Migration and dynamics of particles in complex geometries and flows

实际流动通常包含不稳定的成分，例如由于外部驱动或脉动。这给系统增加了一个额外的外部时间刻度，最终会强烈地影响不稳定性的发生。对这一额外时间尺度的影响的了解是本研究单位动机的核心。外部时间标度的影响对于复杂的流体(即颗粒悬浮液)更为重要，其中涉及到额外的松弛时间标度。本项目旨在了解流体性质、惯性和约束对粒子迁移和不稳定性开始的相互作用。在很低的雷诺数(斯托克斯极限)下，很多关于粒子迁移和结构的知识是已知的，而惯性力是不相关的。在尺度的另一边，在非常高的雷诺数下，湍流充分发展，我们预计惯性将占主导地位。我们将集中讨论雷诺数介于1和1500之间的中间区域。在这里，惯性力的组合以及复杂流体或约束的性质对传输性质具有明确的影响。我们将使用一种模拟技术，将格子Boltzmann方法用于Navier-Stokes水平上的流体动力学，并将离散元算法用于描述悬浮粒子。对于软粒子，将使用有限元/浸没边界方法。该方法在颗粒和流体性质以及限制几何的实现方面具有高度的灵活性。它特别适合于感兴趣的区域：恢复了Navier-Stokes方程中的惯性项，可以解析复杂流体的内部结构，很容易实现复杂的几何和驱动力，并且由于其内在的并行性，它可以扩展到实验上相关的时间和长度尺度。有了这个工具，我们首先将重点放在脉动流中含有硬颗粒和软颗粒的悬浮液中，并研究颗粒体积浓度(从牛顿到非牛顿)和惯性对简单几何形状中颗粒迁移和悬浮输运的影响。我们将研究这些系统是否以及如何发生流动的不稳定性。此外，我们还将研究约束对惯性驱动悬架的影响。我们的目标是了解如何利用通道几何来生成粒子的结构化甚至分类。最后，我们将研究剪切变稀或粘弹性流体在管流和更复杂的几何形状中对悬浮液传输特性的影响。

Practical flows generally contain an unsteady component, e.g. due to an external driving or pulsation. This adds an additional external timescale to the system which eventually can strongly influence the onset of instabilities. The understanding of the impact of this additional timescale is at the core of the motivation for this research unit. The effect of the external timescale is even more important for complex fluids, i.e. particle suspensions, where an additional relaxation timescale is involved. This project aims at an understanding of the interplay between fluid properties, inertia and confinement on the particle migration and the onset of instabilities. At very low Reynolds numbers (Stokes limit), a lot is known about particle migration and structuring, while inertial forces are not relevant. On the other side of the scale, at very high Reynolds numbers, turbulence is fully developed and we expect inertia to be dominant. We will focus on the intermediate regime at moderate Reynolds numbers between 1 and 1500. Here, the combination of inertial forces and the properties of the complex fluid or the confinement have a defined impact on the transport properties. We will use a simulation technique combining the lattice Boltzmann method for the fluid dynamics at Navier-Stokes level and a discrete element algorithm for the description of suspended particles. For soft particles, a finite element/immersed boundary method will be used. The method is highly flexible with respect to particle and fluid properties as well as the implementation of confining geometries. It is particularly well suited for the regime of interest: the inertial term in the Navier-Stokes equation is recovered, the internal structure of the complex fluid can be resolved, complex geometries and driving forces are easily implemented and it scales to experimentally relevant time and length scales due to its inherent parallelism. With this tool at hand, at first we will focus on suspensions with hard and soft particles in pulsating flows and investigate the impact of the particle volume concentration (from Newtonian to non-Newtonian) and inertia on the particle migration and suspension transport in simple geometries. We will study if and how instabilities of the flow can occur for these systems. Furthermore, we will study the impact of confinement on inertia-driven suspensions. We aim to understand how to make use of the channel geometry to generate a structuring or even sorting of the particles. Finally, we will study the impact of shear thinning or viscoelastic fluids on the transport properties of a suspension in pipe flows and in more complex geometries.