EFFECT OF ~ I E C H A N I C AI’KOI)UCED LLY WAVESON ~IONOXOLECTJI~AR LAYERS
3535
The Effect of Mechanically Produced Waves on the Properties of Monomolecular Layers
by Thomas W. Healy’ and Victor K. La Mer Drpartment
of
Mineral Engineering, Columbia University, New Y o r k , New York
(Received January 27, 1961,)
hlonolayers of n-paraffinic alcohols on water were subjected to the action of mechanically produced capillary waves, and the surface pressure-area per molecule isotherms were measured while thc disturbance was present. For high amplitude capillary waves, the surface pressure behavior a t pressures less than about 15 dynes cm. could be understood in terms of the increase in area due to the wave. At higher pressures, this increase in area was not sufficient t o explain the isotherm for the wave-covered surface. Mechanisms relating to submergence and collapse of the monolayer are discussed, and the effect of capillary waves on the ability of monolayers t,o retard evaporation of water is considered.
-’
Introduction It is now well established that monolayers of longchain alcohols and other surfactants can, under suitable conditions, retard the evaporation of water in the laboratory and in the field.2 This principle has found application in field tests in the U. S. and Australia in particular, where significant savings of usable water have resulted. The Columbia University Evaporimeter, developed by Archer and La Mer3a and improved by La Mer and Barnes3bis basically an instrunlent that uses the transport of water niolecules as a probe to examine the properties of monolayers. This Evaporinieter is a surface balance with a desiccant assembly, suspended a few millimeters above the water surface, that records the mass of water per unit time that passes through a known area of the liquid-air interface that is either clean or covered with monolayer. The theory of this phenomenon and of the Evaporimeter have been well established in a series of experiments conducted a t Columbia Gniversity by La AIer and eo-workers over the past 12 years. Iri order to achieve reproducible results, free from the erratic disturbing effects of a current of air, and thus avoid the erroneous results which vitiate the work of earlier investigators, our investigations have been made exclusively under static conditions. It is of interest to extend these studied by introducing a mechanical vibration (ie., waves without wind)4arb on the water
surface and monitor the properties of the monolayer subjected to this disturbance. A monolayer on a reservoir is subjected to continual disturbance by the action of wind. The monolayer moves laterally over a body of water as a “slick.” I n addition, the wind creates waves on the water surface that are either gravit,y waves, Le., of long wave length, or capillary waves, where the wave length is less than about 1.0 em. The movement of slicks and the effect of gravity waves have been and are again receiving invest i g a t i ~ n . ~ -The ~ damping action of monomolecular layers on capillary waves (often referred to as ripples) has been investigated from the theoretical and practical point of ~iew.7-I~Since this investigation is oriented (1) Department of Mineral Technology, University of California, Berkeley, Calif. (2) V. K. La Mer, Ed., “Retardation of Evaporation,” Academic Press, New York, N. Y., 1962. (3) (a) R. J. Archer and V. K. La Mer, J . Phys. Chem., 59, 200 (1955); Ann. N . Y . Acad. Sci., 58,807 (1954); (b) V. K. La Mer and G . T. Barnes, Proc. Natl. Acad. Scd. U.S., 45, 1274 (1959). (4) (a) H . Lamb, “Hydrodynamics.” 6th Ed., Dover, 1932; (b) on this topic, H . Lamb, ibid., p. 60, has noted: “Owing to the irregular, eddying character of a wind blowing over a roughened surface, it is not easy to give more than a general explanation of the manner in which it generates and maintains waves.” (5) W. W . .Mansfield, Australian J . Appl. Sci., 10, 73 (1959). (6) I. K. H . McArthur, Research, 15, 230 (1962). (7) (a) J. T. Davies and E. K . Rideal, “Interfacial Phenomena,” Academic Press, New York, N. Y . , 1961, pp. 265-274; (b) J. T. Davies, Chem. I d . (London), 906 (1962). (8) W. D . Garrett and J. B . Bultman. J . Colloid Yci., in press,
Volume 68,hlumber 12
December, 1964
THOMAS W. HEALYAND VICTORK, LA MEH
3536
primarily toward the retardation of evaporation of monolayers, recourse to some of the wave-damping equations is made with minimal comment only. The prime motivation for studying the effect of capillary wave action on evaporation suppression is that it is the capillary waves arid not the gravity waves that are directly affected (i.e., damped out) by the monolayer OIL the water surface. However, it is also irnportant to keep in mind the interrelation between capillary and gravity waves. Capillary waves are thought to be generated by complex flow patterns either in the water or in the air, particularly in the region of the wave crests. Furthermore, the gravity waves, as they become steeper, can in fact generate a capillary wave pattern, even in the absence of wind, on the face of the gravity w a n L 4 In this way, the capillary waves can play a significant role in the generation of waves by wind, in that they tend to delay the onset of breaking and therefore complete rupture of the monolayer. The fundamental importance of capillary waves on a water surface is that their formation tends to dissipate the energy of the gravity waves.
Theory of the Wave We shall consider a section of water surface of length L cm. and breadth B cm. within which is contained a thin bar slightly less than B cm. long and oriented a t right angles to the length of the water area. Let this bar oscillate in the surface a t some frequency f c.P.s., and with an amplitude of a. cm. If the z-axis is along the length of the trough and the y-axis is at right angles l o the water surface, then the oscillation is in the y-z plane. The wave profile is shown in Vig. 1. The equation of the wave is 2a
y = aoe-'" cos --- x
x
wherc u is the damping coefficient and X is the wave length. We now require the area of the disturbed surface relative to thc static surface. Let d S be the length of an clement of the curve, then dS =
= [l
+ (dy/d~)~]"'
(24
+
[ ' / z ( d y / d ~ )~ '/8(d?j/d~)~ '/ie(dy/d~)~]dx(2b) =
+ '/z(dy/d~)~ldz
(2c)
wherc eq. 2c is approximatcly true, provided X >> a. The area of the disturbed or rippled surface, in terms of the lcrigt h along the damped oscillation is S and is given by So
=
nX -
'/2JnA[
0
l(,,.xx.Tx)]zdz
dx
The Journal of I'h~lsicnl (7hemistry
COS
2
(3)
Y
t
X
+
I Figure 1. Schematic profile of damped oscillation of wave length, A, in em.
The surface pressurearea per molecule curve for the disturbed surface can be calculated from this equation and the corresponding curve for the static surface. Such a calculation involves the assumption that the decrease in surface pressure caused by the disturbance is due solely to the increased area of the rippled surface as compared to the static surface. For the present, a wave lcngt,h (A) of 0.5 em. and an initial vibrator amplitude (ao) of 0.0655 cm. were used for most experiments. The area of water surface onto which the disturbance was applied was 14.1 cm. X 30.0 cm. ( i e . , n = 60). For these conditions, the percentage increase in area of the disturbed surface can be expressed in terms of the damping coefficient (u).Since u is a function of the surface pressure, the increase in area a t a given pressure can be calculated and the pressure-area diagram for a disturbed surface can be determined.
Experimental Apparatus. Our Evaporimeter consists of a Langmuir trough of Pyrex glass, Wilhelmy plate assembly (the plate of roughened mica was suspended a t right angles to the waves), desiccant box assembly to record the evaporation resistarice of the mon01ayer,~,~a and a wave generator. The wave generator was a T-bar lying in the water surface, approximately 10 to 15 em. from the Wilhelniy plate, which vibrated in and out with respect to this water surface. The T-bar was cemented to t,he voice coil of a 24-cm. speaker. The voice coil was approximatcly 1.9 em. in diameter. The speaker ~~
(9) F. C. Goodrich, J . Phys. Chem.. 6 6 , 1858 (1962). (10) P. C. Goodrich, Proc. Roy. SOC.(London), A260, 481 (1961). (11) It. G. Vines, Australian J . Phys., 13, 43 (1960). (12) I t . Dorrenstein, Proc. Acud. Sci. Amsterdam, B54, 260, 350 (1951).
(13) I
