BRIEFS Summary of papers published in this month's research quarterly, I H E C Pundamentals
ACTIVITY COEFFICIENT RELATIONS IN MISCIBLE AND PARTIALLY MISCIBLE MULTICOMPONENT SYSTEMS
EFFECT OF SONIC PULSATIONS O N MASS TRANSFER RATE OF NAPHTHALENE FROM A PLATE INTO AIR
Based on a quasi-lattice model of a multicomponent solution, three equations are derived relating component activity coefficients to the composition of a liquid mixture. T h e equations also apply to systems showing limited miscibility. Temperature dependence of activity coefficients is built in. T h e equations were tested for 16 binary systems, five of which show limited miscibility, and for four ternary systems. T h e enthalpic Wilson equation, one of the three, gives the best prediction of binary vapor-liquid equilibrium. Both the enthalpic Wilson equation and the Orye equations give good results of comparable accuracy for the ternary systems.
Local mass transfer rates of naphthalene imbedded on a flat plate a t zero incidence to a n air stream of 8 to 11 cm per second in a channel were determined. Sonic pulsations of 10 to 13.8 kc per second and 102 to 114 decibels caused a n increase of 10 to 1 0 0 ~ o i n mass flux i n comparison to similar runs without a sound whistle. Based on the boundary layer theory, a model is developed to interpret the contributions of the time-averaged air velocity and the interaction between fluctuating components of velocity and concentration.
Solke Bruin,Laboratory f o r Physical Technology, Eindhoven University o f Technology, Eindhoven, Netherlands
D . E. Honaker and L. C. T a o , University of Nebraska, Lincoln, hTebe6. 68508 IND.ENG.CHEM. FUNDAMENTALS 9, (3) (1970)
IND.END.CHEM. FUNDAMENTALS 9, (3) (1970)
THERMAL REACTION OF PROPYLENE.
KINETICS
Kinetics of the thermal reaction of propylene was studied a t temperatures ranging from 703' to 854OC., atmospheric pressure, and residence times from 0.078 to 3.3 seconds with and without nitrogen dilution. Main primary products were ethylene, methane, hydrogen, butenes, and butadiene in the approximate ratio of 5 : 3 : 1 : 1 : 1 a t initial stages of the reaction. Other primary products were methylcyclopentene, hexadienes, acetylehe, and ethane. Secondary products were cyclopentadiene, benzene, polycyclic aromatics, cyclopentene, and toluene. Selectivities of formation of these products, except acetylene and ethane, showed little dependence on temperature. At higher partial pressure of propylene, the selectivities of ethylene and methane formation decreased to some extent. T h e effect of partial pressure of propylene on the rate of propylene disappearance leads to a three-halvesorder equation. T h e rate constant is given as k = 101506 exp( -- 63200/R T)cc.1/2/(molel/Zsec. ).
DETERMINATION OF RELATIVE VARIANCE AND OTHER MOMENTS FOR GENERALIZED FLOW NEfWORKS OR SYSTEM TRANSFER FUNCTIONS
A method described by Klirikenberg for determining the variance and other moments for a flow network consisting of a series of vessels with backflow is extended to general flow networks and also transfer functions for dynamic systems. T h e usefulness of the cumulants and a method for their indirect evaluation is described. T h e use of these methods is illustrated by their application to the derivation of a simplified model for the response to reflux changes in a packed distillation column section.
U. W . Kropholler, Loughborough liniuersi9 of Technolog), Lacs., England
IND. ENG.CHEM. FUNDAMENIALS 9, (3) (1970)
Taiseki Kunugi, Tomoya Sakai, Katuhiko Soma, and Yoichi Sasaki, University of Tokyo, Tokyo, Japan
EQUILIBRIUM CONSTANT DETERMINATION BY NONLINEAR OPTIMIZATION
IND. ENC.CHEM. FUNDAMENTALS 9, (3) (1970)
I t is difficult to obtain physically meaningful parnincters from experimental data for a chemical reaction systmi \then rhc marhematical model describing the system iiivolvcs noillincar functions. This wporr describes a methodology for changing ccrtain niodcls occurring frequently in practice into a form suitablc for solution by noillinear optimization methods. 111pdrticulnr. tlir a\.c.rage srate of aggregation of pure metal alkoxides as a function of concentration was determined by calculating rhc equilibrium constants of thc system B,-1 B k R,,K , = B , B -lB, and 1 = 1, . . , .2f from experimental data obtaincd by ebullioscopic techniquss.
THERMAL REACTION OF PROPYLENE. MECHANISM
A mechanism for the thermal reaction of propylene is based on kinetic evaluation of the relevant elementary reactions a t 1100 "K. and atmospheric pressure. At low conversion of propylene, around a few mole per cent, initiations: C4Hs-1 -+ CH3. f C 3 H 5 . ; propagation: CHI. f C3H6 e Sec-C4Hg., sec-C4Hg. -+ C4Hs-1f H . , sec-CaH9. --+trans- or cis-CaHs-2.f H . , sec-CaH~.-+ CH-CH-CH-CHa f Hz, CHFCH-CH-CHI -+ C4H61,3 H . , CH3. C3H6 e isoCaHg., isoC4H~.4 isoC4Hs H., CHI. C3H6 -+ C H 4 4- C3H5., H . C3H6 e T I G H T . , n-CaH7. + C2H4 CH3., n-C3H7. -+ Hz C3H5., H . C3H6 Hz -/- C ~ H K C&. ., C&8 -+ methylcyclopentene f H . ; termination: C 3 H 5 . C4H7. -+ C3H6 f C4&-1,3. The initiator, 1-butene, was one of the main products. This mechanism suggested that the amount of ethylene formed is equal to the sum of methane, butenes, and butadiene, that the selectivities of formation of the main products do not depend on the conversion of propylene a t low conversion region, and that the selectivities of the main products are independent of temperatures from 750' to 850°C. This was consistent with the experimental results. T h e rate of propylene disappearance was increased considerably in the presence of about 3 mole % of 1-butene.
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C. E . Biau, R. R. K l i m p d , and I.'. C. Stpiner. .Widland, M i c h . 48G40
IND. ESG.
CIiEM.
DOXI Chemisa/ Co.,
F U N D ~ M E N T 9, A L( 3S, f 1970)
CIRCUMFERENTIAL VARIATION OF INTERCHANGE IN HORIZONTAL ANNULAR TWO-PHASE FLOW
A semi-empirical model can be used to predict the circumferentia 1 variation of interchange from the core to the film in the top half of a horizontal gas-liquid pipeline. T h e model is developed from the equations of motion describing the drop trajectories and is modified by the addition of a constant developed from measurements on a n air water system in a 1-inch pipeline.
Taiseki Kunugi, Katuhiko Soma, and Tomoya Sakai, University of Tokyo, Tokyo, Japan
R. J . Anderson and T. W . F. Russell, University of Delaware, Newark,
IND.ENG.CHEM. FUNDAMENTALS 9, (3) (1970)
FUNDAMENTALS 9, (3) (1970) IND.ENG.CHEM.
Del. 10717
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ANALYSIS OF NONISOTHERMAL MULTICOMPONENT DIFFUSION WITH CHEMICAL REACTION
center as well as reactant mixing. T h e results are valid for any degree of reactant conversion, if initiation by products remains insignificant, and thus extend earlier work on chain center mixing, which dealt only with the initial rate (infinitesimal conversion) problem. Results for a radiation chemical flow reactor illustrate the nature of the derived mixing effects.
T h e problem of nonisothermal multicomponent diffusion in the presence of chemical reactions obeying linear rate expressions is treated. Cases involving time-dependent transport coefficients and reaction velocities are included. Sufficient conditions are demonstrated for the applicability of a diagonalization procedure used extensively in solving isothermal and nonreactive problems, A general eigenfunction technique is presented independent of the geometry. T h e solution thus obtained is shown to be a direct generalization of the scalar binary problem with a time-dependent diffusion coefficient and reaction velocity. The contribution of thermodynamic coupling to the system is considered, and an example indicates the relevance of coupled mass transfer to industrial separation processes.
HEAT TRANSFER BETWEEN A PLANE SURFACE AND AIR CONTAINING SUSPENDED WATER DROPLETS
G. B . DeLancg and S. H . Chiang, University of Pittsbu rgh, Pittsburgh, Pa.
A n analytical and experimental investigation was made to de-
IND. EKG.CHEM. FUNDAMENTALS 9, (3) (1970)
SEPARATION OF DYES I N NONFOAMING ADSORPTIVE BUBBLE COLUMNS
T h e separation achieved in a nonfoaming adsorptive bubble fractionation column was studied by means of a novel colorimetric technique for directly measuring the concentration a t various levels within the column. The effects of gas rate, column dimensions, charge concentration, and chemical environment were examined. Where comparisons are possible, the experimental results agree with recent theory. G. N . Shah and Robert Lemlich, University of Cincinnati, Cincinnati, 0 hio 4522 1 IND.END.CHEM.FUNDAMENTALS 9, ( 3 ) (1970)
R. M . Felder and F. B. Hill, Brookhauen 'Vational Laboratov, Ujton, 1lT.Y. 11973 IND. ENG.CHEM. FUNDAMENTALS 9, (3) (1970)
termine heat transfer and liquid film thickness for a wedge-shaped body in a two-phase two-component stream. T h e rate of heat transfer was increased over that for the gas (air) phase alone as a result of evaporation and sensibly heating the continuous liquid film that formed on the solid surface. Typically, heat transfer rates were increased about 20 times by adding 556 liquid water to the air stream. T h e liquid film formed was 0 to 0.008 inch thick. T h e integral energy equation was solved to obtain local and average heat transfer coefficients. Solutions were obtained i n closed form and compared with measured values. X closedloop subsonic wind tunnel with a 1-sq-foot test section was used i n the experimental phase. This investigation considered the mechanisms involved for a plane surface. T h e liquid film thickness measurements showed good agreement with the analytical solution.
W . C. Thomas, Virginia Polytechnic Institute, Blacksburg, Va. 24061, and J . E. Sunderland, X u r t h Carolina State Uniniversib, Raleigh, N. C. 27607 I N D .ENG.CHEM.FUNDAMENTALS 9, (3) (1970)
ATTENUATION OF LOW FREQUENCY SOUND DURING TURBULENT FLOW OF AIR IN A TUBE
Sound i n the frequency range 200 to 900 H z , at intensities up to 159 dB, did not affect the pressure gradient in turbulent air flow in a 3/4-inch tube, a t Reynolds numbers u p to 52,000. T h e sound attenuation coefficient, after correction for the effects of air flow velocity and pressure distribution, was approximately equal to the attenuation coefficient in the absence of flow, for all flow velocities a t a sound frequency of 900 Hz. T h e corresponding attenuation coefficients a t lower frequencies increased considerably above the predicted values a t the higher flow velocities. An attempt was made to predict these trends by solving the appropriate differential equation for sound attenuation in a tube, using an eddy-viscosity profile calculated from Martinelli's velocity distribution equation for turbulent flow in a tube. This procedure correctly predicted a sharp increase i n the attenuation coefficient beyond a certain critical flow rate, which depended on the sound frequency, but overestimated the magnitude of the effect a t all frequencies.
.I. M . Beeckmans, Bernard Dudon, and Omjrakash Tulsian, UniuersiQ 01
FROST DEPOSITION ON COLD SURFACES
\,Vater frosts were deposited on a liquid nitrogen-cooled plate from a humid air stream. T h e plate formed the bottom of a highaspect wind tunnel. Reynolds numhers were varied from 3770 to 15,800, gas phase humidities from dew points of 14" to 58"F, and gas temperature from 34' to 93'F. Frost densities and thermal conductivities were determined and the heat and mass fluxes measured. T h e data were correlated by a simple analytical model which emphasized the internal diffusion processes within the frost. Density measurements were also made within the thin frost layer. These measurements indicated that within the accuracy of the method used there are no significant density gradients in the frost. This result, though not thoroughly explained, is believed due to a combination of internal diffusion and nucleation with particle transfer by thermal diffusion forces.
Western Ontario, London, Ontario, Canada
P. L . T . Brian, R. C. Reid, and Y . T . Shah, Massachusetts Institute of Technologj, Cambridge, M a s s . 02139
IKD.ENG.CHEM.FUNDAMEKTALS 9, ( 3 ) (1970)
IND. ENC.CHEM. F U N D A M E N T A L S 9, (3) (1970)
MIXING EFFECTS IN CHEMICAL REACTORS. BATCH AND FLOW SYSTEMS
CHAIN REACTIONS I N
Mixing or diffusion of reactants in a batch reactor and radial mixing or diffusion in a continuous tubular reactor increase the conversion obtainable for a given time (batch) or reactor length (flow). This applies to sth-order kinetics (s 2 0 ) , an arbitrary residence time distribution in the flow reactor, and an arbitrary dependence of rhe reaction rate on position (hatch) or radial position (flow) i n the reactor. T h e paper considers applicability of results to reactive systems of varying degrees of complexity. Certain common chain mechanisms conform to the model of earlier work; the treatment is extended to include the effects of chain 72
INDUSTRIAL AND ENGINEERING C H E M I S T R Y
CONCENTRATIOW AND TEMPERATURE DEPENDENCE OF LlQUlD DIFFUSION COEFFICIENTS
Prediction of the concentration dependence of the liquid diffusion coefficient has required the use of activity data in most previous equations and correlations. A method is presented here, based on a modified absolute rate theory approach, to estiinatc thc variation of the diffusivity with concentration changes using only the physical properties of the liquids involved, such as viscosity and molar volume. This inethod is tested on three typrs of systei-ris,containing both associatrd and nonassociated compounds, good predictions resulting in all cases. T h e variation of the diffusivity with
BRIEFS temperature is also discussed, using the modified rate theory equations.
STATISTICAL CHARACTERISTICS OF THIN, VERTICAL, WAVY, LIQUID FILMS
J . L . Gainer, Unzuerszty of Virginia, Charlottesvzlle, V a . 22901
The structure of the gas-liquid interface is explored by analyzing the time-varying film thickness obtained from electrical conductivity measurements and is shown to be random in character and to behave as a “two-wave system.” Large lumps of liquid, which carry a significant portion of all the liquid flowing, move down the interface with no change in speed or shape. Smaller waves imposed on this larger structure lose their identity over small distahces. Methods for calculating statistically meaningful wave celerity, separation distance, amplitude, frequency, and wave shape are presented, with data for liquid Reynolds numbers from 900 to 6000 and gas Reynolds numbers from 0 to 60,000. Comparisons are made with theoretical predictions of celerity, important differences between vertical and horizontal wave flow are demonstrated, and the suitability of the gamma distribution function for amplitude is demonstrated.
I N D .END.CHEM.FUNDAMENTALS 9, (3) (1970)
CONTINUOUS-PHASE AXIAL DISPERSION IN LIQUID-LIQUID SPRAY TOWERS
The diffusion model applies to axial dispersion in the continuous phase of liquid-liquid spray columns. Continuous phase axial dispersion coefficients were determined for methyl isobutyl ketone dispersed in water. A sodium chloride tracer, insoluble in the dispersed phase, was injected into the column and its steady-state concentration was measured upstream in the continuous phase from the plane of injection. The dispersion coefficient was unaffected by continuous phase superficial velocity over the velocity range investigated, but decreased with increased dispersed-phase superficial velocity. I t increased with column diameter but was unaffected by column length. I t increased with drop size at constant dispersed-phase superficial velocity; however, it remained approximately constant with drop size when the number of drops per unit volume of column was maintained constant. Some disagreement with earlier results was noted; however, dispersion numbers calculated from the present study superimpose roughly on those published earlier for liquids in packed beds.
J . E. Henton and S. D . Cavers, Department of Chemacal Engineering, T h e Untversaty of Brittsh Columbia, Vancouver, B . C.
IND.ENG.CHEM.FUNDAMENTALS 9 , ( 3 ) (1970) HEAT CAPACITY OF SATURATED NONPOLAR AND POLAR LIQUIDS
A generalized method has been developed for the estimation of heat capacities of saturated nonpolar and polar liquids by the use of the acentric factor, w , and the fourth parameter, x . Functions for the calculation of the saturated liquid heat capacity, the product of the temperature and derivative of liquid entropy with respect to temperature along the vapor-liquid boundary curve, are presented for reduced temperatures between 0.40 and 0.96. For polar fluids, quadratic terms were wquired in the Taylor series expansion of the heat capacity departure in w and x . Functions for the entropy of vaporization of nonpolar and polar fluids were also determined for low reduced temperatures. The relationships of this study were found to reproduce experimental heat capacities for 21 nonpolar and 16 polar liquids with a n average deviation of approximately 2 %.
Tran-Fu Y u a n and Leonard I. Stzel, Syracuse Universaty, Syracuse, N . Y . 13210 IND.ENC.CHEM.FUNDAMENTALS 9 , (3) (1970)
MATHEMATICAL MODELING OF STEADY-STATE BEHAVIOR I N INDUSTRIAL GRANULATORS
A mathematical model is based o n three assumptions: that the crusher, present in all granulation plants, is the main source of seed particles, that the residence time of particles in the granulator is a probabilistic function, and that particle growth rate is constant. Using these assumptions, the model takes data for the particle size distribution of the granulator discharge stream and calculates a distribution for the recycle stream, in good agreement with plant data. From the two distributions, the model then calculates a value of recycle ratio, which again agrees closely with plant data. Having thus satisfactorily tested the model, the authors demonstrate the relationships among plant recycle ratio, product recycle fraction, and crusher speed.
C. D. Han andIsrael Wilenitz, Polytechnic Institute of Brooklyn, Brooklyn, N. Y . 11201 IND.END.CHEM.F U N D A M E N ~9,A(3) L S (1970)
A . S. Telles and A. E Dukler, Unzversity of Houston, Houston, T e x . 77004
IND.ENG.CHEM.FUNDAMENTALS 9, ( 3 ) (1970)
CONTINUOUS THICKENING OF FLOCCULATED SUSPENSIONS. CgMPARlSON WITH BATCH SETTLING TESTS AND EFFECTS OF FLOC COMPRESSION USING PYROPHYLLITE PULP
Previous postulations on the thickening behavior of flocculated pulps, as related to the floc volume concentration, are confirmed. The correlation between batch settling tests and continuous thickening can be improved by applying mild stirring i n batch settling to prevent channeling and to simulate the dynamic conditions in the thickener. Evidence is provided for the dewatering of the floc in the lower mud zone in a thickener through mechanical compression caused by the weight of the overlying solids. Such a lower mud zone is present when the underflow drnsity exceeds that of the uncompressed flocs.
Keath J . Scott, Chemical Engineerang Group, S.A. Councal for Sctentlfc and Industrial Research, Pretoria, South Africa
IND.ENG.CHEM.FUNDAMENTALS 9, ( 3 ) (1970)
GENERALIZED EQUATION OF STATE FOR GASES
A generalized pressure-explicit equation of state, suitable for nonpolar gases in the T, 2 1.0 region, is proposed. The RedlichKwong equation of state was modified by means of the deviation function approach, using Pitzer’s table as a guide in the development. The proposed deviation function consists of a simple power series of 1/ v . For pure components only T,, P,, and w are required for the calculation. The proposed equation successfully predicted the compressibility factors and the enthalpy departures for several arbitrarily chosen pure substances. Mixing rules for the coefficients of the proposed equation were developed. The applicability of the proposed equation to mixtures is demonstrated by the successful prediction of the enthalpy departure for three binary mixtures.
Hzdezumi Sugip and B. C. -Y. L u , University of Ottawa, Ottawa, Canada
IND. ENG.CHEM.FUNDAMENTALS 9, (3) (1970)
HEAT OF ADSORPTION OF LIGHT HYDROCARBONS AND THEIR MIXTURES O N ACTIVATED CARBON
A thermodynamic analysis is made of heat of adsorption based on the Myers-Prausnitz theory of ideal solution of the adsorbed phase. Ray and Box’s adsorption equilibrium data are analyzed in light of the theory for the calculation of heat of adsorption of methane, ethane, ethylene, propane, and n-butane and their mixtures on VOL. 6 2
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BRIEFS activated charcoal at teiiiperatures of 100’ to 400’F and pressnrrs to about 200 psi.
INFLUENCE OF SURFACE TURBULENCE AND SURFACTANTS O N GAS TRANSPORT THROUGH LlQUlD INTERFACES
C. F . Snyder and Kwang-Chu chao, Oklaliornn State University, Stillwater, Okla. 74074
A new experimental technique is used to measure the effects of stirface turbulence and surfactants on mass transfer rates at gasliquid interfaces. At high turbulence rates the statistical nature of interfaces, with and without surfactants present, may be described by a Danckwerts-type distribution function of surface ages. Measurements of surface film mass transfer resistances show that soluble snrfactants offer no measurable resistancc, while insoluble films show definite resistance to passage of gas molecules. The nature of surface films and their stability in the presence of interfacial turbulence are discussed.
I N I J . E N G . CHEM.
FUKDAhiENlALS 9, ( 3 ) (1970)
THE DRAINAGE OF NEWTONIAN LIQVIDS ENTRAINED O N A VERTICAL SURFACE
T h e drainage of Newtonian liquids entrained on a vertical flat plate was studied under conditions when the profile of the film a t the onsel of drainage is similar to the one assumed by a large sessile drop formed on a horizontal surface. h theoretical expression for predicting the film thicknesses obtained during drainage was derived by extending Jeffreys’ free-drainage theory to include effects introduced by the initial shape of the film. Experimental values for the film thicknesses were in good agreement with the theoretical predictions. I t is concluded that Jeffreys’ free-drainage theory can be used to predict the film thickness of a liquid draining from a vertical flat plate when the drainage time exceeds a critical time that depends on the film thickness prior to the onset of drainage, the viscosity, the capillary length, and the distance from the upper edge of the film.
Costel D . Denson, General Electric CG.,Schenectady, S. Y . IND. ENG.CHEM. FUNDAMENTALS 9, (3) (1970)
THERMODYNAMIC STUDIES OF PHASE EQUILIBRIA IN MOLTEN SALT SYSTEMS. PREDICTION OF LIQUIDUS AND EUTECTIC BEHAVIOR I N MIXTURES HAVING A COMMON ION
A general equation is derived for expressing the liquidus curve in liquid-solid phase equilibria of binary and multicomponent systems in which no compound formation and mutual solubility in the solid phase are observed. This equation is applied to calculate the liquidus in molten salt mixtures with a common ion. T h e regular solution approximation can reproduce the liquidus of binary alkali halides and related mixtures reasonably well, though a complete representation needs two- or three-constant empirical equations. T h e ternary eutectic point can be estimated with reasonable accuracy from binary data alone. Comparison with the literature values indicates that the maximum error in the eutectic composition does not exceed 4 mole yc.
Koichiro iVakanishi, Kq’oto UniiiersiQ, K y o t o , Japan I N D . ENG. (:HEM.
FUNDAMEN’TALS9,(3) (1970)
EFFECT OF WATER VAPOR O N THE LIOH-CO:! REACTION. DYNAMIC ISOTHERMAL SYSTEM
The role o f water vapor in the reaction of cariron dioxidr with 1ithi.um hydroxide in a. dynamic system was evaluated. This parame ter was isolated by utilizing low concentrations of CO,, thus maintaining an essentially isothermal system. LiOIP is shown t o be hygroscopic, and the rate of water pickup is directly related to the relative humidity of the feed system. T h e critical partial pressure of water at 25 “C is approximately 4 Torr. Hydration t o the monohydrate (LiOH. HzO) is a necessary precursor to COr reaction, but the rate of hydration must not exceed the rate o f carbonation if high efficiencies are to be realized. T h e controlled rate of hydration is necessary to maintain the high surface area and porosity of pelletized T,iO€I. The previously acceptrd equation, 2 LiOH COZ -+ Li2CO3 H20, is the summation of the two-step reaction, 2 LiOH 2 HzO e 2 L i O H . H 2 0 . 2 LiOH.1320 COZ-+ LiCOa 3 H20.
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D . D . Williams and R. R. Miller, U S . A’aval Research Laboratov, Washington, D.C. 20390 I N D . E Y G . CEIEM.
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FUNDAMENTALS 9, (3) (1970).
INDUSTRIAL A N D ENGINEERING CHEMISTRY
T . G. Springer and R. 1,.Pi,cfnrd, Uniniverrib of CaliJoinin, Rerkeley, CaliJ. 94720 IND.
ENG.CHEM. FUNDAMENTALS 9,( 3 ) (1 970)
CAPILLARY INSTABILITY OF A THIN ANNULAR LAYER OF LIQUID AROUND A SOLID CYLINDER
In a thin layer of liquid surrounding a solid cylinder, the radial velocity is negligible compared to the axial component. This leads to a simple expression for the rate of capillary breakup. When the layer is thin, the result is indistinguishable from the very complicated expression derived by Goren. This simple keatment can be extended easily to the case of linear viscoelastic behavior. Considering specifically the Voigt and Maxwell models, it is found that the stability is increased in the case of the Voigt model but decreased in the case of the Maxwell model. J . H. Dumbleton, Chemstrand Research Center, Inc., Durham N. C., and J . J . Hermans, Unicersity of North Carolina, Chafiel Hill, 1%’. C. 27514 IND.ENG.CHEM.FUKDAMENTALS 9, ( 3 ) (1970)
SCALING PREDICTIONS FOR THERMODYNAMIC ANOMALIES NEAR THE GAS-LIQUID CRITICAL POINT
Most empirical equations of state for gases have derivatives of all order in density and temperature a t the critical point. This implies definite asymptotic characteristics (“classical”) for thermodynamic anomalies in the critical region. Classical critical anomalies and symmetries are treated in some detail. T h e Ising model of statistical mechanics reveals an essentially different kind of critical behavior (nonclassical). A brief discussion is given. Real gases behave nonclassically. Therefore, classical equations of state cannot be valid in the critica.1 region. T h e homogeneous or scaled equation of state, recently proposed by Widom, Kadanoff, and Griffiths, incorporates nonclassical critical anomalies. Its form and some of its consequences are discussed. Scaling ideas are applied to the correlation of coexistence curve data (for argon and steani) and vapor pressure data (for ( 7 0 2 ) . J . M . 13. Levelt Sengers, National B u r m u of Standards, Washington,
I). C. 20234 IND.ENG.CHEM.FUNDAMENTAL.S 9, (3) (1970)
MASS TRANSFER FROM SPHERICAL GAS RUBBLES AND LIQUID DROPLETS M O W N 6 THROUGH BOWER-LAW FLUIDS IN THE LAMINAR FLOW REGIME
Calculated mass transfer coefficients for the continuous phase arr presented for internally circulating spheres of a Newtonian Auld traveling through a power-law-type continuous phase in the socalled creeping-flow region. T h e Nakano and Ticn strram funr tions allow the Sherwood nurnbrr to b- computed as a fiinction of the Peclet number, power-law index, and a viscosity ratio pa-
BRIEFS rameter. T h e Hirose and Moo-Young relation is shown to be a limiting case of this numerical solution. Mass transfer rates increase as the fluids become more pseudoplastic and/or the continuous phase consistency index increases, all other factors held constant.
R. M . Wellek and C.-C. Huang, University of Rolla, Mo. 65401
Missouri-Rolla,
IND.ENG.CHEM.FUNDAMENTALS 9, (3) (1970)
that the yiscous and kinetic parameters in the Ergun equation are not true constants.
R. E. Hicks, Council for Scientific and Industrial Research, Pretoria, South Africa IND.ENG.CHEM.FUNDAMENTALS 9, (3) (1970)
COMM UNlCATlON VELOCITY PROFILES IN POROUS-WALLED DUCTS
VOID FRACTION MEASUREMENT OF HOMOGENEOUS POWDER BEDS BY FREQUENCY-RESPONSEMETHOD
A theory of pulsating gas flow in a homogeneous powder bed was developed to obtain the basis for this measurement. T h e void fraction of the bed is related to the amplitude attenuation of pulsating pressure during passage of the gas through the powder bed. T h e experiment was carried out with beds of 30- to 200-micron glass spheres formed in a test cylinder. The frequency and amplitude of pulsating pressure applied to the bed were 0.5 or 3 cycles per second and 20 m m of H20, respectively. This method is practicable if a homogeneous powder bed is formed in the test cylinder. T h e measurement can be performed automatically. Extension to a n on-line particle size detector by the permeability technique is suggested.
Yoji Nakajima, Yutaka Ado, Keishi Gotoh, and Tatuso Tanaka, Hokkaido University, Sapporo, Japan IND.ENG.CHEM.FUNDAMENTALS 9 , ( 3 ) (1970)
COMMUNICATION EXPERIMENTAL EVIDENCE THAT WATER HAS N O TIME-DEPENDENT DYNAMIC SURFACE TENSION
An oscillating jet employing a diaphragm-type ellipitcal orifice constructed of 2-mil paraffin-coated Mylar film was used to study the dynamic surface tension of water. Results showed the dynamic surface tension of water not to be significantly different from the equilibrium value over the range of exposure times studied.
J . A. Caskey and W. B. Barlage, Jr., Clemson University, Clemson, N . C.
Exact solutions are given for the low Reynolds number flow of an incompressible Newtonian fluid i n tubes and slits with permeation through the channel walls. A Fourier analysis is used to extend the solutions to arbitrary permeation rates which vary with distance along the duct. This generalization facilitates calculations for the nonuniform permeation rates found in ultrafiltration. At low permeation rates simplified expressions are given which should be valid for all conditions of present interest.
A . A. Kozinski, F. P. Schmidt, and E. N . Lightfoot, Universi$ of Wisconsin, Madison, Wis.53706 IND.END.CHIEM. FUNDAMENTALS 9, ( 3 ) (1970)
COMMUNICATION KINETIC EXPRESSIONS FOR REACTION RATE I N NONCATALYTIC SOLID-GAS SYSTEMS
The concept of reaction order with respect to the solid reactant in a reaction between a gas and a porous solid is analyzed. This reaction order is a function of the porous structure of the solid and according to it may vary as solid is being consumed. T h e reaction order with respect to the solid reactant ought to be less than 1.
R . E. Cunningham and A . Calvelo, Universidad Nacional de L a Plata, L a Plata, Argentina IND.END.CHEM.FUNDAMENTALS 9, ( 3 ) (1970)
COMMUNICATION
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DEGREES OF FREEDOM I N A SIMPLE FRACTIONATING COLUMN
IND.ENG.CHEM.FUNDAMENTALS 9 , ( 3 ) (1970)
By computational methods a study was made of possible restrictions on the particular selection of the degrees of freedom available to the designer of fractionating columns. I n particular, the choice of only intensive variables, all located a t the same point a t one extremity of a column comprising an enriching and a stripping section, was considered. Such a choice is permissible and defines the system completely.
COMMUNICATION STEADY SYMMETRIC SINK FLOWS OF INCOMPRESSIBLESIMPLE FLUIDS
The three-dimensional steady flow toward a point sink and its twodimensional counterpart are studied here for the case of a n incompressible simple fluid. Existing experimental evidence indicates that these flow models might adequately approximate the convergent flows of viscoelastic liquids from a reservoir to a circular orifice and a slot, respectively. T h e general functional of the motions of extension reduces in these cases to one and two material functions of one of the principal stretchings. For a number of subclasses of simple fluids, these material functions are compared with those for homogeneous steady extensions.
Giuseppe Marrucci and R. E. Murch, University of Delaware, fiework, Del. 79771 IND.END.CHEM.FUNDAMENTALS 9, ( 3 ) (1970)
COMMUNICATION PRESSURE DROP I N PACKED BEDS OF SPHERES
Different pressure drop equations applicable over liinited ranges of the Reynolds number are well represented by a single nonlinear equation in the range 300 < R e / ( l - E ) < 60,000. This implies
J . S. Forsyth, Uniuersitv of British Columbia, Vancouver, B. C.: Canada IND.ENG.CHEM.FUNDAMENTALS 9 , ( 3 ) (1970)
COMMUNICATION SURFACE TENSION OBSERVATION IN DISTILLED AND SALINE WATER INTERFACE
I n qualitative experiments saline water jets injected into distilled water showed “interface tension” phenomena-Le., the wavy forms of the jet until its breakup into liquid drops. Interface tension between a small part of a free saline water bubble and a free distilled water surface was observed. More quantitative experiments showed the increase of a saline submerged water bubble in a distilled water medium. These observations proved that a very small interface tension exists between saline and distilled water.
U r i P a t and Hillel Rubin, Technion-Israel Institute of Technology, H a i f a , Israel IND.ENG.CHEM.FUNDAMENTALS 9, ( 3 ) (1970) VOL. 6 2
NO. 8
AUGUST 1970
75
L CELL SYSTEMS-II
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ADVANCES IN CHEMISTRY SERIES NO. 90 Thirty-one papers from the fifth of the biennial Fuel Cell Symposia sponsored by the Division of Fuel Chemistry, chaired by Bernard S. Baker. Topics Include: 0
Comments on an article on step responses of outlet liquid concentration in a simple gas absorption column.
F. P. Lees, Loughhorough Universip of Technology, Loughhorough, Leicestershire, England IND.ENG.CHEM. FUNDAMENTALS 9, (3) ( 1 9 7 0 )
fuel cell power systems
electrode structure use of hydrocarbons e electrode catalysis and mechanisms 0 high temperature fuel cells 0 fuel cell systems 0 0
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Fuel cells are still doing their job well in the space program. Total energy, stationary fuel cell power plants seem worth a commercial push, and some hybrid devices look promising. 4 5 6 pages with index Free set
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Giuseppe Marrucci, Istituto di Principi di Ingegneria Chimica, Uniuersita di ?Japoli, Naples, Italy Roger I . Tanner, Brown Uniuersib, Providence, R. I. 0 2 9 1 2 IND.
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Comments on a n article on estimation of model parameters using quasilinearization.
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E. B. aVauman, Union Carbide Gorp., Bound Brook, S . J . 08805 Ramon L . Cerro and Jose -44. Parera, Facultad de Ingenieria Quimica, Universidad del Litoral, Sante Fe, Argentma
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Comments on an article on coalescence of droplets in fiber beds.
G. A . Dauies, Uniuersip of Manchester, Manchester, England, and G. V . Jeffrey, Unioersity of Aston, Birmingham, England R. nT.Hazlett, U . S. ;l:ai.a! Research Lahoratoiy, Washington, D . C. 20390 IND.ENG.CHEM. FUNDAMENTALS 9, (3) ( 1 9 7 0 )
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