Ind. Eng. Chem. Fundam. 1982,21, 31-36 40
31
surfactants system, it is proposed that a close packing of surfactants, as well as interactions among them, is responsible for the high surface viscosity.
K
0 100 ‘3 250
Acknowledgment
B 500 3c
Mik Literature Cited
a v)
< f 2c 8
?
2 W
2
This study has been partly supported by NSF and DOE.
Adarangi, N. Ph.D. Thesls. Illlnds Instltute of Technology. Chlcago, IL, 1978. American Publlc Health Associatlon “Standard Methods for Examination of Water and Waste Water”, 13th ed.; New York, 1971. Bikerman, J. J. “Foams”; Springer-Verlag, New York, 1973; p 262. Brown, A. G.; Thuman, W. C.; McBain, J. W. J. CoMd Scl. 1859,8,491. Bujake, J. E.; Goddard, E. D. Trans. Faradey Soc. 1865,67. 190. Djabbarah, N. F. Ph.D. Thesis, Illinois InsHtute of Technology, Chicago, IL, 1978.
10
0
I
30
,
I
40
,
I
50
I
I
60
,
I
70
I
I
80
AVERAGE AREA PER MOLECULE, (I?/MOLECULE
Surface viscosity w.the average area per molecule for aqueous solutions o f SLS-LOH a t different values o f the relative concentration of lauryl alcohol.
Figure 8.
t i d y adsorbed at the surface; it displaces only part of SLS molecules and increases the extent of molecular packing at the surface. Furthermore, the surface excess concentrations of the two surfactants increase with the increase in their bulk concentration until they reach a maximum a t the critical micelle concentration of that particular system where the closest molecular packing is achieved. At bulk concentrations in excess of the cmc, the surface excess concentration of sodium lauryl sulfate decreases gradually while that of lauryl alcohol remains virtually constant, indicating the incorporation of SLS in the micelles. When trends in surface composition data are used to interpret trends in the surface viscosity of the mixed
Djabbarah, N. F.; Wasan, D. T. Chem. €ng. Scl. 1981. in press. Elsworthy, P. H.; Myseis, K. J. J. cdldd Interface Sci. 1986,27, 331. Fowkes. F. M. J. Phys. Chem. 1969,67, 1982. Gupta, L.; Wasan, D. T. I d . Eng. Chem. Fundam. 1874, 73. 26. Ivanov, 1. B.; Dimtov, D. S. C O W porvm. Scl. 1874,252 982. Jashanl, I. L.; Lemllch, R. J. coudd Interface Sci. 1974,46, 13. Lemiich. R. Ind. Eng. Chem. 1966,60, 16. Llvingston, J. R., Jr.; Weihnan, W. E. J. Am. OQChem.Soc.1965,42, 417. Lucaseen-Reynders, E. H.; Lucassen, J.; Garret, P. R.; Gibs, D.;Hoiiway. F. A&. Chem. Ser. 197b,No. 744,272. Maas, K. Sep. Sci. 1968,4 , 60. Mahajan, V. M.S. Thesis, Illinois Institute of Technology, Chicago, IL, 1974. Maru. H. C.; Mohan, V.; ,Wasan, D. T. Chem. Eng. Sci. 1979, 34, 1283. Maru, H. C.; Wasan, D. T., Chem. Eng. Scl. 1878,34, 1295. McBaln. J. W.; Wood, L. A. Roc. R . Soc. London, Ser. A 1940,774.286. Muramatsu, M.; Tajima, K.; Sasaki, T. BUN. Chem. Soc. Jpn. 1966,47. 1107.
Niisson, G. J. h y s . Chem. 1957,61, 1135. Poskanzer, A. M.; Goodrich, F. C. J. Phys. Chem. 1975, 79, 2122. Tajima, K.; Mwamatsu, M.; Sasaki, T. Bull. Chem. Soc. Jpn. 1989,42, 2471.
Vijayan, S.; Woods, D. R.; Vaya. H. Can. J. Chem. Eng. 1977, 55, 718. Vljayan, S.; Woods, D. R.; Vaya. H. Can. J. Chem. €ng. 1978,56, 103. Wasan, D. T.; Djabbarah. N. F.; Vora, M. K.; Shah, S. T. “Lecture Notes in Physlcs”, No. 105, Sorensen, T. S., Ed.; Sprlnger-Verlag: New York. 1979 p 205. Well, I . J. Phys. Chem. 1966,70, 133. Wilson, A.; Epsteln, M. B.; Ross, J. J . CO/bH Scl. 1857, 72, 345. Wlrz, J. H.; Newman. R. D. J. W b H Interface Sci. 1978. 63,583.
Received for review August 7, 1980 Accepted August 28, 1981
Calcium Carbonate Crystallization Kinetics Larry D. Swlnney,‘ John D. Stevens,* and Robert W. Petersia Depertment of Chefnlcal Engineering and The Engineering Research Institute, Iowa State University, Ames, Iowa 5001 1
Calcium carbonate crystallization kinetics were determined under mixed suspension mixed product removal (MSMPR) conditions for various reactor residence times, alkalinity distributions, and lnltial hardness levels. Power law models relating the nucleation rate to the crystal growth rate are presented. The kinetic order was correlated with resldual carbonate Ion concentration and residual supersaturation. A change of crystal habit from aragonite to calcite as a function of effluent supersaturation was observed.
Introduction Dissolved calcium is the main source of water hardness. The calcium is often removed by precipitation of calcium carbonate as in the lime-soda ash water softening process ‘Conoco Inc., Ponca City, OK 74603. Deceased. a Address correspondence to t h i s author at E n v i r o n m e n t a l Engineering, school of Civil Engineering, Purdue University, w e s t Lafayette, IN 47907.
0196-4313/82/1021-0031$01.25/0
(Sawyer and McCarty, 1978; Kemmer, 1979). Despite the fact that this process has been in use over a hundred years (American Water Works Association, 1950; Baker, 1948), little is known and understood about the crystallization kinetics of the proms. This report concerns a major fador in the lime softening process, namely the precipitation of calcium carbonate. The objective of this study is to provide more quantitative design information for Calcium carbonate precipitation as well as fundamental information about crystallization of sparingly soluble salts in general. 0 1982 American Chemical Society
32
Ind. Eng. Chem. Fundam., Vol. 21, No. 1, 1982
Background The studies were performed in a reactor-crystallizer in which a stream of hard water (artifically formed from calcium bicarbonate) was mixed with lime feed. The pertinent ionic reactions which occur are represented by the following. COz + 20HHC03- + OH-
F! F?
H 2 0 + C032-
IV
Ca2+ + C032- ~ iCaCO31 . Since the ratio of lime feed to hardness level varies in industrial practice, kinetic analyses were conducted under several different conditions. A few batch and continuous calcium carbonate crystallization studies have been reported in the literature in the past ten years. The batch studies have emphasized the ratio of change in calcium concentration upon the addition of calcite seed crystals (Alexander and McClanahan, 1975; Reddy and Nancollas, 1971; Wray and Daniels, 1957; Wiechers et al., 1975). Nucleation phenomena were not addressed in these studies. Schierholz and Stevens (1975) were the first to perform a continuous calcium carbonate crystallization study using initial hardness levels similar to those found in natural water. However, Schierholz's results are suspect due to his periodic scraping of reactor walls. Also, his study used sodium carbonate rather than lime and thus the calcium levels were considerably lower than if lime were used, as is more common in practice. Maruscak et al. (1971) also performed MSMPR (mixed suspension, mixed product removal) studies but his concentrations were so high that agglomeration of the particles distorted the growth behavior. The total alkalinity of waters used in this study is defined (Sawyer and McCarty, 1978) by (1)
where the brackets represent mol/L as CaC03 and 50 O00 is the conversion to mg/L. Total alkalinity, T , is in mg/L as CaC03. The phenolphthalein alkalinity, P, represents the amount of acid required to neutralize essentially all hydroxyl ions and convert the carbonate ions to bicarbonate ions.
P = 50000([OH-]
+ [CO:-])
(2)
Equations 1and 2 plus knowledge of the pH value allow calculation of the three ionic concentrations after T and P have been analytically determined (Sawyer and McCarty, 1978; American Public Health Association, American Water Works Association, and Water Pollution Control Federation, 1976). The ratio TIP is used in this report to express alkalinity conditions. A continuous mixed-suspension,mixed-product removal (MSMPR) model was used to describe the crystallization kinetics of the reactor in this study. The MSMPR model used assumes steady-state operation, no feed crystals, negligible breakage, and size independent growth. These assumptions incorporated into a population balance around a size range AL and a time period At yield
n = no exp(-L/G.r)
(3)
where n is the population density. The number of crystals in the size range size L to may be shown (Dallons, 1972) to be Q)
N(L,m) = noG7 exp(-L/G.r)
I I1
111
H 2 0 + CO2-
T = 50000([HCO
