Gravity flow instability of viscoplastic materials: the ketchup drip.
In contrast with simple liquids such as water, milk, honey, which easily flow as a continuous jet when poured from a vessel, pasty materials such as mayonnaise, mustard, ketchup, puree, etc., fall by fits and starts in a wide range of flow rates. This may, for example, be observed when ketchup or mayonnaise is pushed from a tube at a sufficient height over a plate: although surface tension effects are generally negligible because of its high viscosity the material drops as successive droplets of more or less similar size (except at large flow rates). Here we demonstrate that this effect is a kind of flow instability which develops when the weight of material becomes larger than a force due to its yield stress, namely a critical stress below which it cannot flow steadily. Furthermore, we show that depending on the exact material behavior surprising phenomena may be observed: the size of the droplet may remain constant or even decrease (for thixotropic materials) as the flow rate increases. This approach, for example, provides tools for controlling the shape of droplets in cooking and the size of extrudates in food and mineral industries.