Scaling laws for the slumping of a Bingham plastic fluid

Bingham plastics exhibit complex behaviors, depending on both geometrical and rheological factors, and are difficult to characterize systematically. This is particularly true in the case of transient flows, where solidlike and fluidlike behaviors coexist in an intermittent fashion. The aim of this contribution is to study the slump of Bingham columns under gravity, while varying systematically and independently both the geometry of the system and the rheological parameters. To do so, numerical experiments are carried out in two dimensions with a non-Newtonian Navier-Stokes code, the Gerris flow solver, using a volume-of-fluid approach. We are able to determine the slump height and the spreading of the column after motion ceased. These characteristics are related to the rheological properties and initial shape through scaling relationships. The results are compared with previous scalings and prediction from the literature. A discussion ensues on the importance of the normalization choice and of unambiguous discrimination between geometrical and material factors. (C) 2013 The Society of Rheology.