Migration and dynamics of particles in complex geometries and flows

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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.