BRIEFS Summary of papers published in this month’s research quarterly, 1@EC Fundamentals RATES OF POISONING IN FIXEDBED REACTORS
T h e timedependent activity of a fixedbed reactor, which is being poisoned by coke formation or irreversible adsorption of a feed component, is evaluated. T h e activity remaining depends critically upon the interacting values of the Thiele modulus and the number of solidphase diffusion transfer units.
J . H. Olson, Unitersity of Delaware, Newark, Del. 19711 IND.ENG.CHEM.FUNDAMENTALS 7,185188 (1968) UNIFORMITY OF DlFFUSlVlTY IN A NICKEL BASE STEAMHYDROCARBON REFORMING CATALYST
Steady state axial and radial counterdiffusion measurements were made on sliced and drilled ‘/z X 1/2 inch cylindrical commercial nickel base steamhydrocarbon reforming catalyst pellets to determine the degree of anisotropic diffusivity. The tortuosity factor, calculated by a parallelpath pore model was high, about 10, but nearly independent of direction of diffusion or position. There was no significant skin effect on the plane or curved surfaces. The size and appearance of this catalyst differed substantially from most smaller commercial pellets and so the results of this study may not be characteristic of commercial catalysts in general.
P . John Cadle and Charles N . Satterjeld, Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Mass. 02139
IND.END.CHEM.FUNDAMENTALS 7,189192 (1968). ANISOTROPIC DlFFUSlVlTlES IN PRESSED BOEHMITE PELLETS
The effective diffusivity in pellets pressed from powdered boehmite varied by a factor of as much as 3 or 4 with axial distance through the compact. Results are interpreted in terms of the density diffusivity in that they influence the porous structure; consequently, measurements made on one pellet size are not necessarily applicable to the same material in another pellet size or shape even when the pellets have the same density.
P. John Cadle and Charles N . SatterJeld, Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Mass. 02139 IND.ENG.CHEM.FUNDAMENTALS 7, 192197 (1968). THERMAL EFFICIENCY OF THE PRODUCTION OF ACETYLENE FROM CARBON AND HYDROGEN
The heat requirement for the production of acetylene from carbon and hydrogen was investigated experimentally using graphite filaments resistively heated by short timed pulses and condenser discharges. Experimental results approached the theoretical value for graphite vaporization.
J. T. Clarke and B. R. Fox, Brookhaven National Laboratory, Upton, N . Y . 11973 IND.END.CHEM.FUNDAMENTALS 7,197201 (1968) GASEOUS DIFFUSION AND FLOW IN COMMERCIAL CATALYSTS AT PRESSURE LEVELS ABOVE ATMOSPHERIC
Counterdiffusion measurements of helium and nitrogen in the absence of forced flow are reported on five commercial catalysts over the pressure range 1 to 65 atm. and a t ambient temperature. Surface diffusion of nitrogen made a n increasing contribution to the total nitrogen flux with increase in pressure and a t the highest pressure was of comparable magnitude to the volume diffusion flux. Effective surface diffusion coefficients were estimated to be 0.3 to 0.9 X 103 sq. cm. per second. The diffusion data were analyzed in terms of a parallel path pore model. The calculated tortuosity factors were sensibly invariant with pressure; it was concluded that the model can be used with confidence to predict diffusion in a particular catalyst under a variety of conditions from a single diffusion measurement. Steadystate simultaneous diffusion and forced flow measurements at ambient temperature and elevated pressures are reported for a prereduced Harshaw methanol synthesis catalyst. The data were analyzed by the three methods developed by Evans. I n terms of their “dusty gas model” their empirical parameter, C , was found to be a linear function of
pressure and independent of the pressure difference. Analysis in terms of the capillary tube model showed that the diffusion tortuosity factor was about 1.8 times the flow term tortuosity factor.
Charles N . Satterjeld and P. John Cadle, Department of Chemical Engineering,’Massachusetts Institute of Technology, Cambridge, Mass. 02139
IND.END.FUNDAMENTALS 7, 202210 (1968) THERMODYNAMICS OF SOLUTIONS. CONSISTENCY OF SPARSE DATA. ACTIVITIES OF NITRIC AND PERCHLORIC ACIDS.
Usual consistency checks for activities can be applied only to fairly extensive sets of data. A new variant can be used even if data are available only for three concentrations. The activities of nitric and perchloric acids are computed in the whole concentration range from total vapor pressure and partly from other data.
0. Redlich, W. E. Gargrave, and W . D. Krostek, University of California, Berkeley, Calif.
IND.END.CHEM.FUNDAMENTALS 7,211214 (1968) SURFACE DIFFUSION OF CHEMISORBED HYDROGEN O N NICKEL
From steadystate flux measurements through a porous nickel disk, the surface diffusion coefficient for hydrogen on nickel a t 37OC. was measured directly and found to be about 3 X sq. cm. per second. The surface diffusion flux was a substantial portion of the total flux only a t low pressurese.g., 40 microns of Hg. The value for the diffusion coefficient agrees with the results of Gomer et al., obtained by field emission microscopy but is much smaller than that predicted by the indirect thermodynamic calculations.
Charles N . Satterjeld and Hiroshi Iino, Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Mass. 02139 IND.ENG.CHEM.FUNDAMENTALS 7 , 214218 (1968). EFFECT OF COMBUSTION TIME O N APPEARANCE OF VIBRATING DIFFUSION FLAMES
Empirical equations for the time required for the preparation and complete burning of an element of fuel in low frequency vibrating flames of butaneair and natural gasair are presented. Using the equation for natural gasair flames in a quasisteady analysis, the appearance of a flame during a cycle of vibration has been predicted satisfactorily. Four examples are given of a flame vibrating without separation, on the threshold of separation, with separation into two parts, and with separation into three parts, the fuel flow being distorted by excitation of the higher harmonics of the fuel supply system. The appearance of low frequency vibrating diffusion flames is strongly dependent on the total time for combustion. The stably vibrating flows observed satisfy Rayleigh’s criterion for phasing of heat release and pressure in the combustion chamber.
B. E. L. Deckker and R. A . Srinivas, University of Saskatchewan, Saskatoon, Canada IND.ENG.CHEM.FUNDAMENTALS 7, 218222 (1968) SHIFT I N THE OPTIMAL POWER INPUT I N A N ULTRASONIC REACTION
The rate of hydrolysis of methyl acetate was studied under the influence of high intensity ultrasonic waves. The yield does not increase indefinitely with increasing power applied to the transducer, but instead it reaches some optimum. This optimum power shifts with temperature because the collapse time increases with increasing temperature and voltage. T h e theory, presented in terms of a modified Rayleigh collapse time for cavitating bubbles, predicts optimum power shift with change in temperature.
Scott Fogler and Deveraux Barnes, University of Michigan, Ann Arbor, Mich. IND.ENG.CHEM.FUNDAMENTALS 7,222226 (1968) VOL. 6 0 NO. 5
MAY 1968
93
BRIEFS SHAPE OF A DROP OR BUBBLE AT LOW REYNOLDS NUMBER
The shape of a gas bubble or liquid drop in steady translation through a n unbounded, quiescent, and viscous fluid medium is determined for the case where the Reynolds number pertaining to the continuous phase and the Weber number are both small and the interface is clean. The inertia forces of the internal circulation do not affect the shape of a gas bubble, and contribute in a minor, but significant, way to the deformation of a liquid drop.
F. Y. Pan and Andreas Acrivos, Stanford University, Stanford, Calif. IND.ENG.CHEM.FUNDAMENTALS 7, 227232 (1968)
VISCOUS HEATING IN PLANE AND CIRCULAR FLOW BETWEEN MOVING SURFACES
The equations of motion and energy for the nonisothermal flow of a Newtonian liquid with exponential dependence of viscosity on temperature between moving parallel surfaces with no pressure gradient are presented and solved. The equations are nonlinear but admit solutions in terms of known elementary functions. Solutions are presented for plane and circular flow between isothermal surfaces and between an isothermal and an adiabatic surface. An interesting feature is that two solutions exist for each value of the applied shear stress. Plots are presented for the temperature and velocity profiles for plane flow and for circular flow with a ratio of outer to inner cylinder radius of 1.6.
Jerome Gavis and Robert L . Laurence, Department of Chemical Engineering, T h e Johns Hopkins University, Baltimore, M d . 2 72 18 IND.END.CHEM. FUNDAMENTALS 7,232239 (1968)
EVALUATION OF POWERMODEL LUBRICANTS IN A N INFINITE JOURNAL BEARING
A journal bearing consists of two right circular cylinders, one enclosed by the other, whose axes are parallel. The forces exerted upon the cylinders are such that the axes do not coincide. A flow is set up in the annular space as the inner cylinder is rotated with respect to the outer cylinder. 4 n “infinite” bearing means that end effects may be neglected. Two previously available inequalities are used to obtain upper and lower bounds on the zcomponent of the torque which a powermodel fluid exerts in the inner cylinder. The results suggest that for a wide variety of reasonable designs, a nonNewtonian fluid is a better lubricant for this geometry than a Newtonian fluid. The results are consistent with the limited experimental data available.
Robert Ehrlich and John C. Slatteiy, Northwestern University, Evanston, Ill. IND.ENC.CHEM.FUNDAMENTALS 7,239246 (1968)
AXIAL PRESSURE CORRELATION FOR ACCELERATING PARTICULATE PIPE FLOW
A semiempirical relation for the”axial pressure distribution of the form P* = [In (ax* f b)]’/n has been obtained for an accelerating particulate choked flow. Values of the constants a , b , and n were determined from experimental measurements over a range of particle sizes (110, 200, and 390 microns in diameter), duct diameters (0.25, 0.625, and 0.75 inch i.d.), and mass loading ratios (0.3 to 7). The values of the constants a , b, and n are essentially independent of particle size and vary slightly with duct diameter. Typically, values of a between 1.0 and 1.3, b between 2.1 and 2.4, and n between 1.7 and 2.5 were obtained for the considered range of conditions. Using numerical methods, RungeKutta technique, calculations for the axial distribution of the gas dynamic parameters (ug, up, To, T,,and f)were made employing the semiempirical pressure correlation. The results indicate that for nearly constant L I D ratio ducts, a variation in the duct diameter has virtually no effect of the axiai distribution of calculated gas dyand T,) within the system, while a namic parameters (ua, up, Tg, variation in particle size for a given flow rate and loading ratio has a marked effect on the gas and particle velocities (u, and up). Val94
INDUSTRIAL A N D ENGINEERING CHEMISTRY
ues of the average friction factor, 7, in the range of 0.0018 and 0.0035 for the stainless steel and copper ducts, respectively, were obtained for the range of flow conditions.
G. J . Trezek and D. M . France, University of California, Berkeley, Calif. IND.END.CHEM.FUNDAMENTALS 7, 247253 (1968) TURBULENT FLOW I N ROUGH PIPES
Surface roughness effects on frictional and temporalmean velocity distributions in conduit and other flows past rigid boundaries are considered and modes of correlating transitional effects between smooth and rough flow are indicated. From study of air flow in 8inch ‘‘natural” roughness and a 3inch sandroughened pipes, frictional pressure drop, near wall velocity profiles and turbulence profiles for pipe Reynolds number range of 1.3 X lo4 to 28 X 104 are presented. These verify transition functions, clarify a n uncertainty in regard to pipe factor formulation, and present new information on turbulence structure. J . M . Robertson, J . D . Martin, and T. H. Burkhart, University of Illinois, Urbana, Ill. IND.ENG.CHEM.FUNDAMENTALS 7,253265 (1968) VELOCITY PROFILES IN A HEATED ROTATING ANNULUS
Photographic analysis of dye injections was used to measure velocities in an annulus of water between an inner, heated cylinder and an outer rotating one. When the upper liquid surface was free, the motion in the annulus due to rotation tended to counteract natural convection so that at a critical rotation speed, the axial flow was essentially zero. When the upper liquid surface was in contact with the top plate, two separate circulations were establishedan upper one which supplemented natural convection and a lower one which induced motion counter to natural convection. In the central region of the annulus, the tangential velocity was accurately predicted from the equations of motion. The effect of radial position upon the axial velocity was calculated at high rotation speeds. Temperature measurements were also made along the inner and outer cylinders.
D . K. Petree, W. L. Dunkley, and J . M . Smith, University of California, Davis, Calif.
IND. ENG.CHEM.FUNDAMENTALS 7,265274 (1968) MASS TRANSFER IN THE FLOW OF GASES THROUGH PACKED BEDS. LOW REYNOLDS NUMBER REGION
Mass transfer factors associated with the vaporization of water and heavy hydrocarbons from the surface of porous spheres, 0.0721 to 0.370 inch in diameter, have been established in the low Reynolds number region (3 < N a , < 230), taking into account a correction for axial mixing. The carrier gas used was air which flowed through packed and dispersed beds of these spheres. To produce a dispersed bed, porous spheres saturated with a liquid were placed in a matrix of dry glass spheres. The results for both types of beds have been correlated with the Reynolds number to produce a single relationship of e j d us. N R ~ .
Louis J . Petrouic and George Thodos, Northwestern University, Evanston, I1I . 6020 I IND.ENG.CHEM.FUNDAMENTALS 7,274280 (1968) SIMULTANEOUS CONDENSATION OF METHANOL AND WATER FROM A NONCONDENSING GAS ON VERTICAL TUBES IN A BANK
Experimental data were obtained on the condensation of water and methanol from an air stream in turbulent flow across vertical cylinders. The composition of the condensed phase and heat flux were measured. A mathematical model, requiring data on the pure components plus vaporliquid equilibrium data, was used to predict the measured results. J . T. Schrodt and E. R. Gerhard, Uniuersiv of Louisville, Louisville, Ky.
IND.ENC.CHEM.FUNDAMENTALS 7,281285 (1968)
OPTIMAL FEEDBACK CONTROL OF A CLASS OF DISTRIBUTEDPARAMETER SYSTEMS WITH SPACEINDEPENDENT CONTROLS
Necessary conditions are discussed for a minimization of a n integral performance criterion for control of a class of partial differential equations, with the control variable a function of time only. For the linear hyperbolic system with a quadratic performance criterion and no boundary forcing, to drive the system from one steady state to another, a linear feedback control law is derived using a conjecture. The feedback gain is not unique. Implementation in principle requires that the state variable be measured at every position and then integrated over the spatial coordinate to generate the optimal control; in practice, a few points are sufficient. I n general, the optimal gain is a function of spatial coordinate and time and must be calculated iteratively. A modified performance criterion yields a gain calculable without itex'ation. Illustrative calculations are given for two examples : heat exchangers with wall flux control and with wall temperature control.
gas flow. The apparatus measures weight changes of the bed by means of strain gages mounted on a cantilever beam. The signal from the gage bridge is amplified and recorded on a chart. Examples of recorder traces show a number of interesting features of holdup and loading phenomena. The apparatus, for which a n accuracy of better than 1% is claimed, could also be used in conjunction with transient mass transfer studies.
N. Standish, Department of Metallurgy, University College, Wollongong, N.S. W.,Australia IND.ENC. CHEM.FUNDAMENTALS 7,312314 (1968) COMMUNICATION. MODIFICATION OF BROKAW'S METHOD FOR CALCULATING VISCOSITY OFMIXTURES OF GASES
A modification of Brokaw's method for computing viscosities of gaseous mixtures improves the reproduction of observed viscosity values and is simple for calculation a t higher temperatures.
L. B. Koppel, Y. P . Shih, and D. R. Coughanowr, Purdue University, Lafayette, Ind.
P. K . Tondon, University of Rajasthan, Jaipur, India, and S. C. Saxena, Purdue University, Lafayette, Ind.
IND.ENC.CHEM.FUNDAMENTALS 7,286295 (1968)
IND.ENG.CHEM.FUNDAMENTALS 7, 314315 (1968)
STABILITY OF INPUTPERTURBATION EXTREMUMSEEKINGSYSTEMS
COMMUNICATION. RELATION BETWEEN BOILING POINT CHANGE AND VIBRATIONAL FREQUENCY SHIFT IN METHYL AND ETHYL HALIDES
A general stability analysis for inputperturbation extremumseeking adaptive systems is presented. The presence of interaction in the dual variable objective function intercouples the adaptive loops, resulting in a locus of critical loop gains with a unique critical frequency corresponding to each gain pair. T h e applicability of univariable techniques for determination of conditional stability in the absence of appreciable interaction or under canonical transformation is discussed. High quality band pass filtering is recommended for reduction of interloop interference, even though no decrease in loop intercoupling is obtained. The critical gains and system cycling frequencies are determined through implicit solution of the frequency characteristic equation of a linearized model. The computational procedure may be applied to almost any specified optimizer or process configuration. The results of the hybrid simulation demonstrate the validity of this analysis for a particular example. J . W. White, G. J . Foley, and R. J . Altpeter, University of Wisconsin, Madison, W i s . IND.END.CHEM.FUNDAMENTALS 7,296305 (1968) EXPERIMENTAL TECHNIQUE. DIFFUSION COEFFICIENTS I N HYDROCARBON SYSTEMS. HOMOGENEOUS PHASES AT ELEVATED PRESSURES
The phenomenon of change in pressure accompanying gaseous diffusion in a closed isochoric, isothermal system has been studied experimentally and theoretically. Special equipment has been developed for measuring pressure differences with a n accuracy better than 0.01 p s i . at total pressure levels of hundreds of pounds per square inch. The theoretical analysis shows that as the system approaches equilibrium, the pressure as a function of time assumes the simple exponential formp peq = ae*Dlz2 wherep., is the equilibrium pressure, 9 1 2 the binary diffusion coefficient, a is a thermodynamic quantity, and b is a constant depending on the size and shape of the diffusion cell. This expression can be used for the determination of 9 1 2 from pressuretime measurements. Measurements upon the system CHI  C3H.3 a t T = 160' F. and pep = 570 p.s.i. have shown the applicability of this method, but more experimental work is required for ascertaining its accuracy.
G. R. Gavalas, H. H , Reamer, and B. H. Sage, California Institute of Technology, Pasadena, Calif. IND.ENC.CHEM.FUNDAMENTALS 7,306312 (1968) EXPERIMENTAL TECHNIQUE. MEASUREMENT OF TRANSIENT CHANGES IN LIQUID HOLDUP IN PACKED BEDS
An apparatus is described which records the transient behavior of liquid irrigation in packed beds with and without a countercurrent
Relation exists between the logarithm of the temperature difference, log A T , between the normal boiling point values of methane and its homologs, CH3X ( X = F, C1, Br, I), and ethane and its homologs, C~HF,X,us. the corresponding vibrational frequencies: va and Y B for methyl halides, and the CX bond stretching and CCX bond bending frequencies in the ethyl halide series.
Jhnis Lielmezs, T h e University of British Columbta, Vancouver 8, Canada IND.ENC.CHEM.FUNDAMENTALS 7,315316 (1968) COMMUNICATION. EQUILIBRIUM SEDIMENTATION IN NONIDEAL MULTICOMPONENT LIQUID SYSTEMS
A solution is obtained for the equilibrium composition distribution for a nonideal, multicomponent, nonelectrolyte, liquid mixture in a centrifugal field. The component mole fraction differences are given in terms of the chemical potential composition derivative matrix, evaluated a t the logarithmic average composition, and the average sedimentation potential vector. A possible application of these results is discussed. Harry T. Cullinan, Jr., State University of New York at Buffalo, Buffalo, N.Y. 74274 IND.ENC. CHEM.FUNDAMENTALS 7, 317319 (1968). COMMUNICATION. PECULIAR REFERENCE FRAME IN MULTICOMPONENT DIFFUSION
The assumption that the diffusion matrix based on chemical potential gradients is diagonal implies that the flux equations hold in a peculiar reference frame. This reference frame exists for ternary systems, but it may not exist i n general.
C. M . Yon and H. L. Toor, Carnegie Institute of Technology, Pittsburgh, Pa. 79273 IND.ENC. CHEM.FUNDAMENTALS 7, 319321 (1968) COMMUNICATION. CONDENSATION OF STEAM IN THE PRESENCE OF AIR. EXPERIMENTAL MASS TRANSFER COEFFICIENTS IN A DIRECTCONTACT SYSTEM
Experiments were run in a directcontact condensation system i n which steam, containing various amounts of air, was condensed onto a flowing stream of cool water. The rates of condensation were measured and, from the experimental data, mass transfer coefficients were calculated. These coefficients agreed with those predicted by boundary layer theory as developed for mass transfer to a moving flat plate with suction.
Shajik E. Sadek, Dynatech Corp., Cambridge, Mars. 0 2 1 3 9
IND.ENO.CHEM.FUNDAMENTALS 7,321324 (1968) VOL. 6 0
NO. 5
MAY 1968
95
BRIEFS COMMUNICATION. VISCOSITIES OF BINARY LIQUID MIXTURES. PREDICTION FROM YX DATA
A model is proposed to predict viscosities of binary liquid solutions based on Eyring's theory of absolute reaction rates. When we use this model and take into account the excess free energy data calculated from the vaporliquid equilibrium data, viscosities of the binary liquid systems phenolbenzene and carbon tetrachloridecyclohexane can be predicted. The predicted data are in fair agreement with the experimental data for the above systems.
(Sodium DGluconate)
M . R. V. Krishnan and G. S. Laddha, Department of Chemical Engineering, A . C. College of Technology, Madras25, India IND.ENG.CHEMFUNDAMENTALS 7, 324327 (1968)
COMMUNICATION. RATES
SeqLesters caIciLm, iron and abm'num 'n caustic soda washing salutans.
SOLVENT EFFECTS O N GASPHASE REACTION
The effect of chemically inert diluents on the rate of a simple, homogeneous gasphase reaction can be predicted by the use of the BrgnstedBjerrum relationship and a valid thermodynamic equation of state for dense gases. The modified Redlich equation has been used to calculate the effect of various diluents on hydrogen iodide decomposition. Diluents exhibiting strong intermolecular forces act to stabilize the transition state and thus augment the rate.
T. R. Mills and C. A . Eckert, Department of Chemistry and Chemical Engineering, UniverJityof Illinois, Urbana, Ill. 67801 IND.ENG.CIIEM.FUNDAMENTALS 7 327330 (1968)
Extends bath life

events farmat'on
CORRESPONDENCE. PREDICTIVE THEORY DIFFUSION COEFFICIENTS
FOR MULTICOMPONENT
Comments on a published article on predictive theory for multicomponent diffusion coefficients and a reply.
Robert G. Mortimer, Indiana University, Bloomington, Ind. Harry T. Cullinan, Jr., State University of New York, Bufalo, N . Y.
BRIGHTENERS
IND.ENG.CHEM.FUNDAMENTALS 7,330332 (1968)
Imparts a finegrained finish to deposited metal when used in copper, zinc, and cadmium plating bath brighteners.
CORRESPONDENCE. LIQUIDS
PAINT STRIPPERS When used with caustic soda, speeds up removal and improves dispersion of loosened paint,
MOLECULAR
THERMODYNAMICS OF
SIMPLE
Comments on a published article on molecular thermodynamics of simple liquids and a rebuttal.
Chenhwa Chiu and F . B. Canfield, University of Oklahoma, Norman, Okla . C. A . Eckert, University of Illinois, Urbana, Ill., H. Renon, Institut Frangais du Petrole, Paris, France, and J . M . Prausnitz, University of California , Berkeley, Calif
.
IND.ENO.CHEM.FUNDAMENTALS 7, 332334 (1968) CORRESPONDENCE.
MULTICOMPONENT MARGULES EQUATIONS
Comments on a published article on multicomponent Margules equations. Improver rust and s:ale removal from steel sLrfaces and depresses tendency
Far information an product applications and technical data, write far catalog.
E. D . Oliver, Stanford Research Institute, Menlo Park, Calif. IND.E m . CHEM.FUNDAMENTALS 7, 335 (1968)
CORRESPONDENCE. MOLECULAR THERMODYNAMICS LIQUIDS. VAPOR PRESSURES
OF
SIMPLE
Comments on a published article on molecular thermodynamics of simple liquids, vapor pressures.
Division of Stauf'fer Chemical Company Cleveland, Ohio 44120 96
Circle No. 16 on Readers' Service Card INDUSTRIAL AND ENGINEERING CHEMISTRY
H. Renon, Institut Francais du Petrole, Paris, France, C. A . Eckert, University of Illinois, Urbana, Ill., and J . M . Prausnitz, University of California, Berkeley, Calif. IND.ENC. CHEM.FUNDAMENTALS 7, 335336 (1968)