On skirted drops in an immiscible liquid

• It is shown that the viscosity of the host fluid causes a tapering of the skirts sometimes seen trailing drops and bubbles.
• This tapering is an essential ingredient in explaining the origin of the finite length of skirts.
• Scalings of the skirt length and volume with the Reynolds, Eötvös and Morton numbers are suggested.

Large drops rising or sinking in an immiscible liquid can develop thin trailing structures commonly referred to as “skirts”. The paper describes a mathematical model for the thickness of these skirts accounting for the viscous boundary layer that develops along the surface of the parent drop and of the skirt itself. Unlike earlier theories, the skirt thickness is found to decrease with distance from the drop rim, which illuminates the mechanism which terminates the skirt at a finite length. A scaling of the skirt length is suggested by an analysis of published data, which also leads to a scaling for the volume of liquid in the skirt. The theoretical predictions are compared with the few experimental results for which sufficiently detailed information is available.