The dynamics of granular-fluid mixtures

颗粒-流体混合物的流动在工业生产和日常生活中广泛存在。这种混合物通常是多分散的，包含表现为颗粒流的大颗粒和悬浮在流体中的小颗粒。预测这些混合物的流变性仍然是一个重大的科学挑战。该项目的目标是提供一个新的数学描述，这种混合物，重点是如何悬浮的颗粒的流体影响的形成一个静态（非剪切）层附近的流动。这将通过在混合物理论的框架内构建数学模型来实现，特别是考虑到颗粒由于重力而沉降时不断变化的流体压力。渐近分析将被用来提供一个领先的顺序简化模型的混合物与高比例的固体颗粒，与确定的基本基本机制，管理这些复杂的流体的流动的目的。

Flows of granular-fluid mixtures occur widely in industrial processes and in daily life. Such mixtures are often polydisperse, containing both large particles that behave as a granular flow, and small particles that are suspended within the fluid. Predicting the rheology of these mixtures remains a major scientific challenge.The objective of this project is to provide a new mathematical description of such mixtures, focusing on the how the suspension of particles by the fluid influences the formation of a static (non-shearing) layer of grains near the base of the flow. This will be achieved by constructing mathematical models within the framework of mixture theory, specifically accounting for the evolving fluid pressure as particles settle due to gravity. Asymptotic analysis will be used to provide a leading-order simplified model for mixtures with a high proportion of solid particles, with the aim of identifying the fundamental underlying mechanisms that govern the flow of these complex fluids.