The dynamics of granular-fluid mixtures

颗粒-流体混合物的流动广泛存在于工业过程和日常生活中。这种混合物通常是多分散的，既包含表现为颗粒流的大颗粒，也包含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。本项目的目标是为这些混合物提供一种新的数学描述，重点研究流体悬浮颗粒如何影响流动底部附近静态(非剪切)颗粒层的形成。这将通过在混合物理论框架内建立数学模型来实现，特别是考虑到粒子由于重力而沉降时不断变化的流体压力。渐近分析将被用来为含有高比例固体颗粒的混合物提供一个先导阶简化模型，目的是确定控制这些复杂流体流动的基本基本机制。

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.