On making holes in a sheet of fluid
It is suggested in this paper that axisymmetric holes in thin sheets of fluid in which surface tension forces predominate will open out if they are initially large in relation to the thickness of the sheet; but that small holes will close up. No exact criterion has been found for the critical hole size in a free falling sheet, but the behaviour of the sheet may be closely simulated by the suspension of a soap film between coaxial circular rings. Theoretical results and experimental observations on catenoid films so formed are described.
For a hole in a sheet standing under gravity on a horizontal plane an equilibrium configuration exists, which is shown to be unstable. It is suggested that in this case the equilibrium position serves to distinguish between holes which open and those which close. Experiments on the behaviour of holes in a mercury sheet reveal a well-defined critical size which is in good agreement with that predicted by the unstable equilibrium.
A further series of experiments on holes made in a sheet of water standing on paraffin wax gave no sharp distinction between opening and closing holes, and holes of a wide range of sizes could remain stationary. This behaviour is associated with changes in the angle of contact with the plane. Independent meniscus observations similar to those of Ablett for a steadily moving meniscus show that the angle of contact θa, for a meniscus about to advance is greater than the value θr for a meniscus on the point of receding. It is seen that this difference will produce a range of hole diameters within which a hole will be trapped and remain stationary. Observations on the minimum size of hole on a water sheet which will remain open are reported. But it was found that the largest holes which would remain stationary were too large in relation to the size of the sheet for reliable results to be obtained.(Published Online March 29 2006)
(Received October 12 1972)