Slow Slumping of a Very Viscous Liquid Bridge

Abstract

A layer of very viscous liquid (e.g. tar, molten glass) spans a chasm between two vertical walls. The slow fall or slump of this initially-rectangular liquid bridge is analysed. A semi-analytical solution is obtained for the initial motion, for arbitrary thickness/width ratios. The formal limits of large and small thickness/width ratios are also investigated. For example, the centre section of a thin bridge of liquid of density ρ and viscosity μ, with width 2w and thickness 2h ≪ 2w falls under gravity g at an initial velocity ρgw4/(32μh2). A finite element technique is then employed to determine the slumping motion at later times, confirming in passing the semi-analytical prediction of the initial slumping velocity.