Rheology of dense granular suspension systems

我的博士项目目标是建立致密颗粒悬浮体系流变学的多尺度连续体理论，该理论对广泛的工程应用具有更大的预测能力。我打算构建一个完整的流变学连续体理论，包括不同流型之间的过渡。一旦一个可靠的连续统理论被成功构建，许多工业过程必将变得更加高效和安全。在Ness和Sun之前的工作中，提出了一个本构模型来捕捉流动模式转变作为固体体积分数，剪切速率和材料性能的函数，该模型已被证明能够预测悬浮粘度相对于固体体积分数的发散行为。然而，该工作基于均匀的简单剪切流，这导致了两个主要的局限性：在构建本构模型时，没有考虑更复杂的致密颗粒悬浮物的非定常流变和共存状态下的流变。为了克服这些局限性，我们必须研究一种具有代表性的非定常流动与型态共存现象。通过初步的研究，我发现间断剪切增稠（DST）完全满足了这些要求，因为在间断剪切增稠状态下的实际流动是不稳定的。此外，DST对应于一种脆弱的状态，它被认为是两种制度的共存。因此，本文采用致密颗粒悬浮液的DST作为本文的基本案例。DST的研究将提供更多的非定常流变的宏观和微观特征，有助于构建更加完善和可靠的致密颗粒悬浮体系连续体模型。不连续剪切增稠表现为随着剪切速率的增大，悬浮液粘度呈不连续数量级增加。DST的一个很好的例子是玉米淀粉，如图1所示，它是烹饪中常用的增稠剂。Wyart和gates提出了一种流变模型来预测不同悬架系统中的DST。他们声称DST发生在高体积分数下。在一定剪切速率下，不同应力条件下存在多种流动状态时，会出现s型流动曲线。Jaeger的实验发现，DST是一种脆性状态，表现为间歇性流动，可以认为是剪切卡塞的前兆，表现为边缘物质既不自由流动也不完全卡塞的行为。临界应力与填料分数无关，因为它只取决于润滑的微观分解。此外，Hermes等人已经在Couette Cell系统中观察到非定常流动，这是最近的理论没有预测到的。人们对DST进行了大量的实验和计算工作。然而，目前还没有一个被广泛接受的理论。综上所述，DST是致密颗粒悬浮液流变学中一个有趣的现象。对DST的研究可以很好地补充Ness和Sun等人先前提出的连续统模型的局限性。

The goal of my PhD project is to establish a multiscale continuum theory for the rheology of dense granular suspension systems, which has greater predictive capability for a wide range of engineering applications. I intend to construct a complete continuum theory of the rheology across flow regimes, including the transition between different flow regimes. Many industrial processes will surely become more efficient and safe once a reliable continuum theory is successfully constructed. In the former work of Ness and Sun , a constitutive model is proposed to capture the flow regime transitions as a function of solid volume fraction, shear rate, and material properties, which has been shown to be able to predict the divergent behavior of the suspension viscosity with respect to the solid volume fraction. However, the work was based on the homogeneous simple shear flow, resulting in two main limitations: more complex unsteady rheology of dense granular suspensions and the rheology in coexisting regimes were not taken into consideration during the construction of constitutive model. To overcome these limitations, we have to research on a representative phenomenon of both unsteady flow and regime coexistence. Based on preliminary investigations, I found that discontinuous shear thickening (DST) satisfies these requisitions perfectly since the real flow in DST regime is unsteady . Futhermore, DST corresponds to a fragile state , which is considered as a coexistence of two regimes. Therefore, DST of dense granular suspensions is employed as the basic case of this proposal. The research on DST will provide more macroscopic and microscopic characteristics of unsteady rheology, which contribute to the construction of a more consummate and reliable continuum model of dense granular suspension systems.The discontinuous shear thickening behavior is that the suspension viscosity experiences a discontinuous orders-of-magnitude increase as the shear rate becomes higher. A very good example of DST is cornstarch, as shown in Figure 1, which is a common thickening agent used in cooking. Wyart and Cates have proposed a rheological model to predict DST in different suspension systems. They claim that DST happens at high volume fraction. The S-shaped flow curves could occur with multiple flow states existing at a given shear rate but at greatly differing stresses. Jaeger's experiment found that DST is a fragile state that exhibits intermittently flow, which can be considered as a precursor to shear jamming and exhibits behavior of marginal material that is neither freely flowing nor fully jammed . The critical stress is independent of packing fraction since it only depends on the microscopic breakdown of lubrication. Moreover, unsteady flow has been observed in a Couette Cell system by Hermes et al , which was not predicted by recent theories. There have been many experimental and computational work on DST. However, a widely accepted theory has not been proposed yet. In summary, DST is an interesting phenomenon in the rheology of dense granular suspension. The research on DST can serve as perfect supplement for limitations of the former continuum model proposed by Ness and Sun .