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.

中文翻译：

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屈服应力流体的拉伸重力流变仪 (EGR)

为了测量屈服应力流体的拉伸流变特性，我们开发了一种流变方法，该方法基于对向下流动的流体挤出物的变形进行分析，并在重力作用下连续拉长液滴破裂。假设径向平面中纵向速度的梯度可以忽略不计，局部瞬时应变率由每个横截面细丝直径的变化推导出，而法向应力则由该点以下材料的加速度和重量计算。及时观察细丝轮廓使我们能够识别变形趋于饱和的固体区域和变形不断增加的液体区域。进一步的分析使我们能够区分纯拉伸应力和应变率分量有效占主导地位的数据，以便可以推导出材料在几十年应变率下的拉伸流动曲线。对于具有不同内部结构的两种典型屈服应力流体（乳液和粘土悬浮液），在这些不同流动条件下获得的所有法向应力与拉伸速率数据都沿着每种材料的单一主曲线下降。在使用与简单剪切略有不同的应变率功率的条件下，标准 3D Herschel-Bulkley 模型似乎很好地代表了伸长率的流动曲线。对于这两种材料类型，以这种方式发现的伸长屈服应力值非常接近简单剪切屈服应力乘以 3 的平方根。