We present an experimental study using mixtures of aqueous superabsorbent polymers (SAP) where we systematically investigate the influence of the size of grains that make up the fluid structure on the mixture effective rheology and its domain of validity. In water, SAP powder grains can swell up to 200 times and form gel grains, $d_g$, whose sizes (typically between 1 and 8 mm) can be controlled by choosing the size of the initial powder grains. The rheology of this mixture (water and touching grains) combines viscous, elastic and plastic aspects. Here, they are characterized using the free-fall of spheres of different densities and diameters ($d_s$). The latter were varied between 3 and 30 mm, therefore providing a range where they become comparable to the fluid gel grains.

We observe five different regimes of motion: (1) A linear regime where the sphere has a rapid and straight fall and reaches a constant terminal velocity. (2) An irregular regime where the sphere’s velocity varies around a constant value. (3) An intermittent regime where periods of no-motion and periods of irregular falls follow one another. (4) A slow fall regime where the sphere’s speed progressively decreases in a logarithmic way. (5) A no-motion regime when spheres are not heavy enough to overcome the yield stress of the mixture, or are too small compared to the grain size.

The sphere trajectories in regimes (1), (2) and (3) are all following a same trend which, in the framework of a Herschel–Bulkley fluid, allows to estimate the effective yield stress ${\sigma }_Y$ and consistency $K_v$ of the SAP mixtures. Both ${\sigma }_Y$ and $K_v$ increase with increasing gel grain size. Regimes (2) and (3) are due to the interactions between the falling sphere and individual gel grains, i.e. the fluid structure. Moreover, the critical Yield number ($Y_c$, which compares ${\sigma }_Y$ to the stress induced by the sphere’s net weight in the fluid) above which there is no motion decreases as $d_s∕d_g$ becomes smaller than 2. So although the characteristic size of the fluid structure influences the magnitude of its rheological properties, the use of a Herschel–Bulkley rheology to describe the trajectories of the spheres breaks down only when the sphere diameter becomes very close to the SAP structure size.

我们目前使用含水超吸收性聚合物（SAP）的混合物进行的实验研究，我们系统地研究了组成流体结构的晶粒尺寸对混合物有效流变学及其有效性范围的影响。在水中，SAP粉末颗粒可溶胀多达200倍，并形成凝胶颗粒，$d_G$，其大小（通常在1到8毫米之间）可以通过选择初始粉末颗粒的大小来控制。这种混合物的流变性（水和接触颗粒）结合了粘性，弹性和塑性方面。在这里，它们的特点是使用不同密度和直径的球体的自由落体（$d_s$）。后者在3到30毫米之间变化，因此提供了与流体凝胶颗粒相当的范围。

我们观察到五个不同的运动状态：（1）线性状态，其中球体具有快速而笔直的下落并达到恒定的最终速度。（2）球体速度围绕恒定值变化的不规则状态。（3）一种间歇性制度，在这种制度中，不活动的时期和不规则的跌落时期相互跟随。（4）一种慢速下降状态，其中球体的速度以对数方式逐渐降低。（5）当球体的重量不足以克服混合物的屈服应力，或者与晶粒尺寸相比太小时，则为不运动状态。

方案（1），（2）和（3）中的球体轨迹都遵循相同的趋势，在赫歇尔-布克利流体的框架下，可以估算有效屈服应力 ${\sigma }_{ÿ}$ 和一致性 ${ķ}_v$SAP混合物。都${\sigma }_{ÿ}$ 和 ${ķ}_v$随着凝胶粒度的增加而增加。机制（2）和（3）是由于落球与单个凝胶颗粒（即流体结构）之间的相互作用而引起的。而且，临界屈服数（${ÿ}_C$，比较 ${\sigma }_{ÿ}$ 到球体在流体中的净重所引起的应力），在此之上，没有运动会随着 $d_s∕d_G$ 变得小于2。因此，尽管流体结构的特征尺寸会影响其流变特性的大小，但仅当球体直径变得非常接近SAP时，使用赫歇尔-布克利流变学来描述球体的轨迹的方法才被打破。结构尺寸。