Within the research unit, experiments are performed in 5 projects (A1 – A5) and numerical simulations in three projects (B1 – B3).
Research unit composition during the Second Funding Period
A1 - Hydrodynamic stability of pulsatile flow of complex fluids
The focus of this project are hydrodynamic instabilities in pulsatile pipe flow. Starting from simplified geometries (straight and curved tubes) we at first separately study the different parameters relevant to cardiovascular flows and identify the respective instability mechanisms. In the next step we study the interaction of different instabilities by varying more than one parameter and by choosing more complex geometries. These are central aspects of the overall program and we closely collaborate with several other projects including project partners that investigate related aspects in numerical simulations. The fundamental insights into the impact of the different parameters on the flow stability will help to understand the often more complex situations studied in other experimental projects where due to additional parameters like wall compliance and bifurcations the complexity is even higher and the individual instability mechanisms may be obscured. Moreover our work will provide important inputs and starting points for theoretical and numerical projects (e.g. B1, B2). A better understanding of possibly modifications to instability modes or of observations of possible new instability mechanisms relies on the collaboration with the numerical/theoretical groups. We will here follow the same strategy that we also followed during the first funding phase where the origin of the helical mode that we observed in experiments was explained by the transient growth analysis carried out in Marc Avila’s group.
A2 - Dynamics and instabilities of particle-laden pulsatile flows in a straight pipe and a T-junction
This project elucidates how particles migrate in pulsatile fluid flows and how they modify the flow themselves, and so adresses a key point in the research unit. In the first funding phase, we could show that particles trigger the helical instability as efficiently as an optimized geometric perturbation (in form of a slightly curved pipe segment, as used in A1). Our results indicate that the periodically repeating acceleration and deceleration phases of the pulsatile flow lead to flow disturbances directly up and downstream of the particles, which are much stronger than for steady flow at the corresponding instantaneous Re. In order to understand the flow dynamics of blood and how e.g. traveling blood cloth modifies it, it is therefore essential to quantify the effect of particles on the flow dynamics. The pulsatile fluid velocity profiles equally influence the particle motion. We could show that the accelerating fluid flow induces a rotation of the particles. In the deceleration phase, this rotation slightly weakens, but in the low velocity phases in which the fluid is nearly quiescent, the rotation pushes the particle towards the pipe center (through the Magnus effect). Our results indicate, that particles in a pulsatile flow might behave very differently compared to a steady fluid flow environment. As observed in A4/5 and B3 red blood cells often rotate in a pulsatile flow while changing between their stable shapes (e.g. slipper, croissant), but experimentally this is very difficult to quantify. Our experiments provide here unique quantitative characterizations of the rotation axis and angular velocities, which can also be used as a benchmark for particle-laden flow simulations (B2, B3).
A3 - Flow-structure interaction in pulsatile flow of non-Newtonian fluids
Our main project aim is to elucidate the impact of flexible walls and fluid rheology on transition to turbulence. This will be achieved by looking
at the stability of pulsatile flow of non-Newtonian fluids in (A) elastic pipes and (B) flexible aortas. The non-Newtonian fluids used will mimic both the
shear thinning and the viscoelastic property of blood. Part (A) is an intermediate step and will provide basic insights on transition in a simpler flexible
geometry, while Part (B) will unveil to what extent these basic insights are relevant in physiological flows.
We closely interact with groups working on transition to turbulence in rigid pipes B. Hof (A1; experiments) and M. Avila (B1; theory and simulations) in a similar Reynolds number range and non-Newtonian fluids. This will allow us to compare different types of instabilities that arise for the rigid and elastic case and to bridge the different levels of complexity from straight pipes (A1,B1) to aorta model with circular cross section (A1) to aorta replicas (A3). Together with S. Recktenwald (A5), we plan to compare wall shear stress distributions between in vivo and in vitro models and collaborate on aspects of non-Newtonian rheology. This project aims at elucidating the transition to turbulence in pulsatile flow through compliant conduits and aorta replicas. We therefore address core areas of the Program, namely the understanding of flow regimes in pulsating systems with complex geometries and we provide a strong link to medically relevant applications. We expect that this research will ultimately allow us to better understand and predict flow regimes in physiological flows and their impact on diseases.
A4 - Effects of volume replacement fluids and polymers on blood flow
Our first main objective is to understand the effects of different volume replacement
solutions and polymers on blood in specific in-vitro and in-vivo situations in pulsatory or
unsteady flow as it exists in the microcirculation. The focus is on length scales where
the dynamics of single cells can be still resolved and we want to understand how the
time scale of the flow and the viscoelastic fluid couples with the characteristic time scale
of single cells, which were characterized in the first funding period for the physiological
(healthy) case. Our second main objective is to understand how different pathological
conditions affect the fluid dynamics of blood. We will especially investigate blood
diseases in which the shape, the flexibility and aggregation of the RBCs are altered.
These objectives are in particular tightly linked to the numerical work by S. Gekle (B3).
All in all, the comparison of in-vivo and in-vitro data will provide insight on how to produce
more realistic in-vitro experiments, both in physiological and pathological cases.
The research unit‘s general topic Instabilities, Bifurcations and Migration in Pulsatile Flows concerns simple and complex fluids, with a special focus on blood. While in the first funding period the focus was on simple fluids, suspensions and blood, we are now also taking polymeric solutions into account. Our goal is to describe the physiological flow of blood with models that are based on the physical properties of the single constituents, namely the RBCs, in their complex environment and it is the exact task of this project A4 to investigate the dynamics of the single cells in pulsating and non-stationary flow. The project‘s set-up with two PIs both from experimental physics and from medicine will assure an optimal exchange between the in-vivo research and the theoretical in-silico projects B2-B3. There is a natural tight interaction with the blood page 8 of 20 flow project A5 where constriction expansion geometries and migration are studied whilst we will focus in our in-vitro experiments on straight channels, bifurcations and T-junctions. The interaction with the other experimental projects A1-A3 that use simpler systems is necessary to understand – by direct comparison – the effect of the different control parameters such as e.g. concentration, shape or flexibility of the suspended objects on the flow instabilities and the influence of shear thinning and viscoelasticity. Especially with respect to viscoelasticity, we expect a close exchange with the project from B. Hof (A1). Furthermore, the results from our experiments with pathological cells and our understanding on the influence of shape and elasticity of RBCs on the flow will be of specific importance for the projects of K. Avila (A2) and J. Harting (B2).
A5 - Effect of polymers on the flow behavior of blood in-vitro
In line with the general theme of the Research Unit for the second funding phase, we will
extend our previous work on margination and constricted RBC flow in-vitro towards viscoelastic
polymer solutions. In contrast to the in-vitro investigations of project A4, which will study single
cell dynamics (lower than 1%Ht) in narrow channels and bifurcations O(10μm), we will here focus on
higher concentrated RBC suspensions (5-45%Ht) and larger microfluidic vessels O(10-500μm)
including complex geometries such as contraction-expansion flows. Together with the numerical
work of projects B2 and B3, and the in-vivo investigations of blood in project A4, we will obtain a
comprehensive understanding of the effects of polymers and viscoelasticity on blood flow.
The research unit‘s general topic Instabilities, Bifurcations and Migration in Pulsatile Flows concerns simple and complex fluids, with a special focus on blood. In project A5, we will focus on in-vitro blood flow in complex flow fields due to constriction-expansion geometry and/or high hematocrit under unsteady or pulsatile driving. These investigations will be performed in Newtonian as well as in viscoelastic non-Newtonian fluids. This project is tightly linked to the investigations of project A4, which will investigate the single-cell RBC behavior. Here, we will extend this work to higher RBC concentrations and bigger vessels. Besides the detailed investigations on blood flow, our work on the flow behavior of viscoelastic polymer solutions in time-dependent flows will complement the experimental projects A1-A3 that will study the impact of complex fluid properties on the transition in pulsatile flow in bigger pipes and channels. Our experimental observations will be compared to the numerical predictions of projects B2- B3 on RBC and particle suspensions under similar flow conditions based on our preceding collaborations.
B1 - Influence of geometry, rheology and compliance on the transition
to turbulence in pulsatile pipe flow
We aim at a better understanding of the physical mechanisms of instability and transition to
turbulence in cardiovascular flows. We do so by simplifying cardiovascular flow to canonical setups
containing the main physical mechanisms. We always consider the flow as pulsatile, and we
systematically combine the unsteady driving characteristic of cardiovascular flows with only one
additional feature at each step: by adding a flexible wall section, by considering non-Newtonian
characteristics of the fluid and by considering the flow in complex geometries. For each case,
we will look for the most dangerous perturbations in terms of turbulence transition. Once we
obtain them, we will perform direct numerical simulations to check the occurrence of turbulence
transition and to study the behaviour of turbulence in each scenario.
This project aims at elucidating the transition to turbulence in pulsatile flow in rigid/flexible straight pipes, and complex geometries for Newtonian and non-Newtonian fluids. We therefore address core areas of the Programme, namely the understanding of fluid-structure interaction, rheology, and geometric effects at large pulsation amplitudes. Direct comparisons to laboratory experiments within the unit (A1, A2 and A3) will be done. We expect that this research will lay the foundations for accurate simulations of physiologically relevant flows.
B2 - Migration and dynamics of particles in complex geometries and flows
We aim at understanding the effect of pulsating flow on the unstable equilibria that we have
observed previously in steady flows. Then we plan to include the effect of particle elasticity and
particle-particle hydrodynamic interactions (solid-solid, solid-elastic and elastic-elastic) on the
distribution of the particles in the channel and on the suspension rheology. Our third objective
is to study how pulsatile flows affect the particle migration in complex geometries (T-junction,
constriction-expansion, and curved channels). As a further focus, we will investigate the onset of
elasto-inertial turbulence in non-Newtonian (shear-thinning and shear-thickening) particle-laden
flows with a special emphasis on the contribution of flow pulsations.
This project focuses on particle-laden flows in simple and complex geometries. We aim at exploring the role of inertia, flow pulsation, particle shape, elasticity and concentration on the rheology and the spatial distribution of the particles in the channel. Our numerical simulations on pipes and complex geometries (T-junction, curved and constriction-expansion channels) will help to interpret the experimental results obtained within this research unit (A2, A4, A5). With (A1), (A5) and (B1) we will focus on non-Newtonian and viscoelastic fluids. With the project (B3), we plan to collaborate on the development of the computational method for viscoelastic fluids.
B3 - Computer simulations of red blood cells in transient flows
Based on the results of the first funding phase and in line with the general theme of the
Research Unit for the second funding phase, we will pursue two scienfific objectives:
O1: In the first phase we have studied how RBCs behave in transient flows induced by time-dependent pressure gradients. In reality, transient flows experienced by an RBC are often caused by its passage through complex geometric features of blood vessels. Here, we will investigate such transient RBC behavior in constriction-expansion geometries (in-vitro with A5) and microthrombi (in-vivo with A4).
O2: Polymer solutions with viscoelastic properties (”plasma expanders”) are routinely injected into patients after acute blood loss. In cooperation with A4 and A5, we will study how viscoelastic effects caused by these polymers influence the dynamics of single RBCs as well as RBC suspensions.
Project B3 is the key numerical project for blood flow simulations within the Research Unit. As such, it very closely connects to the experimental projects A4 and A5. Importantly, the connection with A4 will include not only idealized in-vitro, but also realistic in-vivo geometries such as microthrombi. In general, project B3 will focus on low Reynolds number flows, but interesting comparisons with higher Reynolds number flows such as those studied numerically in B2 and experimentally in A2 will be possible. On the methodical side, we will continue our on-going collaboration with B2, especially regarding viscoelastic extensions of the lattice Boltzmann method.
Research unit composition during the First Funding Period
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
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.