The behaviour of a drop of carbon bisulphide placed upon clean water is also, at first sight, an exception to Marangoni’s rule. So far from spreading over the surface, as according to its lower surface-tension it ought to do, it remains suspended in the form of a lens. Any dust that may be lying upon the surface is not driven away to the edge of the drop, as would happen in the case of oil. A simple modification of the experiment suffices, however, to clear up the difficulty. If after the deposition of the drop, a little lycopodium be scattered over the surface, it is seen that a circular space surrounding the drop, of about the size of a shilling, remains bare, and this, however often the dusting be repeated, so long as any of the carbon bisulphide remains. The interpretation can hardly be doubtful. The carbon bisulphide is really spreading all the while, but on account of its volatility is unable to reach any considerable distance. Immediately surrounding the drop there is a film moving outwards at a high speed, and this carries away almost instantaneously any dust that may fall upon it. The phenomenon above described requires that the water-surface be clean. If a very little grease be present, there is no outward flow and dust remains undisturbed in the immediate neighbourhood of the drop.]
| Fig. 6. |
On the Rise of a Liquid in a Tube.—Let a tube (fig. 6) whose internal radius is r, made of a solid substance c, be dipped into a liquid a. Let us suppose that the angle of contact for this liquid with the solid c is an acute angle. This implies that the tension of the free surface of the solid c is greater than that of the surface of contact of the solid with the liquid a. Now consider the tension of the free surface of the liquid a. All round its edge there is a tension T acting at an angle a with the vertical. The circumference of the edge is 2πr, so that the resultant of this tension is a force 2πrT cos α acting vertically upwards on the liquid. Hence the liquid will rise in the tube till the weight of the vertical column between the free surface and the level of the liquid in the vessel balances the resultant of the surface-tension. The upper surface of this column is not level, so that the height of the column cannot be directly measured, but let us assume that h is the mean height of the column, that is to say, the height of a column of equal weight, but with a flat top. Then if r is the radius of the tube at the top of the column, the volume of the suspended column is πr²h, and its weight is πρgr²h, when ρ is its density and g the intensity of gravity. Equating this force with the resultant of the tension
πρgr²h = 2πrT cos α,
or
h = 2T cos α/ρgr.
Hence the mean height to which the fluid rises is inversely as the radius of the tube. For water in a clean glass tube the angle of contact is zero, and
h = 2T / ρgr.
For mercury in a glass tube the angle of contact is 128° 52′, the cosine of which is negative. Hence when a glass tube is dipped into a vessel of mercury, the mercury within the tube stands at a lower level than outside it.
Rise of a Liquid between Two Plates.—When two parallel plates are placed vertically in a liquid the liquid rises between them. If we now suppose fig. 6 to represent a vertical section perpendicular to the plates, we may calculate the rise of the liquid. Let l be the breadth of the plates measured perpendicularly to the plane of the paper, then the length of the line which bounds the wet and the dry parts of the plates inside is l for each surface, and on this the tension T acts at an angle α to the vertical. Hence the resultant of the surface-tension is 2lT cos α. If the distance between the inner surfaces of the plates is a, and if the mean height of the film of fluid which rises between them is h, the weight of fluid raised is ρghla. Equating the forces—