# Projects

Within the research unit, experiments are performed in 5 projects (A1 – A5) and numerical simulations in three projects (B1 – B3).

### A1 - Instabilities in pulsating pipe flow of Newtonian and complex fluids

The overall objective of this project is to obtain an in depth understanding of the types of instability and the respective stability thresholds that occur in pulsating flows in (predominantly) straight rigid tubes, depending on control parameters. Parameters considered are the pulsation amplitude, the Womersley number and the Reynolds number. Studies are largely restricted to values of those parameters that are relevant to flows in large blood vessels. Flows are subject to geometric perturbations (stenosis and curved pipe segments). In the next step we aim to clarify how the transition threshold changes when the waveform is changed from sinusoidal to a more typical shape for blood flow. Once the influence of above parameters and factors is understood the fluid will be exchanged for a shear thinning liquid and the final goal is to perform experiments with animal blood and to monitor the instability thresholds for this more complex case.

### A2 - Dynamics and Instabilities of particle-laden pulsatile flows in complex pipe geometries

Fluid flows through tubes are usually driven by a pump, which introduces an oscillatory, or at least unsteady, component in addition to the mean flow. Such flows are called pulsatile and despite their relevance for engineering and medicine, with their most prominent example being the blood flow in the cardiovascular system, little is known about the fundamentals of these flows. State of the art experimental and numerical methods allow it nowadays to even investigate the motion of particles suspended in such flows. A better understanding of the particle dynamics in pulsatile flows will help to identify the origin of vascular diseases (e.g. by identifying locations of preferred occurrence of red blood cells) and at the same time will provide useful information for process engineering (e.g. how the pumping frequency influences the particle concentration in the branches behind a junction). In this project the particle migration of neutrally buoyant spheres in a pulsatile flow through pipe networks in the laminar and transitional regime are explored. Three fundamentally different pipe geometries (straight, bending and junction) are investigated experimentally for two different particle sizes. The flow fields and the migration of the particles are measured by state-of-the-art three-dimensional particle image and Lagrangian particle tracking, allowing us to retrieve space and time resolved experimental data. Modern spatio-temporal analysis methods allows us to shed light on the mechanism underlying the particle migration. In addition, the data will be used to validate and improve high-fidelity simulations.

### A3 - Flow-structure interaction in pulsatile flow

The transition to turbulent flow in flexible vessels is not fully understood even for simple geometries, rest alone the more complex physiological cases. Despite numerous studies dealing with individual causes for laminar to turbulent flow transition to date their combined effects at realistic flow conditions are still not well understood. With this project we want to advance the hydrodynamic understanding of flow-structure interactions in flexible pipes and aorta replicas.

### A4 - Cell shapes, cluster formation and irregular flow in the microcirculation

Red blood cells (RBCs) are from a physical point of view highly deformable objects that can pass capillaries and constrictions smaller than their own diameter. They consist of a lipid bilayer membrane that is supported by a polymeric spectrin network, which encloses the inner fluid that contains hemoglobin. Due to their high deformability, RBCs interact strongly with the flow and depending on the type of flow many different shapes have been predicted and observed, both in simple shear and in Poiseuille flow. In this sense, RBCs serve as an excellent model system to study fluid with soft structure interaction. In physiological vascular flow most of the pressure drop occurs along capillaries, where only one single cell can pass at a time, but the interaction of the flow field with the wall induces an additional complexity. In such strong confinements strong temporal dynamics of the cell shape, ranging from simple oscillations up to chaos, are observed even in steady flow. Physiological flow is generally unstationary, either due to the pulsation of the heart or due to flow irregularities caused by the complexity of the capillary network, where local density fluctuations lead to severe pressure and flow rate fluctuations. We experimentally study the temporal dynamics of single RBCs in pulsating flow both in-vitro in a microfluidic geometry and in-vivo in a hamster model. Cell shapes are observed with bright field and fluorescence microscopy and are analyzed by means of a neural network algorithm that was developed in our group. Further, we investigate the stability and the dynamics of cell clusters in pulsating flow. RBCs can interact with each other either due to the plasma proteins (mainly the fibrinogen) and form reversible aggregates that are called rouleaux or simply due to the hydrodynamic flow field. In a pulsating flow field, the formation of clusters might be enhanced or suppressed, depending on the parameter range. Additionally, at least the hydrodynamically induced clusters should show a complex temporal dynamics. The formation of aggregates also affects the local density that causes, together with blocking and jamming at bifurcations and constrictions, severe flow fluctuations. Those flow fluctuations have been observed qualitatively in-vivo for a long time, but we aim to obtain a quantitative understanding on the mechanism of the flow oscillations in the vascular network by a combined in-vitro and in-vivo approach and in close cooperation with a numerical project.

### A5 - Margination and flow transitions in vascular flow

Blood is a suspension of deformable objects, such as the red blood cells (RBCs), white blood cells (WBCs) and platelets. They are suspended in a complex fluid, called the plasma. Plasma itself is only slightly viscoelastic but its proteins have a major effect on the aggregation of the RBCs and are the cause of the pronounced shear thinning behavior of blood. Up to now, most analyses of blood flow model blood as a continuum fluid with either Newtonian or shear thinning viscosity. These approaches do not allow to capture the dynamics of single cells, which is necessary for an understanding of flow instabilities or of the dynamics of the WBCs compared to the RBCs. WBCs make approximately 0.1% of the blood volume compared to 45% for the RBCs and they serve a completely different purpose. RBCs transport mainly oxygen to the tissues while WBCs are key players of our immune system. They are activated at inflammatory sites, i.e. at the vessel walls. It is known that in vascular flow RBCs are concentrated in the center of the vessel blood stream, while the WBCs typically migrate along the vessel walls. This effect is called "margination" and it results from a subtle interplay between wall-forces and some effective pressure due to cell-cell collisions in the blood stream. These forces depend on the size, the shape and the stiffness of the cells, but the quantitative contribution of each of these factors is not yet clear. While previous in-vitro studies have only addressed conditions of steady flow, this is not the case for the physiological situation where blood flow is always pulsatile. Therefore, the project focuses on margination in microfluidic experiments combined with confocal microscopy in its first part. Microfluidic experiments are complemented by in-vivo experiments in an animal model.In the second part of the project, we study by means of microfluidic flow measurements and particle tracking how the interplay between pulsation and the particulate effect of blood affects vortex formation in a constriction-expansion geometry in-vitro as well as in comparable complex situations in a microvascular stenosis model in-vivo.

### B1 - Stability and transition to turbulence of pulsatile pipe flow with rigid and flexible walls

In the past decade, a comprehensive understanding of the transition to turbulence in shear flows, and particularly of pipe flow, has emerged. This has been possible due to precise experiments with well-controlled disturbances and flow rates, quantitative comparisons between these experiments and direct numerical simulations of the Navier-Stokes equations and the theoretical guidance from dynamical-systems approaches. Despite its physiological relevance (e.g. for blood flow in the aorta), the case of pulsatile pipe flow has received much less attention and there are conflicting results in the literature even for harmonic pulsation. Very recently, quantitative agreement has been reached between experiments and simulations in the regime of weak pulsation amplitude, whereas the regime of large pulsation amplitude remains largely unexplored. The goal of this project is to elucidate the physical mechanisms of transition in pipe flow with large pulsation amplitude, and to provide a classification of distinct parameter regimes depending on the pulsation frequency. We use direct numerical simulations of the Navier-Stokes equations, consider the effect of the flow-rate waveform (harmonic and aorta-like waves) and study Newtonian and shear-thinning fluids. In addition to this, the effect of compliance is investigated by considering the pulsatile flow of a fluid in an elastic tube clamped between two rigid pipe sections. The focus is on the emergence of resonances and their interaction with self-excited oscillations. Direct comparisons to laboratory experiments within the unit are performed.

### B2 - Migration and dynamics of particles in complex geometries and flows

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 or polymer solutions, 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 focus on the intermediate regime at moderate
Reynolds numbers between 1 and 500. 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 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. 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 focus on hard sphere suspensions 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 study if and how instabilities of the flow can occur for
these systems. Second, we 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. Third, we aim to understand the impact
of the particle geometry by moving from simple hard spheres to ellipsoids. We therefore
systematically vary the aspect ratio, volume concentration and confining geometry. Then,
we focus on the influence of the particle-particle and particle-surface interactions.
How do attractive or repulsive interactions change the migration and transport? What is
the impact on shear-induced diffusion or the local stresses leading to non-Newtonian
behaviour?

### B3 - Pulsating flows in the microcirculation

The microcirculatory network contains the smallest blood vessels
with diameters between 5 and 100 microns. It represents that region in a
living organism where the particulate nature of blood as a suspension of
red blood cells is most relevant. On the one hand, it is relevant for biological
function such as oxygen exchange or drug delivery. On the other hand, the particulate
nature also determines the flow behavior of blood at these scales. A striking example
in the latter area is the creation of highly pulsatile flow patterns. Such flows can
appear when red blood cells temporarily get stuck at the apex of bifurcations and are
then suddenly released back into the flow. This and many other related phenomena are
still not fully understood. In the present project, we use
Lattice-Boltzmann-Immersed-Boundary computer simulations to elucidate the origin of
pulsatility in the microcirculation but also its consequences on the flow behavior
of red blood cells. For this, we start by considering a single red blood cell
in a straight channel under externally imposed pulsating flow. We aim to understand if
and how pulsatily can influence the fragile dynamic modes of motion of a single red
blood cell such as slippers or parachutes. Subsequently, we investigate how the
interplay of many red blood cells in microvascular networks, starting from simple
two-node bifurcations and then moving to realistic in-vivo geometries, can lead to
pulsating flow patterns even under steady external boundary conditions. This is connected
to in-vitro and in-vivo measurements. Finally, we aim to understand how
margination, i.e. the well-known near-wall migration of stiff particles such as leucocytes
or drug delivery agents, can be affected by pulsating flows. In the long run, we will
also include the influence of the glycocalix, a thin polymer layer coating the wall
of a blood vessel, which may significantly influence red blood cell dynamics especially
under pulsating flow conditions. Our overall goal in this project is to reach a systematic
mechanistic understanding of the two-way-coupling between pulsating flow and red blood
cell dynamics in the microcirculation.