Extensional gravity-rheometry (EGR) for yield stress fluids

In order to measure the extensional rheological properties of yield stress fluids, we developed a rheometrical approach based on the analysis of the deformations of a fluid extrudate flowing downward and breaking in successive elongated drops due to gravity. Assuming the gradients of longitudinal velocity in radial planes are negligible, the local instantaneous strain rate is deduced from the variations of the filament diameter in each cross section, while the normal stress is computed from the acceleration and weight of the material below this point. The observation of the filament profile in time allows us to identify a solid region, in which the deformations tend to saturate, and a liquid region, in which the deformations continuously increase. A further analysis allows us to distinguish the data for which pure elongational stress and strain rate components are effectively dominant so that the elongational flow curve of the material over several decades of the strain rate can be deduced. For two typical yield stress fluids (emulsion and clay suspension) with different internal structures, all the normal stress vs extensional rate data obtained under these different flow conditions fall along a single master curve for each material. This flow curve in elongation appears to be well represented by the standard 3D Herschel–Bulkley model under the condition that a slightly different power of the strain rate than in simple shear is used. For both material types, the elongational yield stress value found in this way is very close to the simple shear yield stress times the square root of 3.