A new model has been developed for the surface energy-driven shortening of a free, cone-shaped fluid ligament of finite length, as a function of ligament diameter, length, mass and head speed. It differs significantly from classical models based on infinitely long cylindrical (Taylor) or conical (Keller) shapes, but leads to overall shortening speeds which are very similar to those provided by Taylor's model for typical drop-on-demand fluids. However, if a realistic initial velocity distribution along the length of the ligament is included, the model predicts more rapid shortening, by as much as 2 m/s for a jet speed of 6 m/s. Such effects should be taken into account when analyzing the behavior of real jets. The model's predictions of shortening speeds for free dropon-demand jets fail to account for all experimental observations, which for some polymer solutions can be as much as 2-3 times as high. This effect is attributed to elastic retraction, and may be a general feature linked to the polymer relaxation time.
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