Comments on a Ruptured Soap Film

Abstract

Subsequent to puncturing at a point, a horizontal soap film develops a hole whose edge, owing to surface tension, propagates outward from the point of puncture at apparently constant velocity. Measurements by Ranz [1] yielded results roughly 10% lower than those calculated on the basis of a simple energy conservation suggested by Rayleigh [2]. The discrepancy was attributed to an additional retarding viscous stress not included in the analysis. It appears, however, that the energy balance quoted [1] neglects an important contribution, indeed related to th viscous effect noted by Ranz, but which reduces the calculated values to 20% below those measured. A more detailed analysis of the motion of the edge gives this result; the neglected contribution arises from inelastic acceleration of the undisturbed fluid up to the velocity of the edge. The concomitant loss in mechanical energy may be identified with viscous dissipation which is estimated to be confined to a relatively thin region. Lack of agreement between calculated and measured values of the edge velocity seems to be causes by a second-order effect in the method used [1] to determine the thickness of the film.