Slow slumping of a very viscous liquid bridge
Tuck EO, Stokes YM, Schwartz LW
Journal of Engineering Mathematics, 32: (1) 27-40 JUL 1997

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 rho and viscosity mu, with width 2w and thickness 2h much less than 2w falls under gravity g at an initial velocity rho gw^4/(32 mu h^2). 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.