Viscoplastic dam breaks and the Bostwick consistometer

We present a theoretical and experimental analysis of the dam break of a viscoplastic fluid in a horizontal channel. A shallow, slow fluid model based on the Herschel-Bulkley constitutive law allows one to characterize the early and late stages of the flow, the final state and the dependence on yield stress and nonlinear viscosity. A particular diagnostic is advanced (time ratios based on the length of time required for the fluid to slump certain distances from the broken dam) that may assist an experimentalist to unravel those dependences. Experiments are conducted with cornsyrup, and aqueous suspensions of xanthan gum, kaolin, carbopol, cornstarch and apple puree. Cornsyrup xanthan gum and kaolin show fair quantitative agreement with theory. Carbopol compares less favourably, due primarily to inertial effects which are missing from the theory. The results for cornstarch confirm that it is shear thickening, but its detailed rheology remains unknown (and unexplored). Apple puree also appears to compare well with theory, although repeating the dam break in a roughened channel leads to substantially different results, suggesting that fluid separation can induce effective wall slip (a problem that also probably plagues the Bostwick device). Finally, theory is compared with Bostwick tests with fruit puree, with limited success.