Bubble Coalescence and Gas Transfer in Aqueous Electrolytic Solutions Richard R, Lessardl and Stefan A. Zieminski Department of Chemical Engineering, University of Maine, Orono, Maine 04473
The purpose of this work was to investigate the effects of inorganic electrolytes on bubble coalescence and interfacial gas transfer in aqueous solution. The coalescence experiments consisted in contacting a number of pairs of bubbles and evaluating the coalescence percentage as a function of solute concentration. The relationship between them revealed the existence of sharp transition concentrations. These concentrations correlated well with ionic entropy of solution and with the self-diffusion ability of water in solution. These were used as guides in determining a possible mechanism for coalescence which was based on ion-water interactions. The mass-transfer experiments consisted in evaluating, by means of a high-speed photographic technique, the mass-transfer coefficients for the dissolving of acetylene gas from bubbles rising in aqueous solutions. The results demonstrated that some ions decreased the resistance to transfer under the conditions of these experiments. Hydrodynamic considerations and a similarity between resistance and salting-out effects indicated that the phenomenon may also be attributable to ion-water interactions.
T h e effects various inorganic salts exert on the coalescence of gas bubbles and on the rate of mass transfer are of interest to the chemical engineer as well as to those engaged in the treatmerit of polluted saline waters (Gurnham, 1965). Tests performed by Zieminski and Whittemore (1971) show that the reduction of bubble coalescence afforded by electrolyte solutions of sufficiently high concentration leads to a n increased gas-transfer rate by enlarging the contact surface. This indicates a potential means of increasing aeration efficiency in saline waters by introducing air into regions of higher salt concentration. I n searching the literature, however, one finds that very little basic work has been done in determining the effects of dissolved ions on this type of system. Though the effects of surface-active agents on aqueous interfacial phenomena have been studied in considerable detail (Carver, 1956; Mancy and Okun, 1965; Zieminski, et al., 1960; Zieminski, et al., 1967; Zieminski and Hill, 1962; Zieminski and Lessard, 1969), the dependence of the degree of bubble coalescence on ionic charge remains unclear and the effects of electrolytes on the resistance t o gas transfer are practically unexplored. Coalescence Phenomenon in Ionic Solution. Anyone who has watched a wave coming onto shore from the sea must certainly have been impressed, either consciously or otherwise, b y the “foaminess” which such a wave possesses as compared to a similar wave in fresh water. This phenomenon, attributable t o t h e high salt content of sea water, is caused by the decreased coalescence of air bubbles trapped by a breaking wave. I n pure water, gas bubbles which are brought together will coalesce as soon as they are contacted. X review of previous work (Foulk, 1929; Foulk and Xiller, 1931; Marrucci and Nicodemo, 1967; Schnurman, 1929; Zieminski and Whittemore, 1971) indicates that the mechanism by which ions hinder the coalescence of gas bubbles in water is unresolved. The identification of this mechanism through a study of the effects of various salts on the coalescence of gas bubbles was one objective of this work. Present address, Esso Research & Engineering Co., Florham Park, N. J. 07932. 260 Ind. Eng. Chem. Fundam., Vol. 10, No. 2, 1971
Mass Transfer from Gases to Aqueous Electrolytic Solutions. There has been much work done on t h e evalua-
tion of gas solubilities in water as a function of electrolyte concentration (Randall a n d Failey, 1927). However, i t seems t h a t there has not been much interest in the kinetics of this process. Adeney a n d Becker (1919) demonstrated t h a t in a system where gas transfer is essentially t o a liquid film, the ratio of the rate of transfer in pure water to that in sea water is in exact proportion to the ratio of the solubilities of a gas. This means that for gas transfer t o thin films, the gas molecules in each situation encounter the same interfacial resistance. T o the knowledge of these authors, however, no one has determined that this is necessarily so for a freely moving surface such as in the case of a rising bubble. I n fact, Downing and Truesdale (1955) mentioned that for identical stirring conditions the oxygen transfer coefficient was higher in sea water than in distilled water. This indication of possible ionic influence on gas transfer deserves further investigation. Such an investigation was the second objective of this work. The Effects of Salts on Bubble Coalescence Experimental Procedure. I n studying bubble coalescence, t h e objective was t o contact pairs of air bubbles a n d determine t h e percentage of t h e coalescing pairs. T h e schematic diagram of t h e equipment used is shown i n Figure 1. It consisted of a threaded socket driven by a Fisher variable-speed motor. I n the socket was a large, similarly threaded bolt so that as the drive made the socket turn, the bolt would rise. The bolt was connected to a platform on which rested the pistons of two precision-made gastight syringes, each with a gas capacity of 2500 11. The tips of the syringe barrels were sealed into needles which were connected to two vertical injection tubes. These tubes were side by side and had glass tips which had been drawn and polished under a measuring microscope to identical orifice diameters. The supports were all made of aluminum and the column was made of Plexiglas. The experimental procedure consisted in switching on the
Figure 3.
Bubbles in salt solution
MgC12, NaCl, LiCl, KCl, and NaBr. It was felt t h a t they would give a fair spectrum of valence and ionic size. They were all Fisher Certified ACS grade with a minimum purity of 99%. Double-distilled water was used in all tests. It mas kept in borosilicate glass containers which had been thoroughly cleaned with hot chromic acid. Results. Figures 2 and 3 represent t h e behavior of bubbles in distilled water a n d salt solution, respectively. I n pure water the bubbles coalesced spontaneously on contact. The results of the tests are plotted in Figure 4. The most surprising feature of the plot is the appearance of sharp transition concentrations. The coalescence in pure water is loo%, regardless of temperature. However, as salt is added to the water a concentration is reached a t which coalescence is drastically reduced. This concentration is characteristic of each salt investigated; e.g., for A1C13, the coalescence is 100% at 0.03 M and 7.5y0 a t 0.04 M. This is a definite indication that some sort of critical concentration is present. At AIC1, concentrations greater than 0.04 M ,the coalescence is less than 5y0 of the number of contacts. The transition concentrations and the sharpness of the drop in “per cent coalescence” are functions of the valence combinations of the salts-3-1 and 2-2 electrolytes begin to prevent coalescelice in the concentration range 0.030-0.036 JI, 2-1 and 1-2 electrolytes in the range 0.056-0.060 M, and 1-1 electrolytes in the range 0.16-0.23 -11. Also evident is a dependence on ionic size for the uni-univalent salts. Thus, LiCl is more effective than XaC1 rvhich, in turn, is more effective than KCI; the effectiveness of the halides is in the order KaC1 > NaBr > S a I . The last of these (not shown in the figure) was ineffective ul) to a concentration of 1.0 X. I n order to enable comparison of the effectiveness of the salts, the concentration resulting in 50% coalescence wa. defined as the transition concentration, Table I gives the respective values.
syRINGEs*li
GASTIGHT-
Figure 1.
Diagram of the coalescence apparatus
Figure 2.
Bubbles in pure water
injection drive and photographing, with a Bolex 16-mm movie camera, 250-300 contacted pairs of air bubbles. The degree of coalescence was determined by counting, on the projected film, the number of coalescing pairs. This was reported as “per cent coalescence” by dividing t h e number of coalescing pairs by the total number of pairs contacted. The reproducibility of the system was very good, not only for specific concentrations (approximately 1 2 y 0 ) but for the entire transition range. The rate of bubble injection ranged between 1.8 and 2.6 sec-1 and the volume of the bubbles was about 25 p1 (spherical diameter 0.36 em). The effect of injection speed was determined by contacting bubbles in a given solution of NaCl at 1.4 and 2.6 contacts/sec. The results were 32 and 29%, respectively, indicating t h a t in the range of contact times used in these tests the injection speed or surface age did not affect coalescence. The head of liquid over the injection region was maintained a t 12.0 em in all the tests. The temperature of all the solutions was 24 i 1OC. The salts studied were AIC13, ?rigsod, NazSO4, CaC12,
Table I. Transition Concentrations Salt
AlgS04
AICI, MgClz CaClz Na2SOd LiCl NaCl NaBr KC1
Transition concentration, M (50% coalescence)
0.032 0.035 0.055 0.055 0.061 0.16 0.175 0.22 0.23
Ind. Eng. Chem. Fundam., Vol. 10, No. 2, 1971
261
100 9c
80 70 W 0
$
60
0 v)
W -I
a 0 u
50 4c
$ 3c 2c IC 0
M O L A R CONCENTRATION
Figure 4.
Concentration vs.
Table II. Coalescence in Sea Water Temp, OC
% Coalescence
6 16 31
12 28 50
To obtain some idea of the temperature effect on coalescence, three tests were made on sea water. The results are presented in Table 11. Discussion. The results obtained by the simple b u t precise technique described above throw some light on the mechanism through which electrolytes hinder bubble coalescence. I n speculating on this mechanism, one must bear in mind t h a t the hypothesis should explain not only the presence of transition concentrations and their separation according to valence and ionic radius b u t also the temperature effect observed in the sea water runs. I n addition, one cannot ignore what previous investigators have found to be important parameters, as discussed below. Marrucci and Nicodemo (1967) noted that the efficiency of the inorganic electrolytes in inhibiting coalescence depends on the valency and the derivative of the surface tension us. concentration curve. However, the authors do not explain why a t a given bulk concentration salts giving a lower interfacial concentration should be more effective in preventing coalescence. It appears also that the use of equilibrium surface tension data might not be justified since the time available for the interfaces to come in contact may be too short to approach equilibrium. Finally, their assumption that the surface potential is proportional to the surface tension gradient may not be correct in consideration of recent data presented by Jarvis and Scheiman (1968). Schnurman (1929) pointed out that there is a very real 262 Ind. Eng. Chem. Fundam., Vol. 10, No. 2, 1971
% coalescence
correspondence between coalescence prevention and solution viscosity. He stated that there is also a secondary effect in electrolyte solution which he attributed to electrostatic interaction between the charged bubbles. In verification of Schnurman’s observations, this work shows t h a t viscosity cannot be the only parameter affecting coalescence in electrolyte solution because KC1 solutions, which effectively reduce coalescence at concentrations greater than 0.20 M , have a negative B coefficient of viscosity (Gurney, 1962) indicating that KC1 actually reduces the viscosity of water. The viscous effects cannot be ignored, however, as shown by a good correspondence between “per cent coalescence” and the viscosity relative to water for the other eight salts investigated (see Figure 5 ) . The viscosity data used are from the International Critical Tables (1929a) and from Sutra (1946).
100
90 80
70 W
x
60
v1 u
3 d
50
;4 0 30 20
10
0 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1 . 0 7 1.08 1.09 1.10 1.11 1 . 1 2 1.13 RELATIVE V I S C O S I T Y
Figure 5. Per cent coalescence vs. relative viscosity for all salts except KCI
8ot
\
.I
70
I
w 0
z w
p. I
.I
60
0
0
I
v)
w
U
50
i
0 0
s
I
40
9
I
I
0
30
. . 0
20
*.
IO -
.ow0 .
e I
I
*. - --
.
The reader will note that a t transition all relative viscosities are between 1.01 and 1.03. Although these are small changes in bulk viscosity, it is possible t h a t they are indicative of larger effects near the surface. The ionic charge or valence effect was examined by plotting “per cent coalescence” against ionic strength (Figure 6 ) , as suggested in the work of Zieminski and Whittemore (1971). The KCl points have been circled to distinguish them from the other salts which again give a good correlation. It seems that since KC1 has a small effect on water viscosity, i t takes a greater concentration of charge to effect the same coalescence prevention as the other eight salts. This is a n important point since it indicates t h a t whatever the mechanism is, it involves a charge-viscosity combination effect. The charge effect, though accounting for valence dependence of coalescence, does not explain the temperature dependence; however, the viscosity effect does. The inference made from a charge-viscosity dependence of coalescence prevention is t h a t the role of salts may possibly involve their effect on the water molecules in and around the surface layers of bubbles; t h a t is, coalescence prevention may be a function of the ions acting on the water molecules. Before two bubbles can coalesce, the liquid lamella between them must drain out t o a critical film thickness (Davies and Rideal, 1963). Once this thickness is reached, the gas molecules are able to bridge the liquid gap. This leads to coalescence. It is probable t h a t anything which prevents or retards the draining of the liquid film from between the bubbles, for the contact times involved, will reduce the “per cent coalescence.” Most of the ions used in these runs are structure formers, which means that they exert a net restraining effect on water molecules. A concise summary according t o Frank, as reported by H u n t (1965), is t h a t cations smaller or more highly charged than K + are net structure formers. On the other hand, C1-, Br-, and I- are increasingly structure
. b
I
I
0
. I
breakers. The structure formers have high electric fields not only polarizing, immobilizing, and electrostrict’iiig nearcstneighbor rvater molecules, but also inducing additional order (entropy loss) beyond the first water layer, encroaching, so to speak, on t,he structure-broken region (Kavanau, 1964). h concentration of such ions near an interface, which is usually negative ( I l t y , 1924, 1926a, 192613; Bakh and Gilman, 1938; Currie and d l t y , 1928; Frumkin, 1924; Jarvis and Scheiman, 1968; XcTaggart, 1914a, 1914b, 1922; Quincke, 1861), should exert a resistance to flow on the liquid layers beneath the surface, possibly preventing attainment of the critical film thickness during the short contact times involved. To test whether a correlation exists b e h e e n coalescence prevention and ion-water interaction, the transition concent’rations of Figure 4 were plotted against Latimer’s (1955) values for the ionic entropy of hydration, AS,. It was felt that if electrostriction of the water prevented coalescence, then those salts which lowered the entropy of the solution most (an indication of ordering of the water system) should require the lowest concentration of salt to decrease coalescence. Figure 7 fully confirms this assumption and shows an excellent’two-line correlation between the entropy values and transitions. Entropy of solution is an attractive parameter because it can be related t o both viscosity and valence. Gurney (1953) points out that the partial molal entropies of the ions have been successfully linked \vith the viscosity B coefficients. Latimer (1955) has related hydration entropies of the ions to their valence and ionic size. The success of the correlation in Figure 7 explains not only the satisfactory relationships between coalescence, ionic strength, and viscosity but also the dependence of t h e phenomenon on ionic radius for the uni-univalent salts. For a given charge, the smaller ions have the greater restricting effect on nearby water molecules because of their larger charge density. The self-diffusion of water is another parameter which can be used t o test the hypothesis that the decrease in bubble !nd. Eng. Chem. Fundam., Val. 10, No. 2 , 1971
263
TRANSITION
Figure
CONCENTRATION
( Moles/ Liter
7. Transition concentration vs. entropy of solution
K CP 0.00
-
a
- -0.10
LT
w I-
W
H
a U
2
-0.20
z
e
v)
3 LL
k -0.30 LL -I
w
co U
-0.40
2 0. IO
0.00
COALESCENCE
Figure 8.
0. 2 0
TRANSITION
CONCENTRATION
0.30
( Moleo/Liter)
Coalescence transition concentration vs. self-diffusion parameter, AI
coalescence is a result of ion-water interaction. Waiig (1954) and Devell (1962) present excellent data in connection with the self-diffusion phenomenon, and Jones, et al. (1965), give a good review of the three ways by which ions can influence the self-diffusion of water. Ions retard water diffusion by obstruction and hydration; they enhance it by “breaking” water structure (hydrogen bonding) , thereby producing more unassociated water molecules. The overall effect of any one salt on the mobility of water as measured by self-diffusion data is thus a n indication of its ability to retard drainage. 264 Ind. Eng. Chern. Fundarn., Vol. 10, No. 2, 1971
If the hypothesis presented above is to be accepted, one would expect some correlation between the self-diffusion of water and “per cent Coalescence.” The McCall and Douglass (1965) self-diffusion parameters “ A I J J were thus plotted against transition concentrations (Figure 8), and, as expected, a relationship similar to that with entropy of solution was obtained. Figures 7 and 8 lend strong support t o the proposition that ion-water interactions are responsible for decreasing coalescence in ionic solution. The above explanation appears to be also in agreement with
F i g u r e 9. D i a g r a m of t h e e x p e r i m e n t a l e q u i p m e n t
the work of Good (1964, 1965, 1966), who noticed that' addition of salts beyond a given concentration does not affect primary hydration. According to him, Lii enhances water structure up to about 0.1 m while for RIg2+ salts and iC'a2S04 the concentration cited is about 0.05 rn. It is significant that these concentrations correspond closely to the transition regions reported in this work, indicating that the coiicentrations a t which coalescence transitions occur may be indicative of the concentrations of maximum hydration. T h e Effects of Salts on M a s s T r a n s f e r
The coalescence work has established t h a t in salt solutioiis of sufficiently high concentration, bubbles are prevented from coalescing. I n a bulk system this leads to a substantial increase in surface area which, in turn, presents to the gas molecules more locations at which they may enter the liquid phase. The question which must now be answered is whether or not the ions affect the resistance to gas transfer. 111determining which salt concentrations to study for resistance effects, the transitions observed in the coalescence phenomeiioii provide a necessary guide since it has been stated that these transitions reflect ion-water interactions. It is intuitive that any change in resistance, if there is one, should be a function of these interactions. Equipment and Experimental Procedure. T h e purpose of this p a r t of t h e work was t o s t u d y t h e effects of ions on t h e rate a t which water dissolves a gas from a single rising bubble. T h e equipment used was in principle t h e same as t h a t used b y Zieminski a n d Raymond (1968) in their study of the behavior of CO, bubbles rising in water. A schematic diagram (Figure 9) and a brief description of the operation is given below. Doubly distilled water was first stripped of all gases by passing helium through it under vacuum and then introduced into a square absorption column. The column was completely filled with water and the
capillary dilatometer was t'he oiily connection to the atmosphere. X precise release system located beneath the absorpt'ion column erisured that the bubble was injected as reproducibly as possible. The temperature was 25OC in all tests. The aim of the experiment was to record on film by means of a high-speed camera a near-continuous history of t'he size, shape, age, posit'ion, aiid volume of the bubble as it rose through a vertical column of mater. This was made possible by placing the camera o n a carefully counter-balanced platform which could be moved manually to follow t'he rising bubble. The size and shape of the bubbles were taken directly from the film and were uied to determine surface area by assuming that the bubble was a n oblate spheroid. This was a reasonable assumption for the bubble sizes used in t'his work (diameter = 3-4 mm). The velocity of rise of the bubble was determined by means of a t'iming light which put a dot on the film every 0.001 sec. The position of the bubble was known from markings on t h e column wall. The volume of the bubble was obtained by projecting into the focal plane of the camera a picture of the position of the water meniscus in the dilatometer. I n this way the rate of the volume change of t,he bubble was determined. The camera speed was such t h a t 600 exposures of the bubble aiid the corresponding dilatometer readings were obtained every second. For a comprehensive description of experiment'al equipment and operating procedures, the reader is referred to the work of Zieminski and Raymond (1968). T o ensnre against any possible interaction between the gas and the electrolytes, acetylene was selected as the gaseous phase. Other reasons for selecting this gas were its high solubility in water and the availability of data giving its solubility as a function of salt concentration (International Critical Tables, 1929b; Flid and Golynets, 1959). The acetylene used was of the purest grade (99.6%) a n d came dissolved in acetone under pressure. Since the latter is Ind. Eng. Chem. Fundam., Vol. 10, No. 2, 1971
265
W ,
‘ER
Needle Valve
4
Acetylene Cylinder
#+
Fi Iter
Figure 10.
where d n / d t is the molar rate a t which the gas dissolves, A is the interfacial area, Co is the equilibrium concentration or solubility of the gas, and Ca is the gas concentration in the liquid bulk. K 1 is a coefficient representing the reciprocal liquid resistance to transfer. Thus for a unit concentration gradient, the rate is a sole function of contact area and resisInd. Eng. Chem. Fundam., Vol. 10, No. 2, 1971
kWater ipping
-0
f
Sampling Needle
Acetylene stripping system
surface-active, a system was designed to remove its vapor from the gas (Figure 10). The stripping procedure was to first rinse the scrubbing tubes with water by closing valve 3 and opening valves 4 and 6, and then completely filling this part of the system with gas-free water. With valves 2 , 4,and 5 closed, and 1, 3, and 6 open, the gas was then slowly introduced first through a filter and then through the stripping tubes. The water in the tubes was thus displaced by acetylene with no possible contamination of the acetylene by air. The gas issuing from the sampling needle was tested for purity in a gas chromatograph and was found to contain no noticeable amount of either acetone or air. At the end of the day, positive pressure was maintained in the system by opening valve 2 and filling the balloon with acetylene. This ensured that no air could contaminate the system overnight. I n introducing the gas into the absorption column, the procedure was to fill a syringe and needle with water, insert this needle into the sampling needle, which had a slightly larger diameter, and expel the water into the stream of flowing acetylene. The plunger of the syringe was then pulled back and in this way an uncontaminated C2H2sample was collected for injection into the release capillary of the absorption column. The salts studied were NaC1, LiCI, KC1, CaC12, Na2S04, and AlClS. I n determining which concentrations t o study, the results of the coalescence experiments were used as a guide, that is, a concentration below, at, and above the coalescence transition was used for each salt. Calculations. T h e general equation for t h e rate of mass transfer from a gas to a liquid is
266
-
tance. For the conditions of these experiments, the ideal gas law applies and dn 1 dlPV) -. = _. .~ dt RT dt Assuming that Henry’s law applies and considering that the concentration of gas in the liquid is negligible (cb = O ) , one gets
Co
=
HP
(3)
Thus
(4) It is here that the derivation differs from other more classical approaches. Xormally, the partial pressure of a gas in a liquid is adequately expressed by P = PB
- Ph - Po
(5)
where P B is the barometric pressure, P h is the hydrostatic head of the liquid, and P , is the vapor pressure of water. Although this is quite reasonable for a stationary gas phase, it may be lacking in some respects when applied to a dynamic situation such as a bubble rising in a liquid. As a bubble rises it must do work on the liquid if it is to change its volume and it is quite possible that an additional term must be included in ( 5 ) in determining the actual pressure of the gas. Zieminski and Raymond (1968) demonstrated that this is actually so by using insoluble helium bubbles. Knowing what the predicted volume should be for any hydrostatic head as the bubbles rose, they showed that the actual and predicted volumes differed significantly and that this difference was a function of the volume rate of change. According to them P
PB
- Ph - Po - 6
(6)
where 6 is a dynamic correction. This additional term was determined as a function of dV/dt for the entire range of volume rates of change used in this work. Letting
P = Ph
+ P, + 6
(7)
Table Ill.
and combining (4), (6), and (7), one gets
K1
=
~
1
RTAH
[-
V
Pg - a
(%) $1 -
(8)
Salt
NaCl
The volume, V , was evaluated from the capillary displacenient (t'he initial volume was 42 p1 in every run). This was plotted against bubble age to determine d V / d t . The surface area, A , was determined by assuming that the shape of the bubble was that of an oblate spheroid. By using mathematical expressions relating the volume and the semiaxes for this geometric shape, the area was calculated from the relat'ionship
A
=
V
1.50 -b
+ 3.14 b2a log l1 +- aa -
KCI LiCl
(9)
~
where b is the minor axis and cy is tlie eccentrichy. This formula had the advantage of including the volume, V , which could be determined accurately, instead of the other semiaxis. Results. I n order to evaluate the effects of salts on masstransfer coefficient, i t was first necessary to establish a confidence interval for the relationship bet,ween equivalent radius and K1 for t,he acet'ylene bubbles in pure water. For this reason, a total of 15 pure water runs were used in arriving a t t'he average Kl as well as the experimental error. Figure 11 shows the results of these runs. The staiidard deviat'ion was 0.0045 cm/rec (8y0a t r e g = 0.175 cni). The coefficient was determined for the range of equivalent, radius 0.15-0.20 cm. This corresponded to a bubble position of from 30 to 56 ern above the bottom of the column. Since the total column of water was 71 em, t'his range of positions excluded possible end effects resulting from the injection and termination phases of the bubble life. Also eliminated \vas the possible interference of reported hydrodynaniic transitions a t an equivalent radius of about 0.15 cni (Levich, 1962). Duplicate runs were used for each salt coiicent~rationiii checking reproducibility and in determining the Kl values. On some occasions it was necessary to make more than two runs for a given eoncentration of salt in order to obtain reproducibility. Tlie reason for this was contamination by a small amount of air probably caused by errors in collecting the gas samples. 1 minute amount of air was sufficient t o prevent a large part of the transfer so that a "bad" run was easily detectable. The standard deviatioii for velocity of rise of the bubble in water was 5%; in salt solutions it was generally 2Y0 or less. The volume change of the bubbles was also more reproducible in salt solutions than in water. The surprising effect of some salts on mass transfer from a rising gas bubble is probably best exemplified by Figure 12. The shaded region indicates the range of K1 for a given bubble
Sa2S04 CaCl? AlClS
and Velocity of Rise of Bubbles in Salt Solutions
-
Molar concn
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
00 09 18 27 91 10 21 30 10 16 30 04 20 02 05 20 02 03 20
KI, cm/rec
0.054 (i,004) 0.053 0.052 0,066 0.068 0.050 0.048 0.063 0.056 0.053 0.061 0.060 0.067 0.060 0.057 0.061 0.057 0.058 0.055
radius in pure water. The solid points are the Kl values in 0.09 and 0.18 111 XaC1 solutions-coiiceiitratioiis below and a t the transition in the coalescence tests. Tlie open circles indicate the A1 values iii 0.27 and 0.91 Jf SaC1-conceiitrntions above coalescence transition. The reader will note that in the latter solutions tlie n i -transfer coefficieiits are actually higher than in pure water while in the former there is 110 indication of an effect on K1. The increases in Kl, amounting to as much as 25y0 of tlie value in pure water, are unexpected even in view of the results of Tlowiiing and True.dale (1955). The over-all effects of the salts on K1are liqted in Table 111. The effect of a given salt concentration is reporteti as El which is the average of the individual Kl values a t bubble radii of 0.190, 0.175, and 0.160 cni. It' felt that reporting Kl in this way would give a better iiidicatioii of the total Kl effect. &Us0listed is the average velocity of rise and its standard deviation (in 7c). For uni-univalent salts there is a consistent iiicrease in K, values a t coiiceiitratioiis above those for which coalescence transition was reported in the coalesceiice experiments. For polyvalent salts the effect is somewhat erratic. The K1 values in SasSOl solutions are higher than in water for a very low (0.04 Jf) as well as for a relatively high (0.20 ;If)
80
X
Z
40,
G-
l
43,
3020
L
0.15
0.16
0.17
0.18
E Q U I V A L E N T R A D I U S , Re(,. (
Figure 1
.
0.19 CII
0.20
10 I 0.15
0.16
!
K L vs. equivalent radius in pure water
0.17
o.ia
E Q U I V A L E N T RADIUS, R:ri
Figure 12.
KL
0.19
0.20
0.21
(ti j
vs. equivalent radius in N a C l solutions
Ind. Eng. Chem. Fundam., Vol. 10, No. 2, 1971
267
Table IV. Relative Molar concn
Salt
0.00 0.09 0.18 0.27 0.91 0.10 0.16 0.30 0.10 0.21 0.30 0.04 0.20 0.02 0.05 0.20 0.02 0.03 0.20
YaC1
n
50,
LiCl
' --_A
700
__--~-:-~--L so0 900
Figure
1
1000 ,
I100 175 C I I
1200
1300
Na2S04
Reynolds number
concentration. For CaClz solutions there is a similar tendency although t'he effect is not as pronounced. X1C13 has no significant effect on K 1 . Discussion. The aim of the mass-t,ransfer experiments was to isolate the influence (if any) of ionic salts 011 the rate of acetylene dissolution in water per unit driving force and per unit contact area, t h a t is, t o determine whether or not ions significantly affect t h e pure water resistance t o interfacial transfer of gas molecules. In view of the effects which ions have on water structure (Gurney, 1962; Horne, 1969; Kavanau, 1964; Robiiisoii and Stokes, 1968)) it was felt that besides their effect, 011 gas solubility (Randall aiid Failey, 1927; Setschenovv, 1892) they might have some secondary influence on the ability of gas molecules to enter the liquid. The results indicate that for all three uni-univalent' salts investigated, the K1 increases significantly within the colicentrat'ioii limits used in t'his work indicating that the resistance is affected by t,he presence of these ions. The fact that this effect is reproducible and in several cases much greater than tlie experimental error (8%) indicates that some ions enhance the ability of gas niolecules to dissolve in water under the conditions of these experiments. There is little evidence that the presence of ions significantly hinder. this abilit'y. Raymond and Zieiniiiski (1970) noticed in their study of COz bubbles dissolving in dilute alcohol solutions that' in those cases where a reduction in K1 occurred, there was an attendant reduction in the hydrodynamic activit'y of the bubble. Similarly, a review of the high-speed movie films used in this work indicates that in those salt runs where Z?, is high, the bubble surface is more active than in the water runs. 4 s the bubble rises its wall fluctuates and "ripples" in all directions and it is evident that there is some connection between this hydrodynamic behavior and the increase in transfer rate. I n order to convey a feeling for the relative bubble activity from run to run, a qualitative interpretation of bubble behavior was made. This is presented in Table IV as a relative bubble dynamism expressed as "turbulenceJ' and is tabulated against the for salt solution relative to that for water. It can be seen that the agreement is not strict but that there is an undeniable indication that a significant increase in K1 is generally accompanied by a rise in turbulence. I n pursuing this reasoning furt,her, Elwas plotted against the Reynolds number (d\rRe), It can be seen (Figure 13) that there is a good correlation between the average mass-transfer coefficient and the W R in~ solution. .hother point of interest is t'he similarity of behavior be268
K C1
-J
REYNOLDS NUI,lEER ( r e [ ,
13. K L vs.
K C P
Ind. Eng. Chem. Fundam., Vol. 10, No. 2, 1971
CaCI2 ,41Cl3
e, against Turbulence -
Kdsalt)/
Ki(Hz0)
1.00 0.99 0.98 1.235 1.27a 1.04 0.99 1 .134 0.93 0.90 1.17" 1.11. 1.24. 1.l l a 1.07 1.14. 1.06 1.07 1.02
Turbulence (qualitative)
Medium Medium Medium Medium-high High Medium Low Rledium-high Low Low High High Very high Medium-high Low Medium-high High Medium-high Medium
Significant increase.
Table V -
Salt cancn
Salting-out coefficient
0.27 Jf S a C l 0 , 3 0 J I KCl 0 . 3 0 .lI LiCl 0 . 2 0 -11 YazS04 0 , 2 0 Jf CaCI? 0.20 a~lclo
0,093 0.062 0.062 0,098 0.058 0.044
KI, cm/sec
0.066 0.063 0.061 0.067 0.061 0.055
tween the I?, values aiid the dt,ing-out coefficieiit.. Table V compares the I?, values obtained in this work n i t h the snltingout coefficients for acetylene (Flid and Golyiiiets, 1959; I-Iarned and Owen, 1958; Randall and Failey, 1927). This table suggests that the trausfer coefficient increase. may be due to some effect which ions have on the water. -1coli si'd eratioii of the reasons given for salt,ing-out (Ben-Saiiii! 1965; Ben-Saini and Egel-Thal, 1965; Green and C'arritt, 1967; Long and McDevit,, 1952) leads to the viewpoint that tlie degree of salting out of a nonpolar solute, such as acetylene, is determined by the extent to which t'he solvent medium is compressed when ions are present, that is, it depends on ion-water interactions. The similarity in t'he behavior of these two coefficients, if not coincidental, would suggest that similar ion-water interactions are also responsible for the changes in the mass-transfer coefficient. Nomenclature
surface area of bubble, cm2 minor semiaxis of bubble, em equilibrium concentration of gas in liquid, moles/cm3 bulk concentration of gas in liquid, moles/cm3 Henry's law constant, moles/cm3 a t m mass-transfer coefficient, cm/sec average mass-transfer coefficient, cm/sec number of moles of gar Reynolds number P = pressure of gas 111 bubble, atni P B = barometric pressure, atm P h = hydrostatic pressure, atni P , = vapor pressure of water, atni R = gas constant, 82.057 atm cm3:moles OK
-1 b
= = Co = Cb = H = = K1 = = n Y R e =
K1
rep
T
= =
t
=
V
=
CY
ASh
= = =
6
=
T
= =
Al
u
radius of equivalent sphere, cm temperature, O K time, sec bubble volume, cm3 eccentricity, [I - 4.19(b3/V)]1’2 AI cCall-Douglasp (1965) self-diffusion parameters corrected entropy of hydration, eu (Latimer, 1955) dynamic pressure correction, a t m PI, P , atm standard deviation
+ + s,
Literature Cited
Adeney, W., Becker, H., Phil. J l a g . 38, 317 11919) Altv. T.. PTOC. ROU.SOC.A 106. 315 119241. Altir: T.: Proc. Ro;. Sot. A 110; 178 (1926a). Alty, T., Proc. Roy. SOC.A 112, 235 (192613). Bakh, Y., Gilman, A., Acta Physzcochani. 9 , 1 (1938). Ben-Naim, A., J . Phys. Chem. 69, 3240 (1965). Ben-Naim. A , Eael-Thal, AI.*J . Phus. Cheni. 69, 3230 (1965). Carver, C‘,, “Biological Treatment” of Sewage and Indiistrial Wastes, Vol. 1, Reinhold Publishing Corp., S e w York, 1956, p 149 Ciirrie, B., Alty, T., Proc. Roy. SOC.A 122, 622 (1928). Davieq, J., Rideal, E., “Interfacial Phenomena,” Academic Press New York, 1963, Chapter 8. Devell, L , Acta Chem. Scond. 16, 2177 (1962). Donning, A., Truesdale, G . , J . Appl. Chem. 5 , 570 (1955). Flid, I1 , Golynets, Y., Khzm. Khim. Tekhnol. 2, 173 (1939). Foulk, C , Ind. Eng. Chem. 21, 813 (1929). Foulk, C , hIiller, J., Ind. Eng. Chem. 23, 1283 (1931). Frumkin, A , , Z . Phys. Chem. 109, 34 (1924). Good, W., Electrochim. Acta 9 , 208 (1964). Good, W., EIectrochzm. Acta 10, 1 (1963). Good. W.. Electrochzm. Acta 11. 767 11966) Green, E.: Carritt, D , Sczrnce i57, 191 (1967). Gurney, I{., “Ionic Processes in Solution,” JlcGraw-Hill Book Co , I n c , Xew York, 1953, p 163. Gurnham. C.. “Indnstrial Wastewater Control,” Acadrmic Press, Xew York, 1965, p 6. Harned, H., Owen, B., “The Physical Chemistry of Electrolytic Soliitions,” Reinhold Book Corp., Xew York, 1938, Chapter 12. Horne, R., “LIarine Chemistry,” ~iley-Interscience,New York, 1969.
Hunt, J., “RIetal Ions in Aqueous Solution,” W. A. Benjamin, Inc.. S e w York. 1965. D 41. “International Critical ’qables,” McGraw-Hill Book Co., New York, 1929a, Vol. 5 , p 12. “International Critical Tables,’’ McGraw-Hill Book Co., S e w York, 1929b, Vol. 3, p 280. Jarvis, X.,Scheiman, M., J. Phys. Chem. 72, 74 (1968). Jones, J., Rowlands, I]., LIonk, C., Trans. Faraday SOC.61, 1384 i196.5i. Kavanaii, J., “Water and Solute-Water Interactions,” HoldenDay, Inc., San Francisco, 1964, p 37. Latimer, W., J . Chem. Phys. 23, 90 (1955). Levich. V., “Phvsicochemical Hvdrodvnaniics.’’ Prent ice-Hall. Englewood Clcffs, N. J., 1962, Chaptkr 8. Long, F., hIcl)evit, W., Chem. Rev. 51, 119 (1952). Mancy, K., Okim, I)., J . TVater Pollzit. Confr.Fed., 212 (1965). RIarriicci, G., Sicodemo, L., Chem. Eng. Sei. 22, 1237 (1967). J . Phys. Chem. 69, 2001 (1965). RIcCall, I)ouglass, McTaggart, H., Phil.M a g . 27, 297 (1914a). McTaggart, H., Phil. J l a g . 28, 367 (1914b). McTaggatt, H., Phil. Mag. 44, 386 (19221. Quincke. Poaa. Ann. 113. 513 11861). Ifandall, JI.:>ailey, C., ?hem. Rev 4, 271 (1927). Raymond, I)., Zienhski, S , 67th A.1.Ch.E. National lleetinp, Atlanta, Ga., Fet) 18, 1970. Robinson. R.. Stokes. R.. “Electrolvte Solutions.” Butterworths,’ London, 1966. ’ Schniirman, I?., Z. Phiis. Chem. 143, 456 (1929). Setschenow, M.,Ann. Chim. Phys. 25, 226 (1892). Siitra, G., J . Chim. Phys. 43, 290 (1946). W R I I J., ~ , J . Ph?js. Chum. 58, 686 (1954). Ziemiiiski, S., Caron, AI., Blackmore, R., ISD. ENG.CHF:M., FL-ND.~M. 6, 233 (1967). Zieminski, R.,Goodwin, C., Hill, It., T A P P I 43, 1029 (1960). Zieminpki, S.,Hill, R . , J . Chem. Eng. Data 7 , 31 (1962). Zieminski, S., Lessard, R . , Ind. Eng. Chem., Proc. Des. Develop. 8, 69 (1969). Zieminski, S., Raymond, D., Chem. Eng. Sei. 23, 17 (1968). Zieminski, S., Whitternore, R . , pitblication pending, Chem. Eng. Sci. (1971). Oire of the aiithors (11. I?. I,.) is indebted to the National Aeronautics and Space Administration for its traineeship siipport. R ~ c x i v i .for : ~ review June 1, 1970 ACCEPTED February 12, 1971 1
A Correlation of Molecular Parameters for Transport Properties of Polar Gases Jae Ho Bae and Thomas M. Reed 111 sf Chemical Engineering, Ihicersity sf Florida, Gainesville, Florida 38601
Department
A method i s presented for estimating the dispersion-energy parameters of the canonically averaged pair potential energy function for polar molecules. The empirical parameters are correlated with critical temperature and polarizability through the principle of corresponding states and the Mavroyannis-Stephen dispersion theory. The method predicts viscosities and diffusivities of dilute gas mixtures which are within experimental uncertainty of measured values.
A
canonically angle-averaged pair-potential energy function has been applied to the correlation of the transport properties of polar molecules and their mixtures in the gas phase (Bae and Reed, 1967, 1971). This potential energy function is ($)ij
=
- $6“)]
eij* 2I*):([
(1)
,* =
e 23 ’
eijo[l
+
pi2pj2P/3eijorijo6
+
(ptzaj
r . .*
= rijo(cijo/ctj*)‘
+
pj*CuZ)/2Ei30rij06]2
‘I!
(2) (3)
(& is the mutual potential energy of the pair ij, t i j o and rile are the const’antscharacteristic of dispersion interact,ion, is the dipole moment, CY is the mean polarizability, and = (kT)-’. This potential contains the leading terms from the canonical ensemble average over the angular coordinates p
in which the parameters, perature
eij*
and
rij*,
are functions o f tem-
P
Ind. Eng. Chem. Fundam., Vol. 10, No. 2, 1971
269
