Gravity draining of a yield-stress fluid through an orifice

We study the draining of a yield-stress fluid from a vertical vessel having a hole or a tube at its bottom. In order to understand the basic process we first study the problem with a Newtonian fluid and show that the flow characteristics can be very well described by assuming that the flow is analogous to that through a straight conduit of given length. For a yield-stress fluid draining through a hole the behaviour is different: the flow stops when the pressure drop across the orifice falls to a finite value which increases as the yield stress of the fluid increases or the hole radius R decreases. All the data collapse onto a master curve when plotted in terms of dimensionless numbers involving a characteristic length which is a function of R. We deduce an empirical model for the flow characteristics in such a case. When a length of tube is added after the hole we show that the characteristics of the flow are similar to those for flow through a straight conduit with an equivalent length equal to the tube length plus a fixed additional length.