Viscous and Inertial Nonlocal Rheology of Dense Suspensions of Frictionless Particles

浸没的颗粒介质或稠密的泥浆是悬浮在粘性液体中的密实颗粒。它们存在于自然环境中，如山体滑坡、泥石流和水下雪崩，以及工业环境中，如推进剂泥浆和陶瓷材料加工。这种材料在环境危害中发挥着关键作用，在环境危害中，由于暴雨、地震和人类影响，大量稠密的泥浆变得流动和坍塌。在这种灾难性的流动中，颗粒可能会在短时间内失去联系并传播很长距离。该奖项的目标是开发实验、理论和计算方法，以准确预测当颗粒没有摩擦接触时这些稠密泥浆的扩散。这一认识对于避免或减少自然灾害的影响至关重要。此外，所获得的数据将对有兴趣开发新工程材料的研究人员有用。这一奖项的结果将被纳入康奈尔大学的课堂，以促进学生在数学和物理方面的主动学习和成功。通过说明工程科学的社会影响，计划开展各种推广活动，以激发K-12学生对工程的兴趣。研究人员最近提供了解决得很好的实验数据，表明在稠密无摩擦悬浮液中，从粘性状态到惯性状态的转变发生在令人惊讶的小颗粒雷诺数。这些结果提出了一种假设，即胶体力和流体动力力的相互作用导致了粒子团的形成，而粒子团主导着动量在材料中的传递。因此，比颗粒大小更大的长度比例可能会起作用。因此，现有的基于二元碰撞和动量传递的局部流变定律不能很好地解释稠密悬浮体的行为及其转变。这一奖项将发展基于碰撞动力学的星团形成的理论描述。通过对离散单元模拟和实验获得的微观结构的深入了解，将推导出考虑作用在团簇上的粘性应力和惯性影响的非局部本构方程。先进的力显微镜将被用来表征纳米间隔下的颗粒间相互作用，并指导模型悬浮液的发展。先进的实验技术，如光学折射率匹配、X射线照相和计算机层析成像，将与传统的流变学技术相结合，在测量宏观应力的同时了解微观结构的细节。将设计和研究存在瞬变效应和非均匀剪切场的实验流动。该理论将被应用于预测实际水流的动力学，如实验室规模的浸没泥沙流动，并将通过将结果与实验测量进行比较来进行改进。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Immersed granular media or dense slurries are densely packed grains suspended in a viscous liquid. They are found in natural environments, such as landslides, mudslides, and underwater avalanches, and in industrial settings, such as propellant slurries and ceramic material processing. Such materials play a crucial role in environmental hazards in which large volumes of dense slurries become mobile and slump triggered by heavy rainfall, earthquakes, and human influences. In such catastrophic flows, grains may lose contact and spread for long distances in a short time. The goal of this award is to develop experimental, theoretical, and computational methods to accurately predict the spread of these dense slurries when the grains are not in frictional contact. This understanding is essential to avoid or reduce the impacts of natural disasters. In addition, data acquired will be useful to researchers interested in developing new engineering materials. Results from this award will be incorporated into classes at Cornell University to promote active learning and student success in mathematics and physics. Various outreach activities are planned to inspire interest in engineering among K-12 students by illustrating the societal impact of engineering science.Researchers have recently provided well-resolved experimental data demonstrating that the transition from viscous to inertial regime in dense frictionless suspensions occurs at a surprisingly small particle Reynolds number. The results suggest a hypothesis that the interplay of colloidal and hydrodynamic forces leads to the formation of clusters of particles which dominate the transmission of momentum across the material. Therefore, larger length scales than the particle size may play a role. Consequently, the current local rheological laws based on binary collisions and transfer of momentum are inadequate in explaining the behavior of dense suspensions and their transition. This award will develop a theoretical description of cluster formation based on collisional dynamics. Nonlocal constitutive equations accounting for the viscous stresses and inertial impacts acting on the clusters will be derived using insight into the microstructure obtained from discrete element simulations and experiments. Advanced force microscopy will be used to characterize interparticle interactions at nanometer separations and guide the development of model suspensions. Advanced experimental techniques such as optical indexed-matching, X-ray radiography, and computed tomography will be coupled with conventional rheometry techniques to understand the details of microstructure while measuring the macroscopic stresses. Experimental flows will be designed and studied in which transient effects and inhomogeneous shear fields are present. The theory will be applied to predict the dynamics of practical flows such as lab-scale immersed sediment flows and will be refined by comparing the results with experimental measurements.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.