J. Phys. Chem. 1995,99, 10420
10420
Solute Effects on Bubble Coalescence H. K. Christenson* and V. V. Yaminsky
1 -
Department of Applied Mathematics, Research School of Physical Sciences, Australian National Universio, Canberra ACT 0200, Australia Received: July 12, 1994; In Final Form: April 27, 1995 Bubble coalescence in aqueous solution is largely inhibited above a critical concentration range of electrolyte, the so-called transition concentration.'-8 Craig et al.738have recently made the intriguing observation that certain electrolytes have no effect on bubble coalescence (as judged by measurements of the turbidity in a gas-sparged column), even at very high concentrations (-0.5 M). Related observations are to be found in the older literatureg-I0but have since apparently been forgotten. There is a model that has been advanced to explain the dependence of coalescence on type and concentration of electrolyte.' Together with several more recent extension^^^^^^ it involves the change in surface tension with concentration, or the surface activity dyldc. This quantity is related to the elasticity E of an interface, which determines the response of the interface to mechanical di~turbance.'~*'~ From the definition of E
'
where A is the area (with a factor 2 for films with two interfaces). When a film is stretched, the area to volume (V = AD, where D is some measure of the thickness of the interface) ratio increases, and the concentration is changed by
electrolyte
dy/dc% A y / c (1 M)
(dy/dc)2
transition concn
CaClz NaCl (CHd4NCl NaC103 CH3COOK HC1 HNO3 (COOH)2 HC104 CH3COOH
3.2 1.6 0.6
10 2.6
Yes yes no no
0.55 0.45 -0.3 -0.8 -0.85 -1.6 -3.2
0.4 0.3 0.2 0.1 0.6 0.7
2.6 10
no no no no Yes Yes
a Surface tension data from ref 14, data on transition concentrations from refs 7 and 8.
Using the Gibbs adsorption equation
r=-&
kT dc
(3)
the elasticity for a film of two interfaces can be written as
E=
4c [dyldc]
kTD
It remains to be seen whether or not more involved models of bubble coalescence would provide a more detailed picture of the effects of electrolytes on the behavior of a gas-sparged column.
Acknowledgment. The authors thank V. S . J. Craig, B. W. Ninham, and R. M. Pashley for discussions. (4)
The elastic response of the interface to changes in film thickness increases coalescence times in solutions compared to pure liquids (the Marangoni effect). This is a general solute effect, and the important quantity is the magnitude of dyldc, or [dy/dcl2. If one takes the data (from refs 7 and 8) for those electrolytes that show a transition concentration to coalescence inhibition and plots the measured transition concentrations against literature values for (dy/dc)2, quite a good correlation is obtained (Figure 1). Electrolytes that lack a transition concentration would be those for which c would have to exceed the solubility limit to give the same elasticity. This is clearly seen by tabulating the (dy/dc)2 values of some of the electrolyte solutions investigated by Craig et aL7s8 (Table 1). Electrolytes that show no inhibition of coalescence are those with small values of (dy/dc)2. The combination rule found by Craig et al. reflects the roughly additive contributions of separate ions (negatively or positively adsorbed) to the surface activity dyldc of a salt. 0022-3654/95/2099-10420$09.00/0
References and Notes (1) Marucci, G.; Nicodemo, L. Chem. Eng. Sci. 1967, 22, 1257. (2) Lee, J. C.; Meyrick, D. L. Trans. Insr. Chem. Eng. 1970,48, T37. (3) Lessard, R. L.; Zieminski, S. A. Ind. Eng. Chem. Fundam. 1971, I O , 260. (4) Sagert, N. H.; Quinn, M. J. Chem. Eng. Sci. 1978, 33, 1087. (5) Oolman, T. 0.;Blanch, H. W. Chem. Eng. Commun. 1986, 43, 237. (6) Prince, M. J.; Blanch, H. W. AIChE J. 1990, 36, 1425. (7) Craig, V. S. J.; Ninham, B. W.; Pashley, R. M. Nature 1993, 364, 317. (8) Craig, V. S. J.; Ninham, B. W.; Pashley, R. M. J. Phys. Chem. 1993, 97, 10192. (9) Pollock, J . A. Philos. Mag. 1912, 24, 189. (10) Foulk, C. W.; Miller, J. N. Ind. Eng. Chem. 1931, 23, 1283. (1 1) Marucci, G. Chem. Eng. Sci. 1969, 24, 975. (12) Gibbs, J. W. The Collected Works of J . Willard Gihhs; Yale University Press: New Haven, CT, 1948; p 300 et seq. (13) Adamson, A. W. Physical Chemistry of Surfaces, 5th ed.; Wiley: New York, 1990; p 549 et seq. (14) International Critical Tables; McGraw-Hill: New York, 1928; Vol. IV, pp 463-470. (15) Ralston, J.; Healy, T. W. J. Colloid Interface Sci. 1973, 42, 629.
JP941742F 0 1995 American Chemical Society
