenfrost point is established for each fluid. I t is concluded that the proposed transport mechanisms correctly describe the phenomenon.
Byron 5'. Gottfried and Kenneth J . Bell, Case Institute Cleveland, Ohio
SUFFICIENCY CONDITIONS IN CONSTRAINED
of
Technolofy,
IND. EKG.CHEM.FUNDAMENTALS 5,561-568 (1966)
COMMUNICATION. BED
HYDRODYNAMIC STABILITY OF A FLUIDIZED
The two-fluid model of Pigford and Baron predicts instability of a fluidized bed when subjected to a general perturbation, since one of the factors of the secular equation is exactly that found by Pigford and Baron for a one-dimensional vertical disturbance. The growth rate of the instability is independent of the horizontal component of the wave vector of the perturbation.
J . E. Chajpelear, Shell Development Co., Houston, T e x . I N D .ENG.CHEM.FUNDAMENTALS 5, 576-578 (1966) CORRESPONDENCE
Comments on a recent correspondence on concentration-dependent physical properties and rates of mass transport.
A . W . Nienow, R a k s L'nahabhokha, and J . 6V. Mullin, University College, London, England IND.
ENG.CHEM. FUNDAMENTALS 5, 578-579 (1966)
CORRESPONDENCE
EXPERIMENTAL TECHNIQUE. VISCOMETER FOR MEAgUREMENT OF VISCOSITIES IN THE RANGE lo8 TO 10" POISES, USING 0.1 ML. OF SUBSTANCE
Comments on a published article on determination of rates of surface transport and a reply.
The viscometer is capable of measuring the viscosities of small approximately cylindrical samples. The accuracy achieved is +20%.
Rzchard 'V. Foster, Hardznp Bliss, and John H . Butt, Yale University, N e w Haoen, Conn. J . M . Smith, University of CaliJornia, Davis, Calif.
W . H. Cogill, Joseph Dunlo), and D. AT. Royal, University of A'ew South Wales, n'ew South Wales, Australia
IND. ENG.CHEM.FUNDAMENTALS 5, 579-581 (1966)
IND.ENG.CHEM.FUNDAMENTALS 5, 569 (1966)
CORRESPONDENCE
EXPERIMENTAL TECHNIQUE. SECOND VlRlAL COEFFICIENTS OF ORGANIC VAPORS FROM DENSITY BALANCE MEASUREMENTS
A vapor density balance may be operated to allow the determination of vapor densities, and hence of second virial coefficients, without reference to the properties of any other material. The 120
INDUSTRIAL A N D ENGINEERING CHEMISTRY
~
Comments on two articles on dynamics of flow-forced systems and a reply.
D. D . Penrod and Edward D . Crandall, University of iVotre Dame, Notre Damp, Ind. Lowell R. Kojjel, Purdue Unnioeisity, Lafayette, Ind.
IKD.ENG.CHEM.FUNDAMENTALS 5 , 581-584 (1966)
