Extensional flow at low Reynolds number with surface tension

The extensional flow and break-up of fluids has long interested many authors. A slender viscous fluid drop falling under gravity from beneath a horizontal surface is examined. After reviewing previous work which has neglected surface tension, a one-dimensional model which describes the evolution of such a drop, beginning with a prescribed initial drop shape and including the effects of gravity and surface tension, is investigated. Inertial effects are ignored due to the high viscosity of the fluid. Particular attention is paid to the boundary condition near the bottom of the drop where the one-dimensional approximation is no longer valid. The evolving shape of the drop is calculated up to a crisis time at which the cross-sectional area at some location goes to zero. Results are compared with those obtained when surface tension is neglected. Near to the crisis time, as the Reynolds number increases and inertia becomes non-negligible, the model assumptions are invalid so that the model does not describe actual pinch-off of a fluid drop.