The formation of thick borders on an initially stationary fluid sheet

Abstract

The formation of thick borders on an initially stationary two-dimensional fluid sheet surrounded by another fluid is examined by numerical simulations. The process is controlled by the density and the viscosity ratios, and the Ohnesorge number [Oh = μ/(ρdσ)0.5].[Oh=μ/(ρdσ)0.5]. The main focus here is on the variation with Oh. The edge of the sheet is pulled back into the sheet due to the surface tension and a thick blob is formed at the edge. In the limits of high and low Oh, the receding speed of the edge is independent of Oh. Different scaling laws, however, apply for the different limits. The speed scales as V ∼ (σ/ρd)0.5V∼(σ/ρd)0.5 in the low Oh limit as proposed by Taylor [Proc. R. Soc. London, Ser. A 253, 13 (1959)] and as V ∼ σ/μV∼σ/μ in the high Oh limit. For low enough Oh, the edge forms a two-dimensional drop that is connected to the rest of the sheet by a thin neck and capillary waves propagate into the undisturbed sheet. The thickness of the neck reaches an approximately constant value that decreases with Oh, suggesting that the blob may “pinch-off” in the inviscid limit. © 1999 American Institute of Physics.