The shape and position of bubbles at horizontal liquid surfaces

The scope of this investigation comprises the determination of the shape and position of a gas bubble floating at the horizontal surface of a liquid. — A starting point towards the solution of this problem is provided by Laplace's law, but this equation is soluble analytically in very few cases only. It is shown that the most useful parameters can be obtained from Princen's table which is a modified version of Bashford and Adams table and other dimensions can be evaluated from the equations as proposed in the context. It is suggested that r√c should be used as the fundamental dimensionless shape parameter and further the radius r of the equivalent sphere can be related to original radius r₀ of the bubble by means of a correction factor. — This system has also been studied experimentally. A photographic technique has been used, both the length x_c and the height h of upper part of the bubble at the surface have been measured on photographs thus allowing a sensitive test of the theory.