BRIEFS Summary of papers published in this month’s research quarterly, I@ EC Fundamentals
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DESALINATION BY REVERSE OSMOSIS
Experimental studies of salt and water transport through cellulose acetate membranes in both forward and reverse osmosis support the simple but useful model of transport by the parallel processes of diffusion and “pore flow.” Data on forward and reverse osmosis using a rotating cylindrical membrane operated over a range of rotational speeds check the theory developed earlier to describe the effect of concentration polarization in the design and operation of equipment for desalination by reverse osmosis.
T . K . Sherwood, P. L . T . Brian, and R. E. Fisher, Massachusetts Institute of Technology, Cambridge, Mass. IND. END.CHEM.FUNDAMENTALS 6,2-12 (1967)
SECONDARY NUCLEATION SOLUTIONS
IN AGITATED, MAGNESIUM SULFATE
Stirred aqueous solutions of magnesium sulfate were supersaturated and seeded. New nuclei were counted photographically as they appeared and the numbers were noted for two rates of cooling and different conditions of seeding. Similar experiments were carried out at constant supersaturation levels. The nucleation process studied occurred in the early time period leading up to the showers of crystals which are characteristic of seeded, supersaturated solutions. The experimental results suggest that these secondary nuclei are dependent upon the original seeds having been present and the level of supersaturation. During this period of early nucleation neither time nor the secondary particles appear to be important variables.
PERMEABILITY AND WASHING CHARACTERISTICS OF FLOCCULATED KAOLINITE FILTER CAKES. HYDRAULIC PERMEABILITY AND PARTICLE ORIENTATION
The hydraulic permeabilities of gravity-settled beds of kaolinite prepared by sedimentation of clay suspensions in various states of aggregation, and after pressure consolidation, were measured as functions of porosity, and compared with predictions of the KozenyCarman equation. Concurrently, the degree of particle orientation in these cakes was independently measured by a low-angle x-ray diffraction technique. At high porosities (ca. 0.8 and higher), cake permeabilities were substantially higher than the predicted values; this is explained by assuming the beds to be comprised of randomly distributed flocs wherein primary fluid flow takes place through large interfloc pores. At lower porosities, (0.8 to 0.45) the measured permeabilities lie substantially below predicted values, depend greatly on the state of aggregation of the clay in the original suspension, and correlate surprisingly well with the degree of particle orientation as revealed by x-ray analysis. I t is concluded that anomalously high hydraulic tortuosities, attributable to orientation, account for deviations from the KozenyCarman equation, and the conditions favoring face-to-face (as opposed to edge-to-face) particle attractions in dilute suspensions favor high orientation (and low permeability) in consolidated kaolinite sediments. Surprisingly, polymer-flocced clay shows greater orientation (and lower permeability) than acid-flocced clay, and salt-flocced clay greater orientation than dispersed clay.
A . S.Michaels, W. E. Baker, H. J. Bixler, and W. R. Vieth, Massachusetts Institute of Technology, Cambridge, Mass.
IND. ENG.CHEM.FUNDAMENTALS 6,25-33 (1967)
N . W. Cayey and J. Estrin, Clarkson College of Technology, Potsdam, N . Y.
IND.ENG CHEM.FUNDAMENTALS 6,13-20 (1967)
BURNING RATES OF DEVOLATILIZED COAL PARTICLES
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The rates of burning of coke particles have been measured during their fall ( R e < 5 ) through a hot furnace tube containing atmospheres with different amounts of oxygen. A comparison of the initial burning rate with the burning time has shown that the rate must fall markedly during combustion. Increasing the ash content, carbon burnoff, particle size, and apparent density lowers the burning rate, and increasing the oxygen concentration and gas temperature increases the rate. The temperature coefficients of the burning rates of cokes prepared from different coals show that two temperature regimes exist in the burning process. Although the higher temperature regime is applicable solely on the basis of diffusion of oxygen to the particle, the lower temperature regime is not wholly explicable on the basis of the chemical kinetics of the process.
M . A . Nettleton, Central Electricity Research Laboratories, Leatherhead, Surrey, England IND.ENG.CHEM.FUNDAMENTALS 6, 20-25 (1967)
PERMEABILITY AND WASHING CHARACTERISTICS OF FLOCCULATED KAOLINITE FILTER CAKES. WASHING CHARACTERISTICS
The washing characteristics of gravity-settled beds of kaolinite prepared by sedimentation of clay suspensions and modified by pressure consolidation were studied, using picric acid as a tracer solute. At high porosities (20.86) the washing behavior of flocculated kaolinite filter cakes is erratic, because of irreproducible cracking, and the displacement efficiency is low. Below a porosity of 0.86, the washing curves are reproducible, show no evidence of significant solute holdup, and are uninfluenced by bed porosity or extent of flocculation. Except at porosities above 0.86, the washing behavior is satisfactorily described as plug flow displacement coupled with axial dispersion of solute. This behavior is consistent with the results of a companion study, in which it was shown that floc breakdown occurs below a porosity of about 0.85, leading to a cake with a normal pore size distribution. The axial dispersion coefficients in such cakes equal the molecular diffusion constant of picric acid, divided by the hydraulic tortuosity of the cake, for the region in which the Peclet number is less than unity.
A. S. Michaels, W. E. Baker, H. J . Bixler, and W. R. Vieth, Massachusetts Institute of Technology, Cambridge, Mass.
IND.ENO.CHEM.FUNDAMENTALS 6, 33-40 (1967) (Continued on page 90) VOL. 5 9
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BRIEFS
LIQUID-VAPOR SYSTEM SOz-NH3-HzO AT 25' C.
In spite of the industrial importance of the S02-NH3-HzO system in connection with ammonium sulfite paper pulping processes, little basic work has been done in recent years to credit claims that HzS03 and ",OH do not exist and that S205-2ion is an important constituent. No complete analyis has been made without assuming ideal solutions. This work uses modified standard procedures to obtain infrared absorption spectra, p H measurements, and electrical conductivity measurements for solutions over the entire range of mole ratios of NH3 to SO*. T h e results indicate that only the species H+, OH-, HS03-, SO-2, NH,+, a solvated form of SOz, and a solvated form of NH3 exist in the solutions in significant amounts. Negligibility cr nsiderations combined with a theoretical treatment allow calculations of species concentration for solutions of pH less than 7.0. Thc treatment i s rigorous and requires no assumptions about ideal solutions.
W. D . Scott and J . L. McCarthy, Unioersity nf Washington, Seattle, Wash.
ESTIMATION OF PROPERTIES OF DILUTE POLAR GASES FROM A POTENTIAL ENERGY FUNCTION
The transport properties of dilute polar gases are reproduced accurately by the 12-6 pair-potential energy function with temperature-dependent parameters, E * and r* (or u ) . These parameters are defined from the classical electrostatic point dipole-dipole and dipole-induced dipole interactions by the canonical average over the relative orientations of the molecules, and adding nonpolar attraction and repulsion terms. The parameters are evaluated from data and the 12-6 tables by a simple, unambiguous graphical intersection point, rather than by the tedious and subjective curvefitting necessary in treatments based upon the Stockmayer potential function.
Jae Hn Bae and T . M . Reed 111, University nf Florida, Gainesuille, Fla. IXD.ENG.CHEM.FUNDAMEKTALS 6, 67-72 (1967)
IND. ENG.CHEM. FUNDAMENTALS 6,40-48 (1967)
MACROSCOPIC APPROACH TO RECIPROCAL RELATIONS IN IRREVERSIBLE THERMODYNAMICS
The validity of the Onsager-Casimir reciprocal relations is reviewed within the theoretical framework of macroscopic nonequilibrium thermodynamics. T h e evidence indicates that reciprocal relations can be established convincingly only by either experiment or appeal to a microscopic theory.
Frank C. Andrews, Unizersity of Wisconsin, Madison, Wis. IKD. ENG.CHEM. FUNDAMENTALS 6, 48-51 (1967)
MOLECULAR THERMODYNAMICS OF SIMPLE LIQUIDS. PONENTS
PURE COM-
Thermodynamic properties of simple liquids are calculated from a n analytical partition function based on a modification of Prigogine's cell theory and on a three-parameter theorem of corresponding states. T h e partition function gives an excellent representation of the configurational properties of 15 liquids ranging in molecular complexity from argon to neopentane. Three characteristic molecular parameters are sufficient to calculate the configurational energy and entropy, volume, coefficient of expansion, and compressibility. These parameters are a molecular size, a pair-potential energy, and a term closely related to noncentral intermolecular forces; this last parameter is a nearly linear function of Pitzer's acentric factor. The main application of this statistical thermodynamic treatment follows from its straightforward extension to liquid mixtures.
Henri Renon, C. A. Eckert, and J . M . Prausnitr, University nf CaliJornia, Berkeley, Calif., and National Bureau nf Standards, Boulder, Cob. IND.ENG.CHEM.FUNDAMEKTALS 6, 52-58 (1967)
A PREDICTIVE THEORY FOR MULTICOMPONENT DIFFUSION COEFFICIENTS
T h e modified absolute rate theory is extended to multicomponent systems, and expressions for the variation of the multicomponent friction coefficients with composition are obtained. These relationships, in terms of the values of the diffusion coefficients of the various binary pairs a t infinite dilution, are confirmed for some recently studied ternary systems. Ternary diffusion coefficients are calculated on the basis of the predicted friction coefficients. T h e theory correctly predicts the relative magnitude of the main diffusion coefficients in all cases with an average absolute deviation of 570. T h e theory is also shown to predict properly the relative magnitude of the cross diffusion coefficients as well as to reproduce the correct sign on these terms.
Harry T. Cullinan, Jr., and M . R . Cusick, State Uniwsity of New York at Bufalo, Bufalo, N.Y . IND.END.CHEM.FUNDAMENTALS 6,72-77 (1967)
ESTIMATING LIQUID DlFFUSlVlTY
The main limitation of the Wilke-Chang correlation for predicting liquid diffusivities has been eliminated by replacing the association parameter of this equation by solvent volume raised to l/3. Based on this, two equations have been proposed for V ~ / V 4 I 1.5 and V2/V1 > 1.5, which represent the experimental data with average deviations of 13.5 and IS%, respectively. VI and V2 represent the molecular volumes of the solute and solvent, respectively.
K . A . Reddy and L. K . Doraiswamy, hrational Chemical Laboratory' Pnnna, India MOLECULAR THERMODYNAMICS OF SIMPLE LIQUIDS.
MIXTURES
IND.ENG.CHEM.FUNDAMENTALS 6,77-79 (1967)
T h e analytical partition function for pure, simple liquids is generalized for liquid mixtures containing any desired number of components. The properties of liquid mixtures are calculated from standard statistical mechanical relations on the basis of Scott's two-liquid theory coupled with a three-parameter theorem of corresponding states. The effect of three molecular parameters on solution excess function is investigated and it is shown that these are very sensitive to the characteristic energy for two unlike molecules; in general, this energy is not sufficiently well approximated by the geometric-mean assumption but must be determined by some mixture property such as the second virial cross coefficient, Bls. Calculated excess Gibbs energies, enthalpies, and volumes agree very well with experimental results for 17 binary systems containing simple, nonpolar molecules.
When the rate of a heterogeneous catalytic reaction between two reactants obeys a Langmuir-Hinshelwood (Hougen-Watson) type of rate equation, the effectiveness factor of a porous catalyst under isothermal conditions may exceed unity and may be multiplevalued. I n the present work, some of the effects of initial reactant concentrations inside and outside the catalyst pellet upon the ultimate steady-state behavior are explored.
C. A. Eckert, Henri Renon, and J . M . Prausnitr, University of California, Berkeley, Calif,, and National Bureau of Standards, Boulder, Colo.
J . S. Hartman, G. W . Roberts, and C. N . Satterjeld, Massachusetts Institute of Technology, Cambridge, Mass.
IND.END.CHEM.FUNDAMENTALS 6, 58-67 (1967)
IND.ENC. CHEM. FUNDAMENTALS 6,80-83 (1967)
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INDUSTRIAL AND ENGINEERING CHEMISTRY
EFFECTS OF INITIAL CONDITIONS ON STEADY-STATE ACTIVITY OF CATALYST PARTICLES
BRIEFS TREATMENT OF ISOBARIC BINARY VAPOR-LIQUID EQUILIBRIUM DATA
A new approach is proposed to treat isobaric, binary vapor-liquid equilibrium data so that correlations will be consistent thermodynamically and also include other physical constraints.
fractional surface coverage by wires. I n addition, the model and the data showed a broad maximum for a fractional surface coverage ofabout 18%.
Dauid G. Thomas, Oak Ridge National Laboratory, Oak Ridge, Tenn.
IND.ENG.CHEM.FUNDAMENTALS 6, 97-103 (1967)
L. C. Tao, University of Nebraska, Lincoln, Neb. IND.ENG.CHEM.FUNDAMENTALS 6, 83-86 (1967) EFFECT OF MEAN FLOW O N THE WALL DAMPING OF FINITE-AMPLITUDE GAS PULSATIONS
DEGREES OF FREEDOM FOR UNSTEADY-STATE DISTILLATION PROCESSES
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T h e usual method of determining the number of degrees of freedom for a distillation column is shown to be incorrect when applied to unsteady-state processes. The error is in neglecting the various holdups in the system, which provide extra degrees of freedom. T h e additional degrees of freedom exactly equal the number of holdups which may be specified. The design of columns for steady-state operation is not affected by these additional degrees of freedom, but they should be considered when developing mathematical models or analyzing possible control systems in which the number of independent controllers is equal to the degrees of freedom.
G. M . Howard, University of Connecticut, Storrs, Conn. IND.ENG.CHEM.FUNDAMENTALS 6,86-89 (1967)
To study the effect of mean flow on the wall damping of finiteamplitude gas pulsations, experiments were carried out in an airfilled 1.5-inch diameter smooth tube having a n oscillating piston a t one end and the other end open to the atmosphere. The mean flow was introduced through a critical-flow orifice in the tube wall near the piston. The pressure amplitude a t resonance decreased with increasing Mach number. This effect was most pronounced a t low Mach numbers, where flow reversal occurred. T h e experimental results were compared to the predicted values by two types of mathematical analyses: a linearized closed form solution of the wave equation including mean flow and damping, and a nonlinear numerical solution using the method of characteristics. Both techniques were able to predict the effect of mean flow, the latter being considerably more accurate. This comparison suggests that the nonlinear effects are important. I n the two cases the friction factor was chosen so that the theory agreed with experiment when no mean flow was present. No additional empirical parameters were used in the treatment of the flow effect. G. E. Klinzing and A . 0 . Converse, Carnegie Institute of Technology, Pittsburgh, Pa.
IND.ENG.CHEM.FUNDAMENTALS 6, 103-107 (1967) TURBULENT HEAT ,TRANSFER TO A NONEQUlLlBRlUM CHEMICALLY REACTING GAS
Numerical solutions have been obtained for heat transfer to a reversibly reacting gas in the turbulent boundary layer on the surface of a rotating cylinder. By restricting the study of cases of a small temperature driving force, very general results are obtained in terms of a n arbitrary reaction rate expression. By presenting these results in a dimensionless form, they are found to be completely insensitive to wide variations in the Reynolds and Prandtl numbers when the Lewis number is fixed. As the Lewis number is changed, significant variations in the results are noted; these variations are correlated in an efficient manner that permits accurate interpolation of the effect of the Lewis number. Finally, the general theoretical results obtained in the present study are compared with previously published data for heat transfer to decomposing nitrogen dioxide gas in the turbulent boundary layer on the surface of a rotating cylinder.
P. L. T. Brian and S. W. Bodman, Massachusetts Institute of Technology, Cambridge, Mass.
GENERAL BALANCE EQUATION FOR A PHASE INTERFACE
A phase interface is viewed as a three-dimensional region which separates the bulk portions of two phases and in which the constitutive equations (for mass flux, stress, energy flux, .) may differ from those applicable in the bulk portions of each phase. T h e interfacial region may include a zingular surface; otherwise, all quantities are continuous functions of position. Two forms of the general balance equation or conservation law (for mass, momentum, energy, . . .) a t a phase interface are derived. The rigorous form requires knowledge of the constitutive equations in the interfacial region. The approximate form follows from the general viewpoint of Buff; to use it one must make what amounts to a constitutive assumption for a distributed source term which accounts for “surface behavior.”
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John C. Slattery, Northwestern University, Euanston, Ill.
IND.ENG.CHEM.FUNDAMENTALS 6,108-115 (1967)
IND.ENG.CHEM.FUNDAMENTALS 6,89-97 (1967) ASYMPTOTIC INTEGRATION OF OVER-ALL MASS AND ENERGY BALANCES FOR NONISOTHERMAL REACTION SYSTEMS
A technique is presented for integrating over-all mass and energy
ENHANCEMENT OF FILM CONDENSATION HEAT TRANSFER RATES O N VERTICAL TUBES BY VERTICAL WIRES
Vertical wires, 0.030 and 0.062 inch in diameter, loosely attached to a ‘/zinch 0.d. vertical tube 42l/z inches long, markedly increase the film condensation heat transfer coefficient. At a heat flux of 2 X l o 4 B.t.u./(hr.) (sq. ft.), four wires obstructing 7.6% of the surface increased the condensing coefficient by a factor of 3.14 (a 214% increase), while 12 wires obstructing 23y0 of the surface increased the condensing coefficient by a factor of 4.53 (a 353% increase). A qualitative model based on the film and rivulet hydrodynamics predicted the observed increase in condensing coefficient with decreasing rate of condensation and increasing
balances associated with certain nonisothermal reaction systems, I n the case of adiabatic systems, the technique yields results which are asymptotically valid for small times and also for large values of activation energy at all times; energies of value no greater than those found typically permit good results. The method can be used for complicated kinetics and variable thermal properties and as such constitutes the only analytical method available for most adiabatic reactions. I t also can be used for nonadiabatic systems, if the heat transfer rate is sufficiently small.
Owen T . Hanna and Robert S. Kapner, Rensselaer Polytechnic Institute, Troy, N . Y.
IND.ENO.CHEM.FUNDAMENTALS 6, 116-120 (1967) (Continued on page 92) VOL. 5 9
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BRIEFS TRANSIENT RESPONSE AND MOMENTS ANALYSIS OF THE BACKFLOW CELL MODEL FOR FLOW SYSTEMS WITH LONGITUDINAL MIXING
Equations have been derived for determining the over-all impulse and step responses of the backflow cell modei and for evaluating the mean time, variance, and skew moments of the cell responses to a n impulse input of tracer in the inlet stream. The moments and the transient respome curves are compared to those of the finite continuous diffusion model with respect to number of cells and degree of backmixing or dispersion.
measurement of the average heat transfer coefficient for a particle of fluidized bed. Temperature differences of several degrees can be measured with estimated errors of less than a few per cent. The cost of developed units could be about $1150, with $900 for the heat source.
James J . Barker, 10 Walden Ave., Jericho, L. I., IT.Y . IND. EKG.CHEM.FUNDAMENTALS 6, 139-142 (1967)
M . H. Roemer and L . D . Durhin, Texas A €8 M Uniiiersity, College Station, Tex. COMMUNICATION. CONVERGENCE OF APPROXIMATION METHODS USED I N MULTICOMPONENT MASS TRANSPORT
I N D .ENG.CHEM.FUNDAMENTALS 6, 120-129 (1967)
EXPERIMENTAL TECHNIQUE. APPARATUS FOR ACCURATE, RAPID DETERMINATIONS OF THE SOLUBILITY OF GASES IN LIQUIDS
An apparatus that accurately and rapidly determines the solubility of gases in liquids consists of a lower bulb containing a measured volume of degassed solvent connected with a n upper bulb into which a measured amount of a gas is introduced. A side arm contains a glass-enclosed, magnetically activated pump, which rapidly pumps solvent into the upper bulb, where it runs down the side continually exposing fresh surface of solvent to the gas. T h e solubility of the gas is calculated from the pressure of undissolved gas. Re-equilibrating at a series of temperatures permits calculation of the entropy of solution.
John Dymond and J . H. Hildehrand, University of CaliJornia, Berkeley, CaliJ. IND. ENG. CHEM.FUKDAMENTALS 6, 130-131 (1967)
A method is given for approximating the flux expressions that can be derived from the Stefan-Maxwell equations or other similar models for multicomponent mass transfer in liquids and gases. T h e conditions for covergence of the method are given.
G . B. Wills, Virginia Polytechnic Institute, Blacksburg, Va. IND. ENG.CHEM. FUNDAMENTALS 6,142-144 (1967)
COMMUNICATION. POROUS MEDIA
FLOW OF VISCOELASTIC FLUIDS THROUGH
The laminar flow of toluene solutions of polyisobutylene is studied in beds packed with uniform glass spheres, sand, and binary mixtures of glass spheres. The data may be correlated by a powerlaw modification of the Blake-Kozeny equation. No evidence of viscoelastic effects is observed.
N . Y . Gaitonde and Stanley Middleman, Unioersity of Rochester, Rochester, N. Y. IND.END.CHEM.FUNDAMENTALS 6, 145-147 (1967)
EXPERIMENTAL TECHNIQUE. EFFECT OF DISSOLVED OXYGEN ON THE REDOX METHOD FOR MEASUREMENT OF MASS TRANSFER COEFFICIENTS
An electrochemical technique was used to measure average mass transfer coefficients at a solid-liquid interface. The effects of electrode length, flow rate, and the presence of air on the measured mass transfer coefficients were studied for a ferro-ferricyanide solution in turbulent flow in a smooth pipe, using a wire electrode mounted flush to the pipe wall, and a ring electrode which constituted a portion of the pipe wall. Experimental results compare well with heat and mass transfer data of other investigators. For the limited flow range ( N R ~ 22,000) and L I D ratios ( L I D 1.0) studied, the Leveque solution predicted coefficients to within +8y0 of the experimental values. IYith certain precautions this technique can be used to measure mass transfcr coefficients in the presence of air. Coefficients measured with the 1/8-inch electrode a t oxygen saturations below 507' are within 370 of the correct value for a n operating time of 170 minutes; those measured with the 1inch electrode are within 1.674 of the correct values for a n operating time of 175 minutes.
