Surface tension has been threshed out pretty thoroughly by articles appearing in the Journals of the American Chemical Society, beginning in 1908.
These articles deal with the drop-weight method (weight of a falling drop) for the determination of molecular weight, critical temperature, and surface tension, and they describe the apparatus used. The work was started by Morgan and Stevens, who wished to investigate what had become known as the law of Tate.
Tate, in 1864, had made a generalised statement about the relation of weight of drop to diameter of tube, the weight that could be raised by capillary action, and the temperature of the drop. Some of their conclusions are that:
- The drop-weight of any liquid is proportional to the diameter of the dropping-tube. These tubes are uniform in diameter, thus differing from the ordinary burettes.
- The weight of a drop, other things being the same, is proportional to the surface tension of the liquid.
- That it is possible to calculate the temperature at which the drop-weight would become zero, namely, the critical temperature of the liquid, for at that point the drop would disappear, there being no distinction between the gas and the liquid.
In the course of these experiments the surface tension of a number of organic liquids in aqueous solution was determined by drop-weight and found to range from 21 up to that of water. The tabulated results cover several pages in the Journal; I have copied a part and condensed into one table, which is given below.
It is to be noted that in all cases the very first addition causes a very considerable lowering of surface tension. The decrease in the surface tension of water caused by the addition of a very small amount of amyl alcohol is especially striking. Thus the presence in solution of even so small an amount as 0.25% changes the surface tension of water from 71.03 to 53.7, or nearly 25% at 30° C.
Morgan and Schramm studied many concentrations of a few salts. They selected the molten hydrated salts for this purpose; those salts which melt below 50° in their own water of crystallisation being especially satisfactory for this purpose, for the reason that concentration in some of these cases could even be carried to super-saturation.
In the case of the salts which they studied it is plain that surface tension is increased by the salts introduced. Where calcium chloride was used, the surface tension was increased from 71.03 to 102.57, approximately 50%. Taking a few specific cases it is noted that to increase the surface tension 10% it would take
20% CaCl2 at 30°
43 % Zn (NO3) at 45°
29% Na2CrO4 at 30°
34% Na2SO3 at 40°
The diagram is appended. See Fig. 30.
The degree of accuracy of Valson’s early generalisation that equivalent salt solutions exhibit identical values of surface tension is shown by plotting the same results reduced to molecules of water to molecules of salt. But one must be careful not to carry generalisations too far because this does not hold with some salts. The diagram is appended. See Fig. 31.
The fact is that some salts elevate while other depress surface tension, but the former predominate. In addition to the salts just mentioned, the tartrates, carbonates, oxalates, citrates, lactates, and a part of the acetates raise surface tension; while the salicilates, the butyrates, part of the acetates, and all the acids lower surface tension.
It is suggested that the liberation of free acid by hydrolysis in the case of salts of weak acids may cause their negative effect on water. All acids lower surface tension, and in the case of the fatty acids experiments have shown that the lowering is proportional to the carbon content of the acid.
It is suggested in these researches that the surface tension of a solution of two salts one of which raises the surface tension and the other lowers it, is an additive property of the two solutions—provided no chemical reaction takes place between them, and the values of the two are not far removed from the value of water. If one of the solutes causes a much larger effect than the other, the value of the mixture lies closer to the one with the greater effect.
Regarding the variation of surface tension with temperature, it is made clear that surface tension increases with decrease in temperature.
In reviewing the subject of flotation in one of the mining journals about two years ago, a leading educator made the statement that heat increases surface tension. Now this is absolutely erroneous in case of pure water and it is not likely that it would maintain in any case. I do not mention this in a fault-finding spirit, but to show that in the science of flotation the metallurgical engineer faces problems in physics and chemistry that are absolutely new to him.
In the work in the chemical journals the surface tension of pure water is taken as 71.03 dynes per cm. at 30°, 69.33 at 40°, and 68.46 at 45°, while Hoover uses 81 with apologies. Again Hoover makes a slip on page 77 where he says that surface tension of water has been determined to be a force of 81 dynes per square centimetre. Here he has confused surface tension in dynes per centimetre with surface energy in “ergs per sq. cm.” Work (in ergs) is the act of producing a change in opposition to a force (in dynes) that resists this change. Now, gravity gives to a gram a velocity of 980 cm. per second. It is therefore equal to 980 dynes. Hence if one gram be lifted vertically one centimetre, the work done against gravity is 980 ergs. Books on physics demonstrate that surface tension (dynes) per unit-width is numerically equal to surface energy (ergs) per unit-area. We should therefore speak of surface tension in dynes per centimetre, and surface energy in ergs per square centimetre.
The above figures on surface tension and surface energy might be applied to the so-called surface tension method of flotation, such as the Wood machine, where the ore is fed dry onto the surface of water and at one place at least, in the West, where the wet oiled pulp is spread upon the surface of water in a spitzkasten.
While 0.0724 gm. (71.03 ÷ 981) per sq. cm. represents the weight that it requires to just break the surface membrane of pure water, there is another factor, and that is the size of the dimple formed. Take the case of galena. The buoyant factors are the membrane and the water displaced. Taking the specific gravity of galena at 7.5, the maximum volume of a dimple on one square centimetre would be 0.0096 cc. (0.0724 ÷ 7.5) or a displacement equal to 0.0096 gm. water. Adding the two quotients we find that 0.082 (0.0724 + 0.0096) gm. galena per sq. cm. would just break through. This is not mathematically correct, but a close approximation— sufficiently close, because we do not know the volume of the foreign water attached and the condition of the water.