Comments on the Article “Longitudinal Instabilities in exit flow from a slit” by V. V. Gokhale in the Light of Renewed Interest in the Ohnesorge Number

Recently there has been renewed interest in the dimensionless number known as the Ohnesorge number denoted by the letter 𝐙, for example a discussion of the biography of Ohnesorge in [1]. This article is concerned with the setting down of a purely mathematical number 0.944261248574953 , which happens to be the critical value of the dimensionless number 𝐙, consisting of a combination of the viscosity, density, surface tension and half slit width (in a rectangular geometry) for the onset of instability. The work was performed by me [2] as a first year graduate student at the University of Delaware as part of a class. Some questions had been raised about the algebra leading to the critical value of 𝐙 after the work was published [3]. I responded to the comments [4] but evidently not with sufficient impact. These questions are settled decisively here with an a posteriori analysis of the magnitude of terms in the associated boundary condition. The idea of such a method of solving problems is implied in the article but was not fully appreciated. Data from [5] is analyzed in the light of this analysis. Keywords - Capillary Instability, Rheology, Surface Rheology, Surface Tension, Thin Film, Viscosity