BRIEFS ~urnmmyo j papers publi.shad in .this month's research ~uarterly,IHEC Fuicdammtals l l l L RWARIANCE PI(WCICLEOF CONTROL'FOR CIIMIKAL PROCESSES
The application of the invariance principle of conml for chemical pmca6es is dlrusscd. The m l 0 from tbcontreal analysis, analog rimulation, and cxpcrimental mcaaurements of heat tramfa in a jacketed, eitrcdtmlr reactor are p"nted, and from t h a e a n u m k of peralized wnclusions M drawn. Aa
.
important gmeralization of Petmv's dual channel wneept is propard for nonlinear s@una. The three requkments that must be 6ati66cdio o r d a to anain invariance are given.
D. E. H d m ond C. M.Sliapdch, Udmdty of O k l a h o , N m m ,
OM& IND. bo. CWU. FUNDAMENTALS 4,241248 (1965) OREEN'S IUKIIONS AND OPTIMAL SYSTEMS. COMPLEX DRERCONNKlED SlWCIURES
The solution of fiaorda variational equations by mcana of Gncn'6 functions is utilized to develop ncccsdsry conditions and wmputational mahod6 for the optimization of plan with wmplex interconnections. A concrete example of a staged 6yltcm and a aptem with both diaemc and eontinuom cknunts ia wmplacly Iolved.
M.M . D m ond Ruthefwd &, Unionri& of Mmnarotn, M k a p d i s , MifUl.
IND. ENo. CWU. FUNDAUUNTALS 4,240257 (1965) OPTIMAL RUCTION W ~ M S WITH
M a e
A mathematical technique har becn dcyelopcd for the dncrmination of the optimal operating policy for the system involvkg a tubular chemical reactm, a s p a r a m , and a recycle *am. The analyria wed the concepts pmpcud hy Ponqagin and the nsults show that one nced only m d i the definition of the adjoint funtiom in odcr m freaf such problems. The muhod is illuatxated by an example to Iind the maximum profit for an i r r d b l e MG tion carried out in a tubular reactor with recycle.
G. S. G. B d g a ond R. S.&hehtsr2 T b Vnim+ of Taxos, Ausfin, TaX. IND. ENO.Cmu. FUNDAMENTALS 4,257260 (1965) OPTlMlUlnON OF INITIAL COMPOSITION. ADIABATIC EQUILIBRIUM OAUHASE REACTIONS IN THE PRESENCE OF INERTS
I

Exprasions arc derived for the initial dimibution of mole fractions of reactant. required to obtain maximum yield in gasphase reactions proceeding adiabatically to equilibrium in the pnce of in. The initial cornpsition neeasary to attain the maximum equilibrium adiabatic temperature is also identilied. The required ~ r r c c t i ~ ntos the daaaic distribution of stoichiametrie ratios involve beat capadtica, the enthalpy of reaction, and the concentration of in. The shifta in composition are nontrivial, and the resulting inmasea in yield and temperature can be substantial in certain casea.
C. J. Pings, California htim of T m M o e , P a r d m , Gdif. IND. ENO.&EM. FlJNOAXENTAra 4,260264 (1965) CONTROL OF A CONTINUOUSFLOW AWATEDTANK REACTOR
The stability critaia far a tanlflow reactor arc reviewed for the case where t b a e is no mixing delay and the dynamies of the cooling system are not impxtant. Stability critaia are then developed for cases where the dynamics of a cooling coil are significant. Zeroarder kinetics arc assumed, so the stability criteria are conacrvativc. A marda, exothermic reaction was simulated in a 2fwt tank. Hot wata was used as a feed and live steam was sparged into the t d to simulate the heat of reaction. The reactor was made inherently stable or unstahle by controlling the change in steam rate with trmpaaturc. The reactor temperature was controlled by the cooling water rate. For a stable reactor,
thesyatcmwasstahleforcontmllagainsbelowacarainmaximum; when the r e m was i n h a a d y unstable, the ayatem was wnditionaUy stable. Good mml was achieved with h u t the same conmller acttinga for both case, beeaw the absolute value of the lagcst time constant was much larger than the ssond lagcrt. Tho W. Webar, slora Udwsity of Naw Yak,Bufdo, N . Y., ond PItn Hm'ott, C d l Udmn'b,Itham, N. Y.
IND. END.CWU FUNDAUUNTAU 4,264269 (1965) DYNAMIC5 OF A CLASS OF WOIIINEAR, DISTRIBUTEDPARAMETER. CHEMICAL REACTORS
The dynamics of a homogaeous tubular flow reactor with ?onlinear kinetics, in napom to changn in feed wnecntration and flow rate, are mlved, u n d a the asmmptions of plug flow, ne ha&mixing, constant pmpcrtiS and i m d h l c n t h a d a dcoompo& tion of a single reactant. The exact solution for this discrihutedparameta, nonlinear, p a r m t r i d y forced system is wmpared with the solutions to the linemized equations m assss the accuracy of representation of such rynemr by their linearized dynamics. It is shown that hear solutions M accurate when disturbanm are lcar than 25% of design Valuca Extmsions of the results to more wmplur reacton are dircuucd.
L. B. K W l , M w Udmsi&, .&fqttte, I d . I m . ENa. &EM. FUXDNS 4,269275 (1965) THEORY OF NONCATALYIK GASSOLID REACIK)HS
The finite m C r C C I l C h fa M&& p& difftid quations auggcned by Dufmt and F r W har proved d d v e in dvkg the mathcptica dacribing this propcud thwry for lidgas reactions. Cornpariaon with the analytical ~ I u t i for o ~ the caxd of pscud&rstorda reaction and insnitely rapid Kaction ahow that the computed d t s are accurate to within 5% of the rate ratio, Q. T h e analytical mlution for the case of W t d y rapid reaction ia prrmted.. The quare root rclafionrhip, suggcacd hy Sbawood and Figford doa not bold
*~$ai I < < IO.
in the range A technique dcsaibed for inmPrrting expimental data id conjunction with the propoaed theory should allow calculation of the reaction rate constant, k, and atimation of the reactant mlids activity, BM.
D. T. h e y 3 J. If. Bourn, ond K . S.Barden, Unionsity of N m South. W d q Kcnringfon,Aushdia IND.ENO.Caerc. FUNDMNTALS 4,275281 (1965) KINEIICS AND MECHANISM OF THE THERMAL DKOMPOIITION OF SODIUM DlTHlONlTE IN AQUEOUS SOLUTION
The thermal decomposition of sodium dithionite was studied in buffered and unbuffered aqueous solutions from 4.8 to 7.0 pH andatdithioniteeonecntrationsfmm5.5to11.5 X 1O'M. From 60' to 80" C. the reaction rate at zero time was found to b t half order with respect to hydmgen ion and thrcxhalva o r d a with w e t to the dithionite ion. Application of the Arrhmius quation to the rate of disappearance of dithionite gave an activation energy of 12 kcal. per mole and a frequency factor of 1.3 X 1CP liters/(mok)(sec.). The free radicals SO,. and HSOI. a p peared to be part of the mechanism. After time zero, there was an induction period in which the concentration of dithionite deereared slowly; then there was an abrupt increase in rate of decomposition which was exponential with respect to time, suggesting an autoeatalytic or degenerate branching chain mechanism.
R . G. Rinksr, Scott Lynn, D. M.Maron, and W. H. Cmoron, Cnlifornia lnrrihrfc of T e c h l o g y , Paradna, Calif. IND.ENO.&EM. FUNDAMENTALS 4,282288 (1965) (Continuad anpoga 715) VOL 57
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AUGUST 1 9 6 5
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Introducing .INFLUX
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MEASUREMENTS
MECHROLAB MODEL 5901A AUTOVISCOMETER. Electronic counter automatically measures efflux time through use of photocell detectors mounted at upper and lower reference points on glass viscometer. Model 5910A Constant Temperature Bath provides precise temperature control, eliminating errors due to temperature fluctuations.
Just push a button, and Mechrolab's new AutoViscometer automatically measures efflux time in glass capillary viscometers. Not only are viscosity measurements more efficient, they're at least 10 times more accurate than stopwatch techniques. Here's why: 1. Automatic influxing eliminates possible errors due to differences in technique. 2. Efflux time is automatically measured with an electronic counter which has a resolution of 0.001 second up to 100 seconds, * 0.01 second to 1,000 seconds. 3. Constant Temperature Bath provides tem
*
perature control and stability of better than *O.O05"C from ambient to 75'C. fO.Ol°C between 75 and 150'C. 4. Efflux times are digitally displayed on the counter readout and remain there until intentionally erased by the operator. There's also provision for a remote programmer and digital printer. Applications? Intrinsic viscosities: molecular weights: molecular shapes of natural and synthetic polymers. To learn more about automated viscometer measurements, contact your HewlettPackard office or write to us at 1062 Linda Vista, Mountain View 4, Calif.
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114
I#.I8 m i R~I~OIS' Sovice C u d
l N V U S l R l A 1 AND ENGINEERING C H E M I S T R Y


BRIEFS  4
g W U W M E M IAc1oR FOR WRWS CATALYSTS. NINSN~WOODKINETIC EXPR
uwoMu(k
A generalized method of predicting the catalyat dstivmcr factor has been developed for kinetic M of the l..anpuLninahelwood typc, forthe e a r o f a singlerraefantin which acborption of F.Tcdw or reactant may be lignifunt. Gmaalizcd cham for putation are preen& and the mcthod illumatcd by a tvpi..1 rt of data for the reaction of m b o n dioxide With h e l y pmou carbon.
expaimentr in which the agitation rate was varied, it was dctermined that tdk diffusion b not a limiting step in the reaction over the range of experimental wnditions. Rata of convenion were b u d to be inrm*tive to catalyrt partide size in the range studied, indicating Wt neither bulk diffusion nor pore diffusion is ratelimiting, and the oltmt of the m e m e reaction was insignificant. H o m ~ . ,an inmarc in initial water Concentration markedly demand the rate of formation of methyl salicylate. To explain tha d t s , a kin& expraaion based on a LangmukHinshelwood model ha8 been developed which provides a satisfactory fit
G. W.Robmts and C. N. SdwfiLf, M a s m W Imlihrrr of Tedmlosr, Cmnbdge, Mars.
ofthedataovcrthemngcofconversion.
IND. ENO.Caeu. FUNDAMENTALS 4,288293 (1965)
N.J.; and W. R. Vidh and A. 3. Rodger, Murachurslfs Imfifufeof T ~ h d o g yCmnWge, , Mus. IND. ENo.k w . FVUDAMZNTALS 4,314317 (1965)
DIFFUSIONAL EFFECTS IN OAWOUD IC*S
T h e interaction of physical h d a WWKS and chcmical reaction is considered for the reaction of a gar and spherical pellet of d i d reactant. The convmsiontime dationahip is daivcd for both isothermal and nonisothcrmal m n d i t i o ~for which man and e t r a d e r as w d as reaction raistanm are imporrant. For isothermal conditions the conversion CM be e x p d in tama ofa dimensionlea time and two parameten, while for nonimthennal ayltemr three additional parammn arc nemssary. For an emthermic reaction, there is a region of unstable operation bounded at the upper temperahre lcvel by a stable diffusionwntml regime and at the lower lcvel by a atable kindecontml regime. A p w mate criteria are daivcd fm the limits of instability. A numerical application is given showing the tranaition fmm the diEwion to kinetic regime. (1965)
ANALYSIS OF FREE DIFFUSION EXPERIMENTS
m WARY
n
m
~
A method of analping binary free diaudon uperimenc which cmncts for the dect of volume changeon mixing is developed. The daivcd cxpea*on for the mutual diaUriDn cculkimt is of some what simpler form than an alternative equation @ d y derived by R a p . Scvaal e a ~ lof free diEVdon in an ethyl alcoholwater *em are analyzed to demminc the magnitude of the effect of a volume change dvring mkiq. This analysin h w a that kgc aram in the calculated values of M w i o n cocfficlcn ‘ t s
canarircwhcnBnallehangaofvolumeduring~annot included in the analysin of the free &don pmea. M*hodr of minimidng these arors arc also crtablished. 3. L. M a and 3. S. Vrmfas, T h h C h i c d CO., Midland. Mich. IND.ENO.
CHEY.
FUNDAMENTALS 4,301408 (1965)
SLOW P A R W E DIFFUSION IN ION EXCNANOE COLUMNS
A general solution has been derived for the behavim of an ion exchans wlumn u n d a the condition8 of partide W%on control and irreversible equihbdum. This solution indudes time d e pendcnce, and doca not rcly on the mal “conatant pattan” assumption. A numba of diffusion mod& WQC examined, including the linear and quadratic foxing term appximaciona and the exact solution for diffusion into sphaer. The quadratic approximation was found to be in dole agrcrmmt with the exact solution. The exact solution was in the form of a double infinite d e s , which was daw to conwge in m ain cased, and a single d e approximation was developed which had more rapid COnVUgenCC.
R. S.C W , Lor AI
IIMULTANEOUS AIUOICTION OF HYDROOEN SULIIDE AND CARBON DIOXIDE IN AQUEOUS HYDROXIDE SOLIITIONS
The chemical reactions involvcd in the procesd of simultaneous aborptinn of H a and COI in aqueous hydroxide solutions are studied, and the shape of the concentration profiles in the liquid phase is dkused. It is shown that the theory of simultaneous absorption as formulated by Roper,Hatch, and F‘igford cannot be applied to the system considered, which displays a marked sekctivicy for hydrogen sulfide. Exppimental results confirm the predicted khavior. Giani Arfmifaand Franc4 Gioia, Unimnfyof NOplu, Najlu, I f d y IND.ENa. C m w . FUNDAMENTALS 1,317320 (1965)
John Shm and 3. M . Sntifh, Uniwsif~of Cdijanii,Dam‘s, C d i j IND.ENo. Caew. FUNMKWTALS 4,29>301
M . B. B o c k and S. M . Garbar, Arnaricon Cyanamid Co., B o d Brook,
&mt$ic Laboratory, Lm A l m s , N. M .
IND.ENO.Caem FUNDAMENTALS 4, 308313 (1965)
S I M I W O R E AND THIKFILM MODELS OF POROUS O M
~ DIFFUSION W R O D D I
Two physical mod& for the mode of operation of porous 6%difhuion electmdes for fuel cells are discussed. For nonwetted e l d e s , the simplepore model is proposed, in which reactant g a dipolva in elcctrolytc and diffuses to the submerged eleetmdc d a c e near the thncphare boundary of solidliquidgas. For n o d gar solubilities and diffusion coefficients, this model will lead to low hanrportlimited currents unleas the pore diameter is lear than about 1 micmn. For wcned doublelayer strucNK d d e , the thinfilm model appears reasonable on the bada of cxpnimentalobsuvafinn. An approximate mathematical bcarmmt of thir d e l leads to uaeful simple solutions, which can form the basis for de+ of experiments to test the model.

L. G.
Aurfin, T h Pnuuylounia S f d a Uaiocrsi(y, Uniwsily Park, Po., Mm‘o h i d andR. D. Walker, Unioersifyof Florida, Gaincsmlle,Fla.; and G. E. Wood ad R. H.Comyn, H o w Diamond Lobmatorier, U. S.Army Morn*I Commd, Waskingla,D . C.
IND.ENO.CHBU.FUNDAMENTALS 4,321327 (1965)
ESTIMATION OF SATURATED LIQUID HEAT CAPACITIES A B O M THE BOIUNO POINT
A technique for estimating the heat capacities of saturated liquids at reduced temperatures kom 0.70‘ to 0.95‘ is presented. By r~01Vingan equation first sugqerted by Watson for the heat capacity of a saturated liquid as a h c t i o n of the twoparameter law of corresponding states, and expandinK it with a threeparameter correlation with the critical compressibility as thc third parameter, it has becn possible to calculate thc heat capacities in the critical =ion with a satisfactory d g m of accuracy. Experimental and calculated valua of the heat capadties of 15 compounds are campared o v a the temperature range 0.70’ < T,< 0.95‘.
R. C. R d and 3. E. Sobel, Marsachefl$Imfihlte of Technology, Camhidge, Mars. An exprimcntal study was d e d out to cvaluate the pdormance of a cation exchange resin in the a d d form as a cacalyat for the ataification of d i k acid with methanol. From the d u of
IND.ENO. Clsu. FUNDAMENTALS 4, 328331
(1965)
(Contimud on jog6 717)
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AUGUST 1 9 6 5
115
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BRIEFS VISCOUS HEATING IN CAPILLARIES.
THE ADIABATIC CASE
In measuring viscosity or viscoelastic behavior with capillary viscometers, considerable heating can occur at high shear rates. An experimental program has shown that a temperature rise of as much as 350" F. can occur at the capillary wall when a 10poise oil is forced through an insulated capillary at 2000 p.s.i. This heating can reduce the apparent viscosity by 7070, which completely vitiates viscosity measurements. A mathematical (computer) solution of the Bow and temperature pattern in the capillary gives very close agreement with the experimental data over a surprisingly large range of conditions. Pressure drop, bulk temperature rise, and the axial and radial temperatures in the capillary are all computed to within 5 % of the experimental values. The data reported are all for an insulated capillary (adiabatic case); the case of the isothermal wall is to be the subject of a subsequent paper. However, experimental data show that the adiabatic case is far more prevalent than believed. J. E. Gerrard, F. E. Steidler, and J . K. Appeldoorn, Esso Research and Engineering Go., Linden, N. J. IND.ENG.CHEM. FUNDAMENTALS 4, 332339 (1965)
magnitude of the average heat flux. At higher intensitye.g., 80,000 B.t.u./(hr.)(sq. ft.)the local heat flux oscillated with the same wave frequency as the ripples on the film surface. At lower intensitye.g., 30,000 B.t.u./(hr.)(sq. ft.)but at the same ripple frequency, heat flux oscillations were less frequent and of smaller amplitude. At still lower heat flux, the oscillations disappeared entirely. A qualitative explanation is offered to describe the mechanism of the heat transport. Ramesh Chand and H. F. Rosson, University of Kansas, Lawrence, Kan.
IND.ENG.CHEM.FUNDAMENTALS 4, 356359 (1965) COMMUNICATION. PREDICTION OF RESIDENCE TIME DISTRIBUTION FROM THE UNSTEADY BEHAVIOR OF CHEMICAL REACTING SYSTEMS
The unsteady behavior of continuous flow isothermal systems with variable inlet stream concentrations and firstorder reaction is considered. The timedependence knowledge of the reactant concentrations of inlet and outlet streams makes prediction of the residence time distribution possible. Ugo Lelli, Universitb d i Bologna, Bologna, Italia IND.ENG.CHEM.FUNDAMENTALS 4,360361 (1965)
HEAT TRANSFER IN TWOPHASE FLOW OF GASLIQUID MIXTURES
Twophase heat transfer was investigated for airwater and airethylene glycol mixtures in a forced circulation system at low gasliquid ratios, An 11inch long electrically heated tube of 5/8inch I.D. was used a s the test section. All the results were correlated by the same relationship. It was found that dependence of twophase heattransfer coefficient on mass flow rate and gasliquid ratio was small, much smaller than is usually associated with high gasliquid ratios for annular type of flow, thus producing a different correlation for the low gasliquid ratios examined. A . A . Kudirka, Argonne National Laboratory, Argonne, Ill., and R. J. Grosh and P. W . McFadden, Purdue Unaversitj., W e s t Lafayelta, Ind. IND.ENG.CHEM.FUNDAMENTALS 4, 339344 (1965) MASS AND HEAT TRANSFER RATES FOR LARGE GRADIENTS OF CONCENTRATION AND TEMPERATURE
Data on the evaporation of water, benzene, carbon tetrachloride, and heptane into hot air, at tempeatures as high as 545' F., and dissolution of 2butanone, methyl formate, and cyclopentanone into water at room temperatures were obtained and compared with the predictions of an integral boundary layer analysis. Stagnation regions and a turbulent boundary layer on a flat surface were chosen as general flow configurations. Attention was focused on simultaneous transfer (with measurement of wetbulb temperature and heat transfer rate), large gradients in concentration and temperature, large concentrations of diffusing component (with mass fractions as high as 0.8), convection caused by diffusion, and boundary conditions. W . E. R a n z and Philip F. Dickson, University of Minnesota, Minneapolis, M i n n . IND.ENG.CHEM. FUNDAMENTALS 4,345353 (1965) POSSIBLE INTERPRETATION OF THE MECHANISM OF DRAG REDUCTION IN VISCOELASTIC LIQUIDS
COMMUNICATION. GASLIQUID FLOW
MASS TRANSFER IN HORIZONTAL ANNULAR
The momentummass transfer analogy appears to be applicable to the COrwater data of Bollinger and the NHswater data of Anderson, Bollinger, and Lamb for horizontal annular flow. Average absolute deviations of 17 and 11 % are obtained between calculated and experimental data for the COzwater and NHswater systems. G. A. Hughmark, Ethyl Gorp., Baton Rouge, L a .
IND.ENG.CHEM.FUNDAMENTALS 4, 361363 (1965) COMMUNICATION, NATURE OF THE UNCOUPLED MULTICOMPONENT DIFFUSION EQUATIONS
If the flux of each species in a multicomponent system is assumed to be proportional only to its own gradient, the diffusivities of all nondilute components must be the same if the diffusion equations are to be selfconsistent.
H.L. Toor and K . R. Arnold, Carnegie Institute of Technology, Pittsburgh, Pa. IND.ENG.CHEM.FUNDAMENTALS 4, 363364 (1965) COMMUNICATION. GIBBS' LAW FOR ABLATING LIQUIDS
Gibbs' law for determining the concentration of a surface active agent in an ablating liquid is derived. The result is obtained by assuming a linear velocity and concentration profile in the ablating liquid film. These assumptions are valid only for liquids with small viscosities and therefore substances such as glasses, polymers, etc., are excluded from the analysis. This is not a serious restriction, since diffusion in high viscosity liquids is too slow to be of any practical importance for the discussed purposes. Two applications of Gibbs' law for ablating liquids are given: the stabilization of films and the enhancement of ablation performance by adding surface active compounds.
An interpretation of the mechanism of drag reduction in the turbulent flow of viscoelastic liquids is proposed, based on the consideration of the frequencies of the noninviscid eddies, which are shown to be higher than the inverse of the relaxation times of those liquids which are usually considered viscoelastic. Gianni Astarita, University of Naples, Naples, Italy IND.ENG.CHEM.FUNDAMENTALS 4, 354356 (1965)
CORRESPONDENCE. BATCH AND CONTINUOUS THICKENING. PREDICTION OF BATCH SETTLING BEHAVIOR FROM INITIAL RATE DATA WITH RESULTS FOR RIGID SPHERES
LOCAL HEAT FLUX TO A WATER FILM FLOWING DOWN A VERTICAL SURFACE
Comments on an article published on batch and continuous thickeningprediction of bath settling behavior from initial rate data with results for rigid spheresand a rebuttal.
A thin water film with ripples on its surface was caused to flow down a heated vertical plate. The local heat flux to the film was studied near the beginning of the heated section of the plate. The effect of the ripples on the local heat flux was dependent on the
J . E. Buchanan, University of N e w South Wales, Kensington, New South Wales; P. T. Shannon, Dartmouth College, Hanouer, N . E?.; and E. M . T o ~ yBrookhaven , National Laboratory, Upton, Long Island, N . Y. IND.ENG.CHISM. FUNDAMENTALS 4, 366368 (1965)
Bernard Steverding, Army Missile Command, Redstone Arsenal, A l a .
IND.ENG.CHEM.FUNDAMENTALS 4, 364366 (1965)
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