BOUNDARY TENSION BY PENDANT DROPS1 J. M. ANDREAS, E. A. HAUSER, AND W. B. TUCKER Department o j Chemical Engineering, Massachusetts Institute of Technology, Cambridge, iMassachusetts Received July, 1, 1988
Boundary tension is a measure of the free energy of a fluid interface. The term is derived from the superficial analogy between the surface of a liquid and a stretched membrane. For, just as it has proven to be convenient to express the potential energy of a fluid mass in foot pounds per pound as a “head” in feet, it has been shown to be useful t o speak of the free energy of a fluid surface in ergs per square centimeter as a “tension” in dynes per centimeter. Surface tension is the boundary tension at an interface between a liquid and a gas or vapor, and interfacial tension is the boundary tension a t a phase boundary between two incompletely miscible liquids. Nearly all of the common specific properties of fluids, such as the density, boiling and freezing points, optical rotation, and thermal conductivity, are properties of the main body of the fluid. The boundary tension is the best known property of liquid surfaces. For this reason it is of outstanding importance in colloid chemistry, which frequently is called the chemistry and physics of surfaces and surface reactions. The usefulness of boundary tension measurements has been limited in the past by the great difficulty of making determinations. with satisfactory speed, accuracy, and precision. A great many procedures have been developed for the determination of boundary tension, of which the majority are just barely workable and are characterized by low precision and lack of versatility. Of seventeen methods listed by N. E. Dorsey (6) in 1926, only a few are in common use. These depend upon observing: (a) the behavior of a liquid in a capillary tube (24, 35, 46); ( b ) the force required to pull a wire ring or staple out of the liquid surface (29, 36); ( c ) the weight or volume of drops falling from a vertical tube of known size (15, 16); or ( d ) the maximum pressure required t o form bubbles in a liquid from a tube of knoxn size (47, 53). Each of these methods has serious limitations (1). This lack of a generally satisfactory method of measurement suggested that it would be profitable to resurvey the field in search of some possiPresented a t the Fifteenth Colloid Symposium, held at Cambridge, Rlassachusetts, June 9-11, 1938. 1001
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J . M. ANDREAS, E. A. HAUSER A N D W. B . TUCKER
bility which had been overlooked by the earlier workers and in the hope that a new method could be developed which would succeed where others had failed Previous work (8) had demonstrated that the method of pendant drops has a number of outstanding advantages over other methods. Outstanding from the colloid chemist's point of view is the fact that this method is a static one. Once the surface is formed, it is not subjected to any changes due to outside influence prior to or during the measurement. It is the only known method which permits an accurate study of changes in surface composition with time, a phenomenon of predominant importance in the study of various colloidal systems. Accordingly, the focus of our attention was on the design of apparatus and the development of mebhode with which its possibilities could be explored. I n addition to this a n extensive series of measurements was made of typical liquid systems t o S ~ I O T Vt h e range of usefulness of the new method and to show the sort of resiilts which can be expected thod which was dwided upon consists in suspending a small drop of id to be tested from the end of a vertical tube which is mounted in a ttieirnoftat The surface of the drop will be a surface of revolution whoqe shape and size can be determined by measurements made on a large photographic image obtained with a special camera built for the purpose. Since the equations determining the equilibrium of the drop are known, the boundary tension of the liquid can be calculated from a few simple measurement> made on a photograph of a hanging drop. This method has been undeservedly in disrepute for a number of years, because the first workers (11, 55) who attempted to employ it had no saticfactory pendant drop camera and used method> of calculation which 1% ere tedious and of low precision. These difficulties hare now been overcome APPARATUS
The apparatus consists, essentially, of a light-source, a thermoitat chamber, a set of drop-forming tips, and a precise camera having a fixed image distance and a telecentric lens system (figure 1). Experience shows that monochromatic light gives slightly more satisfactorji images than white light. It can conveniently be obtainedbyusing a mercury arc lamp (GE, Type H-3, 85-watt, high pressure) and gelatin filter (Wratten N o . 77-A) combination. The drop hangs from a vertical, cylindrical tip in a glass cuvette inside the thermostat (figure 2). I n this way the drop is maintained a t all times in physical equilibrium with its surroundings. The inner chamber of the thermostat must be totally enclosed t o prevent loss of liquid by evaporation, and it should be held t o within f 0 05" C. of the desired temperature, since solubilities, vapor pressures, and boundary tensions all change with
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temperaturr. Our thrrmostat ~ n mnintainrd s to uithin =t0.01' C. hy a sensitive thrrmorrgiilator. To guarantee surh constant trmprratirrrs, watrr lrom a tank rontaining the thermorrgrilator was piimprd through t h r thrrniostat a t a rate of 30 gallons per minutr. Vihrationr set rip hy t h r puml' WPP ahaorhed hy
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h;. 2. Thrnnostst rontninittg cuvvttc. R e . 8 . Cuwttr rind drop-forming tip pwp:w~dfrcm I l q n h r t n i c ~syvit>K must be incorporated in any casc. It is essential for the drop to be photographed with rays of light whirli are parallel to the optical axis, if error due to perspective is to be avoiclcd. We accomplished this hy using standard microscope object,ives of 48 or 24 nim. focal lengths which were equipped with telecentric stops. The camera should be built t o make pictures on glass plates and to have an optical magnification of from 10 t o 30 diameters. CALCULATIONS
A . The method of the plane of iri,j%ction 'l'lic 1)oiindary tcwsion can bc computed directly froin an :tnalynis of thcl stresses in a static, pendant drop. The inath~niaticaltreatment is based on two fiuidttnicntnl equations. T h r first of thrw state- t h a t tlic pressure ( , : t i i d Iiy tlic (4rirv:itiirc of tlic siirfaw i h cqiral to tlrc, protlnrt of tlw I ~ o r ~ n t l t I i a t , \vli(x~i t lit, :iry tcxtisioir : i i i t l t t i c i i i w t i t,iirv:Ltiirp,2 Tlir rrcwiitl tltwl) is i i i ( ~ ( l i i i l i l ) t . i i l l i i , I t i ( % vrbr.tic.:il IOIYY+:u
