BRIEFS of articles in this month's quarterly - ACS Publications

BRIEFS Summary of papers published in this month's research quarterly, I@EC Fundamentals Subscription rates for this and associated quarterlies: U.S.

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MECHANISM OF CALCIUM SULFATE SCALE DEPOSITION ON HEAT TRANSFER SURFACES

Investigation of C a s 0 4 scale deposition in an annular heat exchanger shows that surface nucleation along a heated tube occurs a t a nonuniform rate, is highest a t the downstream edge, and leads to the formation of a correspondingly nonuniform scale layer, thickest at the downstream edge. Rates of nucleate front propagation and scale-layer growth increase with surface temperature, decrease with increasing flow velocity, diminish with fine filtration, but are unaffected by the degree of recirculation. Transient nucleation is a predominant mechanism in C a s 0 4 scale formation. A kinetic model based on this mechanism is presented.

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FREQUENCY RESPONSE OF NONLINEAR SYSTEMS

The equations used to describe the dynamic operation of most chemical processes either are nonlinear or have variable coefficients. Previous discussions of the dynamic response of these systems normally have been based on a linearization of the state equations. A procedure which can be used to determine whether or not the linearized analysis is valid for both lumped and distributed parameter process is presented. It can be used to assess the potential advantages of periodic operation of a stable process.

A . B. Ritter and J . M . Douglas, CTniterszty of Rochester, Rochester, .V.Y. 14627

Datid Hasson and Joseph ZahaL'i, Technion-Israel Inrtitute of Technology, Haifa, Israel

IND.ENC. CHEM.FUNDAMENTALS 9, 21-28 (1970)


DETERMINATION OF DYNAMIC MODEL PARAMETERS USING QUASILINEARIZATION

RATE-CONTROLLING PATH FOR CATALYTIC BUTANE DEHYDROGENATION

In an experimental study of the nature of the rate-controlling steps in the dehydrogenation of butane to butenes and the reverse hydrogenation reaction over a commercial chromia-alumina catalyst, runs were made in a differential continuous flow reactor containing 40 grams of pelleted catalyst. 14C-taggedbutane and 1-butene were used as tracers to follow independently the unidirectional rates while the over-all reaction was simultaneously observed. The system was studied over a range of ratios of forward to reverse reaction rates from 0.02 to 10; an apparent stoichiometric number close to unity was observed. Chemisorption or desorption of hydrogen is not a rate-controlling step, or very high apparent stoichiometric numbers would have been observed using 14C as a tracer. One or more rate-controlling steps exist in the elementary reactions involving transformation of the hydrocarbon skeleton.

John Happel and R: S. Atkins, New York University, Bronx, Nr Y. 70453

IND.ENG.CHEM:FUNDAMENTALS 9, 11-14 (1970)

PROBLEMS IN CHEMICAL REACTOR ANALYSIS WITH STOCHASTIC FEATURES. CONTROL OF LINEARIZED DISTRIBUTED SYSTEMS ON DISCRETE AND CORRUPTED OBSERVATIONS

The stochastic control problem for linear first-order partial differential equations has been solved by Denn, but his solution requires a knowledge of the state a t all times and places. Here we consider the problem of estimating the state at all places from measurements made from a discrete set ofpoints. A set of filtering equations of structure similar to the usual Riccati form may be developed and used in the optimal control. Calculations for a tubular interchanger with constant wall temperature are exhibited, in which measurements are made at three points.

T . M . Pell, Jr., and Rutherford Aris, University of Minnesota, Minneapolis, Mznn. 55455 IND.ENG.CHEM.FUNDAMENTALS 9, 15-20 (1970) 62

INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY

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Quasilinearization was applied to determining numerical values of the parameters in a dynamic model. It can be used to identify a dead time (time delay or transport lag) along with other parameters such as time constants and gains. The region in parameter space from which convergence will occur can be increased by incorporating Marquardt's method into this portion of quasilinearization. The model equation instead of the fundamental solutions can be used to calculate the output and its derivatives for each iteration. The effect of data density and the number of significant figures in the data on the convergence of quasilinearization are discussed, and performance of quasilinearization is compared to multidimensional search techniques used on similar problems.

B. L. Ramaker, C. L. Smith, and P . W. Murrill, Louisianu State Unzversip, Baton Rouge, L a . 70803 IND.ENC.CHEM.FUNDAMENTALS 9, 28-34 (1970)

INTEGRAL ACTION IN THE OPTIMAL CONTROL OF LINEAR SYSTEMS WITH QUADRATIC PERFORMANCE INDEX

In the application of optimal control theory in the design of feedback control of linear systems with quadratic performance index, the time integral of the output variable is introduced as a new variable. Integral action is thus obtained. Offset due to step change of lead variable and/or to modeling error can be avoided. Examples of continuous and sampled-data control systems arc given.

Yen-Ping Shih, Cheng Kung Unzversity, Taznan, Taiwan, China IND.END.CHEM. FUNDAMENTALS 9, 35-37 (1970) A CONTROL OF A FIXED-BED CHEMICAL REACTOR

Disturbances in a fixed-bed reactor are controlled by exploiting the interaction between the traveling waves of temperature and concentration within the bed. A secondary reactant stream, injected at an intermediate point along the bed and modulated in accordance with temperature measurements only, provides a localized and traveling corrective action that annihilates a disturbance by the time it reaches the reactor effluent. Calculations for a first-order, homogeneous, exothermic reaction show that

a temperature upset is the most difficult disturbance to control. Further, because of the dominance of the slower thermal wave in these reactors, the task of composition control is similar to that of temperature control. An approximation technique, developed to match both the short- and long-time behavior of the reactor and its controllers, simplified the study of the dynamics of the reactor under control. B. E. Stangeland and A . S. Foss, University of California, Berkeley, Calty. 94720 IND.ENC. CHEM.FUNDAMENTALS 9, 38-48 (1970)

BRANCH AND BOUND SYNTHESIS OF INTEGRATED PROCESS DESIGNS

The branch and bound techniques of problem solving can be used to guide the design engineer during the invention of integrated process designs. When confronted with a design problem for which no method of design is known, the engineer gainfully can branch to simpler design problems which bound the original problem. Often, the optimal solution to the original unsolvable design problem can be inferred from the solutions to bounding problems. These ideas are illustrated in the design of a n energy exchange system.

K . F. Lee, A . H. Masso, and D. F. Rudd, University of Wisconsin, Madison, Wis. 53706 IND.ENC.CHEM.FUNDAMENTALS 9, 48-58 (1970)

NEAR-OPTIMAL CONTROL BY TRAJECTORY APPROXIMATION. TUBULAR REACTORSWITH AXIAL DISPERSION

A new method for obtaining near-optimal control policies is based on the use of weighted residual techniques to solve approximately the state and adjoint differential equations which result from application of Pontryagin's maximum principle to the optimal control problem. The technique, trajectory approximation, is applied to the determination of optimal temperature profiles for a tubular reactor with axial dispersion, and the results are compared to numerical solutions obtained by quasilinearization. The results indicate that the method is computationally sound. I n fact, it could lead to the realization of on-line near-optimal control for many chemical processes. L. L. Lynn, E. S. Parkin, and R. L. Zahradnik, Carnegie-Mellon University, Pittsburgh, Pa. 15213 IND.ENC.CHEM.FUNDAMENTALS 9, 58-63 (1970)

CORRESPONDENCE PRINCIPLE FOR TRANSPORT PROPERTIES OF DENSE FLUIDS. NONPOLAR POLYATOMIC FLUIDS

THERMAL CONDUCTIVITY OF GASES. ATMOSPHERIC PRESSURE

ORGANIC COMPOUNDS AT

Thermal conductivity measurements, k*, available in the literature for organic compounds in their gaseous state and at atmospheric pressure, were used to obtain the product, k*X, where the parameter, X = M1/ZT,"/6/P,2/3. This product is temperaturedependent and represents the composite contribution of translational, rotational, and vibrational modes of energy transfer. The translational contribution, (k*X),, is identical to k*h for monatomic gases. The difference, k*X - (k*X)t = X, represents the contribution due to vibrational and rotational effects. Specific relationships of X/X,vs. TRwere obtained for the alcohols, oxygencontaining compounds (esters, ketones, aldehydes), halides, amines, and cyclics. Group contributions were also developed which permit the establishment of X I , the value of X a t TR = 1.OO for these classes of compounds. Thermal conductivities calculated for 52 organic compounds were compared with corresponding experimental values to produce a n average deviation of 3.0% for 291 points considered. Dipak Roy and George Thodos, Northwestern University, Evanston, Ill. 60201

IND.ENG.CHEM.FUNDAMENTALS 9, 71-79 (1970)

PREDICTIONOF VISCOSITY OF LIQUID HYDROCARBONS

The liquid viscosity of four series of homologs-n-paraffins, n-lalkenes, n-alkylcyclohexanes, and n-alkylbenzenes-is estimated from density and molecular weight data. An empirical equation for each of the series, n-paraffins to n-alkylbenzenes, gives average errors of 1.78, 1.95, 2.39, and 3.46y0, respectively.

M. L. Druin and S. I . Kreps, Newark College of Engineering, Newark, N.J. 07102

IND.ENC.CHEM.FUNDAMENTALS 9, 79-83 (1970)

VARIATION OF LIQUID DIFFUSION COEFFICIENTS WITH COMPOSITION, BINARY SYSTEMS

The predictive capability of the Vignes equation is limited, with considerable deviations encountered in a number of systems. A modification of this expression is developed accounting for solution viscosity. Comparison with data for a large number of known systems shows that this modified version improves the over-all predictability. The concept of segmental diffusion is used to explain the results for mixtures of n-alkanes.

J o h n Lefler and Harry T. Cullinan, Jr., State University of New York at Buffalo, Bufalo, N . Y . 14214 IND.ENC. CHEM. FUNDAMENTALS 9, 84-88 (1970)

A model for hindered rotation a t high densities is based on a simple harmonic oscillator theory. The expression for the Hamiltonian so obtained, substituted into the time correlation function expressions for the transport coefficients, gives rise to a more general principle of corresponding states. The reduced equations contain a rotational coupling coefficient which acts as a third parameter; however, only two independent variables are needed in the correlation. For monatomic fluids, or in the low density limit, these equations reduce correctly to the simple two-parameter correspondence principle. The proposed relationships give good agreement for viscosities, thermal conductivities, and self-diffusion coefficients of the 25 fluids tested over a wide range of temperatures and pressures. The model accounts in a reasonable way for thermodynamic properties of polyatomic fluids.

The modification of the Vignes equation, proposed and demonstrated for binary liquid systems by Leffler and Cullinan, is extended to the case of a dilute species diffusing in a mixture of two solvents. Experimental results are reported for the three dilute limits of the systems hexane-benzene-cyclohexane, acetone-benzene-cyclohexane, and acetone-hexane-carbon tetrachloride. These data and previous results are used to test the proposed predictive equation. Agreement is generally good.

M. J. Tham and K . E. Gubbins, Universib of Florida, Gainesville, Fla. 3260 7

J o h n Lefler and Harry T . Cullinan, Jr., State University of New York at Bufalo, Bufalo, N. Y. 14214



VARIATION OF LIQUID DIFFUSION COEFFICIENTSWITH COMPOSITION. DILUTE TERNARY SYSTEMS

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BRIEFS INTERNAL PRESSUREMEASUREMENTS AND LIQUID-STATE ENERGIES

Internal pressure, P, = (bE/dY),, was measured on cyclohexane over a 7OoC temperature range. These data are compared with energies of vaporization, AEJ’. The ratio, ( P % P / A E V ) ,is often interpreted as an exponent, n, in the energy-volume relation E = - a / P “ . Present data, however, show that ( P * P - A E v ) is equal to 3RT/2, within experimental error, with n equal to unity and a a function of T. This difference can be attributed to the potential energy associated with the external vibrational modes of the cyclohexane molecules in the liquid state. I t appears that the total liquid-state energy can be given as the sum of the various energetic contributions, allowing separability of dispersion, polar, and even hydrogen-bonding energies in agreement with treatment given by Blanks and Prausnitz and Hansen.

E. B. Bagley, T . P. Nelson, J . W . Barlow, and S-A. Chcn, Washington University, St. Louis, Ma. 63130 IND.ENG.CHEM.FUNDAMENTALS 9, 93-97 (1970)

ADSORPTION INTO IRROTATIONAL STAGNATION FLOW. CASE STUDY IN CONVECTIVE DIFFUSION THEORY

Ideal potential flow a t a perfectly free surface contains the most important effect convection can have on simple transfer between fluids, and leads to convective diffusion problems that can be solved exactly for physical insight and theoretical modeling, especially of turbulent transfer. One problcm is solved by means of the convective diffusion potential and separation of variables, invariance properties and a similarity transformation, or material coordinates and warped time, these latter suggesting new lines of attack of convective diffusion. The solution for unsteady absorption into steady flow shows plainly that relative motion of liquid a t different levels close beneath a n interface may not always be disregarded, and that “film” and “penetration” models of interphase transfer are limiting cases a t best. Flow toward the interface generally enhances transfer; flow away diminishes transfer. W. C. Chan and L. E. Scriven, Universib of Minnesota, Minneapolis,

Minn. 55455 IND.ENG.CHEM.FUNDAMENTALS 9, 114-120 (1970) APPLICATION OF BRANCHING PROCESS FOR LIQUID ATOMIZATION

The stochastic analysis due to Fillippov was applied to liquid atomization. Comparison with the empirical size distribution function obtained by Nukiyama and Tanasawa indicates that the mechanism of atomization may be explained in terms of the stochastic branching process.

Yoshisuke Nakano, U. S. Army Terrestrial Sciences Center, Hanover, N . H. 03755, and Chi Tien, Gracuse Universib, Syracuse, N . Y.


LOCAL AND OVER-ALL MASS TRANSFER RATES AROUND SOLID SPHERESWITH FIRST-ORDER HOMOGENEOUS CHEMICAL REACTION

Numerical solutions to the problem of forced convection mass transfer with first-order homogeneous chemical reaction around solid spheres have been obtained by using the Crank-Nicolson finite-difference technique. Hydrodynamic behavior around a single sphere has been evaluated from the Stokes solution a t low Reynolds numbers and by boundary layer theory a t high Reynolds numbers. For multiparticle systems velocity profiles based on the free surface cell model have been applied. Results are presented in terms of generalized correlations involving the single parameters iVpe1/3/p for N R , ~> 1. These correlations can be used over wide ranges of reaction rate and hydrodynamic variables. W. C. Chen and Robert Pfejer, Cab College of CiQ Universiv of N e w YOrk, New York, N.Y. 10031


FINITE-AMPLITUDE, LONG WAVES O N LIQUID FILMS FLOWING DOWN A PLANE

A theory for predicting the wave forms of finite-amplitude, long waves on liquid films flowing down a plane is presented. I t is a power series expansion in wave number, retaining surface tension in the first-order terms. A major result is that equilibrium amplitudes for most highly amplified waves are expected to be a function of a single group (1.2 NR* - cot I ~ ) ~ / N R ~ N New ~ , data . for viscous oils are adequately correlated by this group, but the data of Kapitza and Kapitza for water and alcohol are not in agreement with those for the oils.

William 3.Krantr and Simon L. Goren, Universib of California, Berkeley, Calif. 94720 IND.ENG.CHEM.FUNDAMENTALS 9, 107-113 (1970) 64

INDUSTRIAL A N D ENGINEERING CHEMISTRY

SEPARATION OF A THREE-COMPONENTGAS MIXTURE IN A N AXISYMMETRIC SUPERSONIC JET

.A numerical analysis is presented on the diffusive separarion of a three-componcnt gas niixrurr of 36.\r, ;O.\r, and TIe in an axisymmetric supersonic j e t , \virh account taken of thc pressurr diffusion in the jet. .An approximate rquation gives the inrrqral mass f!ux of 35.\r along a streamline of argon gas, o n thc basis of a grncralizccl form of the Stcfan-.\i:tx\vrlI cqciations. The flott. ficld of a n axially symmetric frec jrr of ;1 gas misture \vas compuvtl by thc numerical method of characteristics, and both the streainlincs of aryon gas and thc integral diKusion flux of 3c.\r \vcrc calculatcd by using these rcsults. l h c results of the ca!cu!arion arc i n rcasonablc agrcemcnr \virh the experimental data prcrrnred by Beckcr ei al.

Hisashi .\fikami! Ktrrarch L a b o r a t q of .YncIpm Rpacror, sizrute of T t c h n d o g j , Oo/.q;ama. .lftgxro-/;,i, Tu/:J.o, Jufim ISD. Esc. CIit-.\t.FUNDAMLSIALS 9, 121-128

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MEASUREMENTAND CORRELATION OF WATER FROST THERMAL CONDUCTIVITY AND DENSITY

Water frost densities and thermal conductivities were measured in the temperature range of -20” to- 145°F when the frost condensed from air under forced convection conditions on a flat plate in the test section of a wind tunnel. Correlations are presented to predict these frost properties and a structural model based on cinephotomicrographic studies is suggested to explain the observed behavior of the frost crystal deposit.

Gabriel Biguria and L . A . Wenzel, Lehigh Unioersity, Bethlehem, Pa. 18075


ROLE OF COUPLING I N NONISOTHERMAL DIFFUSION. GAS ABSORPTION

An analysis is developed for multicomponent gas absorption accompanied by the heat effect of solution. T h e results are used to

illustrare the interactions of the coupled fluxes in the ammoniawater system and in a hypothetical quinary system.

G. B. DeLancey and S. H. Chiang, University of Pittsburgh, Pittsburgh, Pa. 15273

IND.END.CHEM.FUNDAMENTALS 9, 138-145 (1970)

SIZE DISTRIBUTIONOF AGGLOMERATES IN COALESCING DISPERSED PHASE SYSTEMS

The concepts of “free-in-space” and “restricted-in-space’’ agglomeration for coalescing dispersed phase systems have been developed. Free-in-space agglomeration is characteristic of aerosol or colloidal coagulation, while restricted-in-space agglomeration refers to the pelletization or granulation of nuclei. Comparison of these two types of size enlargement mechanisms shows that the resulting size distribution of the agglomerated species is identical in both the cases. In either case, it is characterized by the “extent of agglomeration,” defined as the ratio of the number of agglomerates a t a given time to the initial number. A combinatorial model for the random coalescence process with a monosized initial distribution agrees with the deterministic model. The combinatorial model can also predict the variance of the number of the species of a given size, which cannot be calculated from the deterministic model, and must otherwise be obtained from a complicated stochastic analysis.

K. V. S. Sastry and D. W . Euerstenau, University of California, Berkeley, Calif. 94720 IND.ENG.CHEM.FUNDAMENTALS 9, 145-149 (1970)

EFFECT OF ADSORBED MONOMOLECULAR FILMS ON THE EVAPORATION OF VOLATILE ORGANIC LIQUIDS

To investigate the effect of adsorbed surface-active films on the rate of evaporation of volatile organic liquids, a series of partially fluorinated compounds was studied as monolayers adsorbed from solution or insoluble films spread a t the liquid-vapor interface. I n no instance was the rate of evaporation significantly reduced by the presence of a monomolecular film. Insoluble multimolecular films of polydimethylsiloxanes, however, effectively reduced the rate of evaporation, if the film thickness was sufficient to decrease the rate of diffusion of the solvent molecules through the film to a value below their rate of diffusion through the saturated, nonturbulent vapor layer overlying the surface. Thin layers of water, containing suitable fluorocarbon spreading agents, also reduced the rate of evaporation of certain volatile organic liquids.

M . K. Bernett, L. A . Halper, N . L. Jarvis, and T. M . Thomas, Naval Research Laboratory, Washington, D.C. 20390 IND.ENG.CHEM.FUNDAMENTALS 9, 150-156 (1970)

SOLVENT EFFECTS ON ?HE VOLUME OF A TRANSITION STATE

The partial molal volumes in solution of the transition state of the Menschutkin reaction between pyridine and methyl iodide have been determined. Accurate partial molal volumes of both reactants have been measured and used in conjunction with existing high-pressure kinetic data to find the volumes of the complex. Such results are useful in the interpretation of the structure of the transition state and its intermolecular interactions in solution.

J . R. McCabe, R. A . Grieger, and C. A. Eckert, University of Illinois, Urbana, Ill. 6 180 7 IND.END.CHEM.FUNDAMENTALS 9, 156-160 (1970)

SPATIAL DISTRIBUTIONOF ELECTRONDENSITY AND ELECTRIC FIELD STRENGTH IN A HIGH-FREQUENCYDISCHARGE. CRITERIA FOR SIMILARITY

The development of electric discharge processes of direct industrial application has generated an interest in the relationship between the rates at which activated species are formed and the electrical properties of the discharge. Since the rates of discharge processes are related to the electron density and the electric field strength, there is an interest in their spatial variation. These two distributions are examined for a helium discharge sustained between parallel plates of a radio-frequency discharge. The electric field and density distributions are used to calculate the voltage across the discharge and the volume-averaged power density. By maintaining pa, and (l=) constant, the rates of excitation in two reactors of different size can be made identical.

Alexis T . Bell, University of California, Betkeley, Ca1;f. 94720


DIRECT MEASUREMENTOF CRYSTAL NUCLEATIONAND GROWTH RATE KINETICS IN A BACKMIXED CRYSTAL SLURRY. STUDY OF THE K~SOISYSTEM

A novel method of generating a fine crystal-size distribution in the 0- to 50-micron size range was developed. This distribution was generated in a mixed suspension of larger-sized crystals, obeyed the exponential population decay law, and was measured by in situ particle counting in the crystallizer discharge using a Model B Coulter particle counter. The specific system studied was K2S04 but the method is applicable to other crystal systems. Quantitative nucleation and growth rate kinetics for the K2S04 system were obtained by fitting the experimental fine crystal-size distribution to the theoretical exponential distribution. Nucleation rate was found to correlate with power-law kinetics of the form J , = kNMTaabwhere J, is the nucleation rate, kw, a , and b are constants, M y is the solids concentration, and s is the supersaturation. Linear crystal growth rate, r , was found to be proportional to supersaturation. Thus r = k g where k , is a constant. A . D. Randolph and Krishnaswami Rajagopal, University of Florida, Gainesville, Ela.

IND. ENG.CHEM.FUNDAMENTALS 9, 165-171 (1970).

VERSATILE CONSTANT TRANSMISSION PHOTOCHEMICAL REACTOR

A photochemical reactor has been designed which permits constant transmission of the light energy incident on the reactor wall by minimizing the effect of wall deposits through continual scraping of the reactor wall or interface between the light source and reacting solution, the reactor operates over a wide range of solution viscosities. It can be operated as a batch, continuous-flow stirred tank, or wiped-film reactor and is highly suited for conducting photopolymerization or reactions of difunctional molecules.

W. B. Isaacson and S. T. Ting, 3M Co., St. Paul, Minn. 55707 IND.ENC.CHEM. FUNDAMENTALS 9, 171-173 (1970)

SAMPLE-EXTRUSION APPARATUS FOR HIGH-PRESSURE VAPOR-LIQUID EQUILIBRIA. COMPOSITIONS AND DENSITIES AT PRESSURES UP TO THE CRITICAL

A static equilibrium apparatus has been developed for measuring compositions and densities of both phases in high-pressure vaporVOL. 6 2

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liquid equilibria. The apparatus operates a t pressures up to 1000 atm. and at temperatures from -50" to +l5O0C. Samples for density and composition measurements are extruded from the equilibrium cell with no change in cell conditions. Gas chromatography is used for chemical analysis.

B. L. Rogers and J . M . Prausnitz, Department of Chemical Engineering, University of CaliJornia, Berkeley, Calif. IND.ENG.CHEM.FUNDAMENTALS 8, 174-177 (1970)

formation of vapor occurred. The resulting rates of heat transfer were considerably greater than that predicted for a saturated fluid or for forced convection from the constant temperature sphere formed by the liquid-vapor interface. If it is assumed that the film does not exist, a poor correlation exists between the experimental and theoretical results; this assumption cannot be justified, since a film was observed in all cases.

R. IV. Jacobson and F. H. Shair, California Institute of Technology, Pasadena, Calif. 9 1 109 IND.EKG.CHEM.FUNDAMENTALS 9,183-185 (1970)

DETERMINATICM OF SPECIFIC VOLUME OF POLYMER MELTS

Specific volurr~esof polymeric liquids can be measured accurately and conveniently using a thermostated cylindrical vessel, such as the barrel of a laboratory extrusion rheometer. A machinist's dial gage is used to measure the height of a column of weighted polymer confined undFr a weighted piston. Errors due to entrapped air are avoided by using compression-molded specimens and a polyterrafluoroethylene piston head. A single measurement can be completed in about 30 minutes, and the data compare well with those from standard techniques.

K . K . Chee and Alfred Rudin, Uniuersity of Waterloo, Waterloo, Ontario, Canada IND.ENG.CIIEM.FUNDAMENTALS 9, 177-179 (1970)

COMMUNICATION SETTLING OF SPHERES IN DRAG-REDUCINGPOLYMER SOLUTIONS

The fall velocities of spheres in drag-reducing polymer solutions were determined at 20' and 40OC. Drag reduction occurs at Reynolds numbers below the limit lo4 specified by Sanders, a.nd the value of Reynolds number alone is not an adequate indicator of whether the phenomenon is present or not.

Walter W. Carey and R a f l M . Turian, Sjracuse University, Gracuse, N.Y. 13270


CORRESPONDENCE COMMUNICATION ANALYTIC DRIVING-FORCE RELATION FOR PORE-DIFFUSION KINETICS IN FIXED-BED ADSORPTION

An equation describes the course of pore-diffusion breakthrough in fixed-bed adsorption in terms of bulk concentrations a t each point in the bed.

Comments on an article on bubbling bed model-model of gas through fluidized bed.

for flow

L. S. Leung, Department of Chemical Engineering, Universip of Queensland, Brisbane, Australia IND.ENG.CHEM.FUKDAMENTALS 9, 187 (1970)

Theodore Vermeulen and R. E. Quilici, University of California, Berkeley, Calzy. 94720 IND.ENG.CHEM.FUNDAMENTALS 9, 179-180 (1970)

COMMUNICATION DYNAMIC SIMILARITY IN CONTINUOUS STIRRED-TANK REACTORS

The effect of agitation on the residence time distribution function of a continuous stirred-tank reactor was determined experimentally for three reactor sizes. The conditions of dynamic similarity agreed with the three conditions stated by Danckwerts. The influence of the Reynolds number on the flow dynamics of the reactor was established quantitatively for the reactor geometry under study. The residence time distribution function, I(B), was used as a criterion to measure the degree of mixing. It proved more sensitive to changes in the agitation speed than any of the other time distribution functions.

CORRESPONDENCE

Comments on an article on strategy for estimation of rate constants from isothermal data.

John Erjavec, Uniuersip of Wisconsin, Madison, W i s . 53706 J . M . Eakman, University of Nebraska, Lincoln, Neb. 66508

IND.ENG.CHEM.FUNDAMENTALS 9,187-188 (1970)

CORRESPONDENCE

Comments on an article on momentum, heat, and mass transfer analogy for turbulent flow in circular pipes.

L. C. Thomas, University of Akron, Akron, Ohio G. A. Hughmark, Ethyl Gorp., Baton Rouge, La. 7 0 8 2 1 IND.ENG.CHEM.FUNDAMENTALS 9, 188-190 (1970)

Ramon L. Cerro and Jose M : Patera Facultad de Ingenieria Quimica, Santa Fe, Argentina

IND.END.CHEM.FUNDAMENTALS 9, 181-183 (1970)

CORRESPONDENCE

Comments on an article on some problems in chemical reactor analysis with stochastic features. COMMUNICATION

R. P. King, National Institute f o r Metallurgy Research Group, University

FILM BOILING FROM A SPHERE DURING FORCED CONVECTION OF SUBCOOLED WATER

of Natal, Durgan, South Africa

Forced convection film boiling from a sphere was investigated. The water was subcooled and a vapor film existed in which no net 66

INDUSTRIAL AND E N G I N E E R I N G CHEMISTRY

T . M . Pell, Jr., Tennessee Eastman Go., Kingsport, Tenn. 37662, and Rutherford Aris, University of Minnesota, Minneapolis, Minn. 55455 IND.ENG.CHEM.FUNDAMENTALS 9,190-192 (1970)

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