## 532 Mechanik der Fluide; Mechanik der Flüssigkeiten

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A non-invasive ultrasonic flow meter is studied for which the pipe remains unperforated and without obstructions in its interior. Elastic waves that are excited inside the pipe wall interact with the adjacent fluid to form quasi-guided waves. These can be either of leaky or trapped kind. The radiation of the leaky waves is exploited to insonify the pipe‘s interior. The quasi-guided waves are studied in-depth with particular emphasis on their radiation behavior. Highly reliable and efficient computational methods are developed for this purpose. The ultrasonic transit time in the flow meter is modeled systematically based on the aforementioned waves. Thereby, the effects of fluid flow and temperature are included explicitly in an analytical manner. Compared to conventional ultrasonic flow meters, we find that devices based on quasi-guided waves exhibit a strongly reduced cross-sensitivity to temperature, which is also confirmed experimentally. The developed analytical and numerical techniques enable a systematic optimization of such devices with regard to their temperature-dependent behavior, geometrical uncertainties, material aging, as well as scaling and deposition of other layers.

Based on the idea of energy cascades on wavelet dyadic trees and the energy cascade, wavelet cascade models are proposed. A series of turbulent scales are constructed in each level of wavelet space. On the one hand, the length of inertial and dissipation ranges, the binomial cascade and the Reynolds number regarding the cascade processes are studied. The high-order velocity statistics generated by the models are compared and validated with experimental and theoretical results. The derived dissipation rate calculated from the present models not only agrees with the existing experiments, but also suggests that the dissipation rate is not an independent variable with respect to the Reynolds number. On the other hand, the velocity dynamics are imposed on the multifractal models by a refined multilevel Euler mapping (MEM) in the Lagrangian framework. Additionally, the potential application of the present models to Large-Eddy Simulation is investigated by construction of the sub-grid scale velocities. The prior tests show the models are able to capture the important properties statistically for both homogeneous and inhomogeneous flows.

This work explores several ways in which the presence of dissolved ions in a liquid can drive
the formation of ordered structures. Chapter I illustrates the importance of electrostatic effects
in liquids, spanning a wide narrative arc from Coulomb’s 18th century experiments, across the
mechanics of curdling milk and up to the self-assembly of biological membranes. Any theoretical
foundations used in more than one chapter of the thesis are laid out in chapter II. Chapters III-V
lay out my core results obtained from numerical simulations of three different systems.
• Chapter III presents hydrodynamic simulations of sedimenting, electrostatically interacting
same-charge particles. The core question here is how the range of interparticle repulsion
affects the sedimentation speed as a function of concentration. As the repulsion range
increases, a transition from a random, gas-like particle distribution to a liquid-like arrangement coincides with a minimum in the slope of the sedimentation speed. Throughout a
wide parameter range this slope of the sedimentation function can be described by a simple
fit function with two parameters (the location and sharpness of the gas-liquid transition).
This fit models short-range repulsion as an increased effective hard sphere radius, whereas
sufficiently long-ranged repulsion leads to an ordered distribution of equidistant particles
independent of the exact repulsion range.
• Chapter IV is a study of the quenched demixing of oppositely charged liquids, combining
lattice Boltzmann simulations with phase field model theory. The underlying aim here is
to understand what determines the types of mesoscale structures formed by antagonistic
salts in polar/nonpolar liquid mixtures. The model consists of two otherwise identical, by
themselves immiscible, liquids coupled to positive and negative dissolved ions. Each ion
type is preferentially solvated by a different liquid phase, leading to some degree of charge
separation. Complex structure formation can occur when the solvation potential driving ion
separation dominates electrostatic ion-ion interactions. When solvation is weak compared
to electrostatics the liquids demix unhindered into two bulk phases and the ions form thin
double layers at the interfaces. Under strong solvation, liquids mixed at equal volume
fractions form lamellar patterns which progressively orient in parallel at a rate following a
power law. However, if the electrostatic forces acting on the liquids grow strong enough,
e.g. due to a high salt concentration, they drive the liquids to mix homogeneously. The
system is shown to be described well by the Ohta-Kawasaki model for structure formation
in diblock copolymers, enabling the prediction of structure sizes and morphology from two
dimensionless numbers.
• Chapter V can be considered a continuation of chapter IV using molecular dynamics to
model the self-assembly of antagonistic salts on an atomistic scale. The simulations confirm
previous suppositions from experiment that antagonistic salts in water/oil mixtures form
monomolecularly thin anion leaflets sandwiched by equally thin layers of oil molecules. By
comparing with a partially coarse-grained model I show that the size of the anions alone
suffices to explain their peculiar aggregation in spite of their electrostatic repulsion. The
leaflet structure results as a compromise between hydrophobic aggregation and electrostatic
repulsion as it allows each anion to remain comparatively close to a counterion in the
separated water phase. Chapter V concludes with a phase diagram of additional structures
found. Depending on solvent volume fractions the 2D leaflets may fray or contract into
1D chains instead. A topological transition occurs at high salt concentrations, where both
lamellae and chains interconnect in three dimensions to form a sponge-like structure.
Chapter VI concludes with a summary of the three main results chapters and a short exploration
of their interconnections. In addition I present some possible avenues of future research to
continue my present work.

In this thesis a framework for modelling two coupled hypersurfaces evolving in a three-dimensional domain
that is filled with a fluid is developed in terms of partial differential equations that can be classified as free
boundary problems. In particular, the coupling of both hypersurfaces depends on particles of a species that
evolve on one of the surfaces. Since they influence the surface tension, they can be understood as surfactants.
We use two common approaches for modelling free boundary problems, namely sharp and diffuse interfaces
by using similar physical arguments for their derivation as well as a formal asymptotic analysis. From the
modelling framework, we specify particular models for the evolution of biomembranes, and, even more specific,
for studying the biological phenomenon of cell blebbing. Properties of these models are investigated by means
of rigorous mathematical analysis showing existence of solutions, existence and stability of stationary solutions
where possible, as well a singular limits. We also present numerical algorithms for simulative studies of cell
blebbing models and report and interpret results obtained from their computations. Thus we can validate that
our models qualitatively reproduce phenomena that have been reported in the biological literature.

In this work, the influence of process and material parameters on the draw resonance instability in film casting and fiber spinning is investigated both theoretically and experimentally. Draw resonance generally occurs if the draw ratio, i.e., the ratio of outlet to inlet velocity, exceeds a critical value, and manifests itself in steady oscillations of the flow velocity and the geometric properties of the fibers and films.
Several Newtonian and viscoelastic models for film casting and fiber spinning are derived and the critical draw ratio is determined by means of linear stability analysis in order to investigate the influence of various effects like gravity, inertia, neck-in and strain hardening on draw resonance. Moreover, physical mechanisms underlying the instability are revealed and alternative stability criteria are reviewed and extended. Employing control parameters with strong connection to practical application, the results are visualized in stability maps, which enable both a quick determination of the critical draw ratio and a partition of the parameter space into several dynamical regimes. The theoretical results are completed by an experimental study on draw resonance in fiber spinning. Using an effective relaxation time, the measured critical draw ratios can be well described by the theoretical predictions.

The increasing interest in microfluidic applications in recent years resulted in a constantly growing demand for computational fluid dynamics on micro-/mesoscopic scales. The corresponding methods have evolved from a topic mainly of relevance for fundamental research to a crucial tool for engineering
applications. The physically correct modeling of the boundary interactions is critical on these scales, as the influence of boundary effects increases inversely proportionally with the characteristic length. Mesoscopic particle-based approaches, that is, methods where the fluid is modeled using discrete particles, are able to capture these effects correctly. The applicability of many existing simulation tools, however, is rather limited with respect to systems of complicated shape. Yet such shapes are necessary for
microfluidic devices in order to perform, for example, the continuous sorting of cells. Furthermore, as the computational cost of mesoscopic particle-based methods is high, the simulation tools have to be optimized for modern high-performance computing systems and be able to exploit the parallelism of today's supercomputers.
The aim of this work is to develop methods and algorithms required for a general, yet efficient simulation framework able to handle boundary conditions of complicated shape. The description of the computational domain using unstructured grids, combined with additional obstacles defined by combinations of geometric primitives is suggested. This hybrid approach combines the
universality of unstructured grids constructed by applying conventional meshing tools with the fully analytical description of boundary surfaces. This analytical description aligns conceptionally with the particle-based modeling of fluids and completely avoids the necessity to perform a discretization of the boundary. We devise an efficient and numerically robust algorithm for the
maintenance of neighbor lists in such complicated geometries. Various physically motivated boundary conditions are tightly integrated into this algorithm, allowing for the simulation of fluid flows in complex geometries. A thorough validation using standard test cases is performed to ensure the correct working of the implemented particle models. Several example applications for flows through complicated geometries are presented, such as
the flow around a particle cluster and the flow through a highly porous medium.
Using the unstructured grid as a basis, a fully object-oriented simulation framework is developed, which is easily extendible by separating the physical models from the data handling and parallelization scheme. The efficiency of the proposed parallelization scheme is assessed via benchmark runs on different
machines, highlighting the versatility and quality of the simulation tool.

Granular materials are composed by macroscopic solid particles where interactions are characterized by dissipative collisions. This kind of material is present in our daily life, for example, sand, coal, nuts, rocks etc. In this thesis we study different phenomenon presents in rapid granular flows by means of hydrodynamic simulations of the Navier-Stokes granular equations.
In Chapter 2, we introduce the Navier-Stokes equations and two different approaches for the transport coefficients for fluidized granular materials. One of
the consequences of the inelastic interaction between the particles is that the flow developed is supersonic and sharp-profiles of the hydrodynamic fields arise. To deal with this problem, we use a high-order shock-capturing method. In Chapters 3 and 4 is shown the model used to solve the hydrodynamic equations and its successful parallelization.
Due to the inelasticity, granular gases form dense clusters of particles. This
phenomenon is studied for a force-free granular gas in Chapter 5. The kinetics
of the cluster formation is analyzed and compared with the presently accepted
mode-enslaving mechanism. We observed that the mode-enslaving theory cannot
explain the process of cluster formation. Nevertheless, a direct correlation between
the appearance of the shock waves and formations of clusters is observed. Another effect specific to granular systems is the collapse. Considering gravity, a granular gas will become at rest if there is no energy supply. In Chapter 6,
we analyze the evolution of the granular gas throughout different stages before
the collapse, where regions of supersonic and subsonic dynamics are observed.
In the supersonic regions, the system develops shocks followed by sharp profiles
of the temperature and the density fields moving upwards. In the last stage of
the sedimentation, the energy decay has been studied and compared with previous
studies. In agreement with all of them, we confirmed that the entire system collapse simultaneously.
Similarly as is described for liquids, a vertical vibrated granular layer develops
characteristic patterns for certain intervals of frequencies and amplitudes of oscillation. This phenomenon called Faraday instability is an interesting example of granular collective behavior. In Chapter 7, we study numerically the formation of Faraday waves using two approaches of the transport coefficients described in Chapter 2 and comparing with event-driven molecular dynamics simulations. We observed that the two approaches work quite well, although there is a discrepancy related with the expression of the heat flux.

In this thesis we use the bead-spring microswimmer design as a model system to study mechanical microswimming. The basic form of such a swimmer was introduced as the 'three-sphere swimmer' in Najafi & Golestanian, Phys. Rev. E (2004) and has found wide use in theoretical, numerical and experimental research. In our work, we have modified and extended the model in various ways, which, as explained in this thesis, allow us to gain insight into many general principles of microswimming, for instance the interplay between fluid drag force and swimmer elasticity in determining the efficiency of motion. The work presented here consists of both analytical solution of the equations of motion in the different investigated cases and corresponding numerical study.
We begin this thesis with an introduction (chapter 0) to the world of low Reynolds number locomotion, and in particular to that of microswimming, explaining the current state of knowledge in the field regarding biological microswimmers and models thereof, both theoretical and experimental. We then explain in chapter 1 the details of, and the differences between, the Golestanian three-sphere swimmer and our bead-spring model. The Golestanian model consists of three spheres aligned along one line with the distances between two neighbouring spheres in each pair being changed in a controlled manner (which determines the swimming stroke), leading to propagation of the assembly. In the bead-spring model, we replace the specification of the stroke by that of the forces driving the motion, allow non-spherical and shape-varying beads in the design, and, in the last part of the thesis, investigate swimmer motion beyond the low Reynolds number (Stokes) regime. These changes result in a more comprehensive description of the motion with the influences of different factors such as the fluid viscosity, the energy input, the elasticity of the swimmer and its instantaneous and mean shapes all becoming important, unlike in the Golestanian swimmer where these influences are all subsumed in the specification of the swimming stroke. We use our model to calculate the velocity of our swimmer both with rigid and deformable spheres, and to different orders in the relative magnitude of bead size and bead separation.
In chapter 2, we explain the two simulation methods used by us, the Walberla system and the LB3D code. Both of these are based on the lattice Boltzmann method (LBM), and their main difference lies in their being coupled respectively to a rigid body physics engine, which allows us to simulate any combinations of rigid objects in fluids, and an immersed boundary method (IBM) solver with which we can simulate deformable membranes.
In chapter 3, we compare the swimmer velocities as obtained from theory and the two simulation systems for swimmers with rigid beads. We find good agreement which expectedly becomes better as the simulation systems become more idealised, such as by an increased simulation domain size and smaller Reynolds numbers of motion. We also explain how and why some microswimmers swim faster in more viscous fluids. We show that this puzzling phenomenon, observed experimentally for many species of bacteria, can occur in fully Newtonian fluids--a result which runs counter to the prevailing wisdom in the field--and arises from the dichotomous effects that the drag force has on motion at low Reynolds number. In particular, the so-called `aberrant' regime of motion, wherein the swimmer gets quicker as the fluid viscosity increases, is expected to show up for all mechanical microswimmers swimming due to the influence of sufficiently weak driving forces. The simulations fully support the theoretical prediction for the onset of the aberrant regime.
In chapter 4, we use the LB3D code to simulate swimmers with deformable beads, to answer the question of whether passive shape changes--which are the changes in shape of a deformable swimmer in response to the fluid, not as a driving mechanism for motion--can be beneficial for swimming. This relates to the as yet unexplained phenomenon of metaboly, wherein spirochetes, which otherwse swim by flagellar propulsion, regularly change their shapes during their motion, without its being clear whether these shape changes are beneficial for locomotion, for food capture, or some other purpose. Restricting our attention to our model, we show that passive shape changes can result in both faster and slower swimming, and that this response depends on the swimmer's elasticity. The theory accurately predicts both the regimes, where the shape changes respectively promote and hinder the motion, that are visible in the simulations.
In chapter 5 we look at active effects of shape, by studying the different swimming speeds of swimmers with rigid beads of different shapes. For this we allow the beads to be ellipsoids of revolution, and calculate the optimal aspect ratios of the ellipsoids (given a fixed volume or surface area) that maximize the swimming velocity for equal driving forces. We find that depending on the stiffness coefficient of the springs, the same shape (for instance, the ellipsoid of the lowest drag coefficient) may result in the fastest or the slowest swimmer, owing to the different energy costs of deforming springs of low and high stiffness. We show that this happens due to the swimming in the two cases being dominated either by a reduction in the drag force opposing the beads or by the hydrodynamic interaction amongst them.
In chapter 6 we expand the scope of our study to incorporate the onset of non-Stokesian effects in microswimming. Using the Walberla simulation system, we systematically increase the forces driving the beads, thereby raising the Reynolds number of motion and ultimately pushing the swimmer beyond the Stokes regime. We show that the limit of this regime may be determined by matching the coasting exhibited by the swimmer to that of an underdamped harmonic oscillator, with the damping constant arising from the Stokes drag law. The effective radius of the swimmer thus found agrees excellently with that obtained from theory, and indicates that inertial effects in microswimming set in at increased driving forces (or, equivalently, larger swimming strokes) or at increased swimmer masses. Building on this heuristic investigation, we modify our theoretical model by adding a mass acceleration term in the governing equations of motion of the three beads, and show that solution of the resultant system predicts swimmer velocities which are in good agreement with those observed in simulations (and which differ significantly from the Stokes-regime calculation results). These calculations confirm the identification of the Stokes, non-Stokes and intermediate regimes seen in the simulations.
We conclude in chapter 7 by a discussion of the main results presented in our work, and future possibilities for its extension.

The manipulation of liquid crystals by external potentials, such as electric or magnetic fields, is of great importance in many industrial and research applications. To gain insight into the impact of the different mechanisms in such a complex multi-particle system is a scientific challenge. Interactions between particles and external potential, particle-particle interactions, and, in case of colloidal systems, hydrodynamic interactions lead, in their interplay, to fascinating dynamical states and unusual diffusion behavior.
This work presents new insights into the dynamics of colloidal liquid crystals with computer simulations. For this purpose several model systems of increasing complexity are studied. The first model system is the most basic model system possible: a system of hard spherocylinders that only interact via excluded volume. In a next step Brownian motion, the random motion of colloidal particles in a fluid, is included via Langevin Dynamics. Finally, also the impact of hydrodynamic interactions between the particles is studied within a Lattice Boltzmann framework.

The adsorption process and the resulting dynamic surface tension in the context of protein foams were studied. A diffusion–advection equation is solved using a lattice Boltzmann method (LBM) in order to simulate the adsorption of surfactants on a surface. With different adsorption isotherms, different surfactants can be modelled. The advection is driven by a flow field coming from the LBM. The phase transition is implemented with a free surface LBM approach where the liquid–gas two-phase flow is simplified to a single-phase free surface flow by using a volume of fluid approach. Looking at the different time scales for diffusion and advection, which are determined by the diffusion coefficient and the viscosity, respectively, the LBM is limited due to time and space resolution. The rates of protein transport to a surface by diffusion and by advection are investigated which indicate that diffusion is only relevant for modelling long-time studies. For those time ranges and low concentrations, the diffusion of proteins from a bulk to a surface of a droplet is simulated and compared with the literature. As a next step, situations as in protein foams are assumed. High concentrations of proteins, e.g. as in milk, result in a simplified scenario where neither diffusion nor advection is important. This is analysed theoretically which suggests an instantaneous change of surface tension. To examine the stability of foam lamellae, this is used for further simulations. Two bubbles rise close to each other with globally different surface tensions as for pure water and water with proteins. Depending on these surface tensions and the initial distance, the bubbles coalesce faster for high surface tensions and show less secondary motions for lower surface tension. It is concluded that bubbles in protein foams coalesce only at shorter distances than in pure water.

Molecular Structures of Dialkylimidazolium Ionic Liquids at the Hydroxylated Solid-Liquid Interface
(2016)

Dialkylimidazolium ionic liquids – salts with a melting point well below room temperature – are a novel class of versatile fluids with a broad spectrum of potential applications, including electrochemistry, synthesis, catalysis and gas separation, to name but a few. Based on their unique, favorable properties such as negligible vapor pressure, a wide electrochemical window and their task-specific tunability, ionic liquids are slowly starting to replace conventional solvents and electrolytes in both science and industry.
While downsizing technology, interfacial effects can play a crucial role in the proposed applications. Pronounced molecular structuring at the solid-liquid and liquid-vapor interface has previously been reported for several ionic liquids and substrates. So far, however, no coherent explanation of these phenomena has been given.
Combining experimental X-ray reflectivity and molecular dynamics simulations in an unprecedented complementary approach, the work presented in this thesis provides reliable structural information of the solid–ionic liquid interface with atomic level detail for the first time. Reflectivity experiments have been performed at a modern third-generation synchrotron source while well-established, dedicated force fields have been adopted from the relevant literature to form the basis of the computational studies.
The results contain a cohesive picture of molecular structuring in dialkylimidazolium ionic liquids at hydroxylated oxide substrates, elucidating interface normal layering, lateral ordering, preferential ion orientation/conformation and liquid-substrate interactions. Cations, forming hydrogen bonding with the interface via the acidic ring proton, are favored by the hydroxylated substrate, consequently leading to a depletion of anions in the immediate vicinity. The positive net charge of the interfacial region, in turn, gives rise to an alternating sequence of anion/cation enriched monomolecular layers, extending about four to six iterations into the bulk liquid phase.

Understanding and predicting the behaviour of liquids at interfaces poses formidable scientific challenges and is highly relevant for the thriving fields of micro- and nanofluidics. External friction forces, such as in liquids slipping over solids, play a central role.
This work presents a well-founded extension of (generalised) fluctuating hydrodynamics to systems with slip boundaries or more general external friction forces. The theory naturally includes thermal fluctuations, which become important on small length scales. Moreover, they are fundamentally related to dissipative processes and reveal microscopic details of friction. A resulting fluctuating slip boundary condition is applied to derive stochastic thin film equations on slip substrates and to calculate the autocorrelation function of the tangential interaction force at a liquid-solid boundary.
In addition, a complementary approach for arbitrary small (classical) scales offers an alternative description. The formalism transfers notions from macroscopic hydrodynamics to the microscale, and external friction appears as a combination of static external forces and additional viscous dissipation.