## Dr. rer. nat. habil. Matthias Schröter

**Research Projects**

**Function**

Privatdozent

**Phone**

09131 85-70498

**Room**

03.151

**Teaching**

**Info**

Privatdozent

09131 85-70498

03.151

Rev. Sci. Instrum. **90**, 025108

(2019)

Soft Matter **14**, 4987-4995

(2018)

Soft Matter **14**, 7310-7323

(2018)

Physical Review Fluids **3**, 024304

(2018)

Physical Review Letters **120**, 055701

(2018)

Review of Scientific Instruments **88**, 051701

(2017)

EPJ Web of Conferences **140**, 06007

(2017)

Physical Review E **95**, 062903

(2017)

EPJ Web of Conferences **140**, 01008

(2017)

Review of Scientific Instruments **88**, 051809

(2017)

Soft Matter **13**, 394-401

(2017)

Scientific Reports **6**, 35650

(2016)

Soft Matter **12**, 3991-4006

(2016)

Applied Optics **55**, 3165-3169

(2016)

Energy & Fuels **29** (10), 6271-6276

(2015)

We present the first study of fluid distribution inside porous media imaged by neutron tomography. We demonstrate that this technique has matured sufficiently to deliver pore level results. The major advantage of neutron tomography is the contrast mechanism of using deuterated phases. This allows high contrast imaging without the need to add large amounts of inorganic salts as dopants, required to achieve adequate contrast for X-ray tomography studies. Measurements were performed at the Antares beamline (MLZ, Garching) with a voxel size of 11.8 μm. We propose this technique as a useful tool for studying mutliphase phenomena in porous media where the results are known to depend on the salinty and species of ions present, such as low salinity water, surfactant, and polymer flooding.

New Journal of Physics **17**, 093023

(2015)

Three fundamental segregation and pattern formation processes are known in granular mixtures in a rotating cylindrical drum: radial segregation, axial banding, and coarsening of the band pattern. While the mechanism for the first effect is well understood and for the second effect, several models have been proposed, the long-term coarsening mechanism remained unexplained so far. We demonstrate that the unidirectional flow between the bands in an axially segregated pattern is driven by small differences in size of the small beads at the band edges. Due to a process of microsegregation inside each band of small particles, which was so far unrecognized, this difference in diameter will be effective in all experiments with polydisperse beads. In consequence the stability of individual bands can be easily controlled by minor alterations of their composition. Our results make evident that a new mechanism as the driving force behind the axial particle flow has to be sought. We suggest possible hypotheses for such a mechanism.

arXiv, **1501.04472**

(2015)

The mechanical properties of a granular sample can depend on the way the packing was prepared. However, the variables which store this information are often unknown. Here we present an X-ray tomography study of tetrahedra packings prepared with three different tapping strengths. Our main result is that the relative contribution of the three different contact types possible between tetrahedra — face-to-face (F2F), edge-to-face (E2F), and point contacts — is one variable which stores the preparation history. We show this by preparing pairs of packings that differ either in their bulk volume fraction ϕglobal or in their number of mechanical constraints per particle C, where C is determined from all three contact types which each fix a different amount of constraints. For the pairs with the same ϕglobal the number of E2F and point contacts varies with preparation, while the number of F2F contacts stays constant. For the iso-constraint packings the relative contribution of all three contact types stays the same. We then perform a local analysis of the contact distribution by grouping the particles together according to their individual volume fraction ϕlocal computed from a Voronoi tessellation. We find that the probability distribution of ϕlocal depends only on ϕglobal, not on C. The number of F2F and E2F contacts increases in all experiments with ϕlocal; the number of point contacts, while always being the largest, decreases with ϕlocal. However, only the number of F2F contacts can be described by an universal function of ϕlocal. This behavior differs from spheres and ellipsoids and posses a significant constraint for any mean-field approach to tetrahedra packings.

Europhysics Letters **111**, 24002

(2015)

In particulate systems with short-range interactions, such as granular matter or simple fluids, local structure plays a pivotal role in determining the macroscopic physical properties. Here, we analyse local structure metrics derived from the Voronoi diagram of configurations of oblate ellipsoids, for various aspect ratios α and global volume fractions ϕg. We focus on jammed static configurations of frictional ellipsoids, obtained by tomographic imaging and by discrete element method simulations. In particular, we consider the local packing fraction ϕl, defined as the particle’s volume divided by its Voronoi cell volume. We find that the probability P(ϕl) for a Voronoi cell to have a given local packing fraction shows the same scaling behaviour as function of ϕg as observed for random sphere packs. Surprisingly, this scaling behaviour is further found to be independent of the particle aspect ratio. By contrast, the typical Voronoi cell shape, quantified by the Minkowski tensor anisotropy index β=β2,00, points towards a significant difference between random packings of spheres and those of oblate ellipsoids. While the average cell shape β of all cells with a given value of ϕl is very similar in dense and loose jammed sphere packings, the structure of dense and loose ellipsoid packings differs substantially such that this does not hold true. This non-universality has implications for our understanding of jamming of aspherical particles.

Phys. Rev. Lett. **114**, 158001

(2015)

In particulate soft matter systems the average number of contacts Z of a particle is an important predictor of the mechanical properties of the system. Using x-ray tomography, we analyze packings of frictional, oblate ellipsoids of various aspect ratios α, prepared at different global volume fractions ϕg. We find that Z is a monotonically increasing function of ϕg for all α. We demonstrate that this functional dependence can be explained by a local analysis where each particle is described by its local volume fraction ϕl computed from a Voronoi tessellation. Z can be expressed as an integral over all values of ϕl: Z(ϕg,α,X)=∫Zl(ϕl,α,X)P(ϕl|ϕg)dϕl. The local contact number function Zl(ϕl,α,X) describes the relevant physics in term of locally defined variables only, including possible higher order terms X. The conditional probability P(ϕl|ϕg) to find a specific value of ϕl given a global packing fraction ϕg is found to be independent of α and X. Our results demonstrate that for frictional particles a local approach is not only a theoretical requirement but also feasible.

ASABE **57**, 555

(2014)

The ability to mark bulk goods from different origins with RFID markers is of industrial interest, as such a method would improve the traceability of, e.g., cereals. However, due to a number of open technical questions, this method has not been utilized on a larger scale yet. This article studies the amount of segregation occurring between RFID markers, which are simulated as grain-sized plastic capsules, and marked wheat using two different setups. This segregation could occur during handling and transport due to the slightly different physical properties of the markers and the grains; it would then lead to erroneous results during subsequent quantitative analysis. In the first experiment, two samples of wheat, one marked with RFID dummies, were discharged in several steps from a test silo. A comparison of the marker concentration in the samples with the amount of associated wheat showed no discernible segregation. An additional statistical analysis allowed us to establish a relationship between the marker concentration and the error margin. In the second experiment, a mixture of wheat and markers was vertically shaken in a container, mimicking transport of wheat in large vessels. The position of the markers inside the container was determined by three-dimensional scans using x-ray tomography. We found that shaking induced some segregation due to sidewall-driven convection rolls, which indicated that the simulated markers were not optimally matched to the wheat grains.

Soft Matter **10**, 4208

(2014)

Jammed packings of granular materials differ from systems normally described by statistical mechanics in that they are athermal. In recent years a statistical mechanics of static granular media has emerged where the thermodynamic temperature is replaced by a configurational temperature X which describes how the number of mechanically stable configurations depends on the volume. Four different methods have been suggested to measure X. Three of them are computed from properties of the Voronoi volume distribution, the fourth takes into account the contact number and the global volume fraction. This paper answers two questions using experimental binary disc packings: first we test if the four methods to measure compactivity provide identical results when applied to the same dataset. We find that only two of the methods agree quantitatively. This implies that at least two of the four methods are wrong. Secondly, we test if X is indeed an intensive variable; this becomes true only for samples larger than roughly 200 particles. This result is shown to be due to recently measured correlations between the particle volumes [Zhao et al., Europhys. Lett. **97** (2012) 34004].

Phys. Rev. Applied **2**, 034002

(2014)

Pressure-controlled displacement of an oil-water interface is studied in dense packings of functionalized glass beads with well-defined spatial wettability correlations. An enhanced dissipation is observed if the typical extension *ξ* of the same-type wetting domains is smaller than the average bead diameter *d*. Three-dimensional imaging using x-ray microtomography shows that the frequencies *n(s)* of residual droplet volumes s for different *ξ* collapse onto the same curve. This indicates that the additional dissipation for small *ξ* is due to contact line pinning rather than an increase of capillary break-up and coalescence events.

AIP Conf. Proc. **1542**, 377

(2013)

Disordered packings of ellipsoidal particles are an important model for disordered granular matter. Here we report a way to determine the average contact number of ellipsoid packings from tomographic analysis. Tomographic images of jammed ellipsoid packings prepared by vertical shaking of loose configurations are recorded and the positions and orientations of the ellipsoids are reconstructed. The average contact number can be extracted from a contact number scaling (CNS) function. The size of the particles, that may vary due to production inaccuracies, can also be determined by this method.

Phys. Rev. Lett. **111**, 028001

(2013)

We prepare packings of frictional tetrahedra with volume fractions *ϕ* ranging from 0.469 to 0.622 using three different experimental protocols under isobaric conditions. Analysis via x-ray microtomography reveals that the contact number *Z* grows with *ϕ*, but does depend on the preparation protocol. While there exist four different types of contacts in tetrahedra packings, our analysis shows that the edge-to-face contacts contribute about 50% of the total increase in *Z*. The number of constraints per particle *C* increases also with *ϕ* and even the loosest packings are strongly hyperstatic, i.e., mechanically overdetermined with *C* approximately twice the degrees of freedom each particle possesses.

Phys. Rev. E **88**, 042201

(2013)

We present a new mode of transport of spherical particles in a horizontally vibrated channel with sawtooth-shaped side walls. The underlying driving mechanism is based on an interplay of directional energy injection transformed by the sidewall collisions and density-dependent interparticle collisions. Experiments and matching numerics show that the average particle velocity reaches a maximum at 60% of the maximal filling density. Introducing a spatial phase shift between the channel boundaries increases the transport velocity by an order of magnitude.

EPL **97**, 34004

(2012)

We measure the two-point correlation of free Voronoi volumes in binary disc packings, where the packing fraction Φ_{avg} ranges from 0.8175 to 0.8380. We observe short-ranged correlations over the whole range of Φ_{avg} and anticorrelations for Φ_{avg} > 0.8277. The spatial extent of the anti-correlation increases with Φ_{avg} while the position of the maximum of the anticorrelation and the extent of the positive correlation shrink with Φ_{avg}. We conjecture that the onset of anticorrelation corresponds to dilatancy onset in this system.

3D Res. **3**

(2012)

The screen is a key part of stereoscopic display systems using polarization to separate the different channels for each eye. The system crosstalk, characterizing the imperfection of the screen in terms of preserving the polarization of the incoming signal, and the scattering rate, characterizing the ability of the screen to deliver the incoming light to the viewers, determine the image quality of the system. Both values will depend on the viewing angle. In this work we measure the performance of three silver screens and three rear-projection screens. Additionally, we measure the surface texture of the screens using white-light interferometry. While part of our optical results can be explained by the surface roughness, more work is needed to understand the optical properties of the screens from a microscopic model.

Soft Matter **8**, 9731

(2012)

The theoretical description of granular materials, or assemblies of macroscopic particles, is a formidable task. Not only are granular materials out of thermal equilibrium, but they are also characterized by dissipative interactions and by static friction. Following a suggestion by S. F. Edwards, researchers have investigated the possible existence of a statistical mechanics of static granular systems, which would permit the description of macroscopic properties of mechanically stable granular assemblies from just a few parameters. The formulation and the validity of such an approach is still a matter of debate. This “emerging area” focuses on three important questions concerning such a statistical mechanics approach. First, we consider how the phase space of interest is affected by the requirement of mechanical stability. Second, we explore how the intensive parameters analogous to temperature can be determined from experimental or numerical data. Finally, we contrast different ways to express the granular counterpart to the classical Hamiltonian, known as the volume function.

J. Acoust. Soc. **129**, EL101

(2011)

Sound propagation in water-saturated granular sediments is known to depend on the sediment porosity, but few data in the literature address both the frequency and porosity dependency. To begin to address this deficiency, a fluidized bed technique was used to control the porosity of an artificial sediment composed of glass spheres of 265 μm diameter. Time-of-flight measurements and the Fourier phase technique were utilized to determine the sound speed for frequencies from 300 to 800 kHz and porosities from 0.37 to 0.43. A Biot-based model qualitatively describes the porosity dependence.

EPL **93**, 64003

(2011)

We measure shear response in packings of glass beads by pulling a thin, rough, metal plate vertically through a bed of volume fraction Φ, which is set, before the plate is pulled, in the range from 0.575 to 0.628. The yield stress is velocity independent over 4 decades and increases exponentially with phi, with a transition at Φ≈0.595. An analysis of the measured force fluctuations indicates that the shear modulus is significantly smaller than the bulk modulus.

Phys. Rev. E **84**, 031306

(2011)

A method of modifying the roughness of soda-lime glass spheres is presented, with the purpose of tuning interparticle friction. The effect of chemical etching on the surface topography and the bulk frictional properties of grains are systematically investigated. The surface roughness of the grains is measured using white-light interferometry and characterized by the lateral and vertical roughness length scales. The underwater angle of repose is measured to characterize the bulk frictional behavior. We observe that the coefficient of friction depends on the vertical roughness length scale.

EPL **90**, 3001

(2010)

Langmuir **26**, 17184

(2010)

We study the formation of capillary bridges between micrometer-sized glass spheres immersed in a binary liquid mixture using bright field and confocal microscopy. The bridges form upon heating due to the preferential wetting of the hydrophilic glass surface by the water-rich phase. If the system is cooled below the demixing temperature, the bridges disappear within a few seconds by intermolecular diffusion. Thus, this system offers the opportunity to switch the bridges on and off and to tune precisely the bridge volume by altering the temperature in a convenient range. We measure the bridge geometry as a function of the temperature from bright field images and calculate the cohesive force. We discuss the influence of the solvent composition on the bridge formation temperature, the strength of the capillary force, and the bridge volume growth rate. Furthermore, we find that the onset of bridge formation coincides with the water−lutidine bulk coexistence curve.

Phys. Rev. E **79**, 010301

(2009)

Phys. Rev. Lett. **101**, 018301

(2008)

Using sedimentation to obtain precisely controlled packings of noncohesive spheres, we find that the volume fraction *ϕ*_{RLP} of the loosest mechanically stable packing is in an operational sense well defined by a limit process. This random loose packing volume fraction decreases with decreasing pressure *p* and increasing interparticle friction coefficient *μ*. Using x-ray tomography to correct for a container boundary effect that depends on particle size, we find for rough particles in the limit *p*→0 a new lower bound, *ϕ*_{RLP}=0.550±0.001.

PNAS **104**, 9580

(2007)

Past work has shown that ions can pass through a membrane morereadily in one direction than the other. We demonstrate here in a model and an experiment that for a mixture of small and large particles such asymmetric diffusion can arise solely from an asymmetry in the geometry of the pores of the membrane. Our deterministic simulation considers a two-dimensional gas of elastic disks of two sizes diffusing through a membrane, and our laboratory experiment examines the diffusion of glass beads of two sizes through a metal membrane. In both experiment and simulation, the membrane is permeable only to the smaller particles, and the asymmetric pores lead to an asymmetry in the diffusion rates of these particles. The presence of even a small percentage of large particles can clog a membrane, preventing passage of the small particles in one direction while permitting free flow of the small particles in the other direction. The purely geometric kinetic constraints may play a role in common biological contexts such as membrane ion channels.

EPL **78**, 44004

(2007)

We find that a column of glass beads exhibits a well-defined transition between two phases that differ in their resistance to shear. Pulses of fluidization are used to prepare static sedimented states with well-defined particle volume fractions in the range 0.57–0.63. The resistance to shear is determined by slowly inserting a rod into the column of beads. Force measurements and bed height measurements both indicate that the transition occurs at = 0.60 for a range of speeds of the rod.

EPL **79**, 24003

(2007)

We have discovered an invariant distribution for local packing configurations in static granular media. This distribution holds in experiments for packing fractions covering most of the range from random loose packed to random close packed, for bead packs prepared both in air and in water. Assuming only that there exist elementary cells in which the system volume is subdivided, we derive from statistical mechanics a distribution that is in accord with the observations. This universal distribution function for granular media is analogous to the Maxwell-Boltzmann distribution for molecular gasses.

Physical Review E **76**, 042301

(2007)

Vertical shaking of a mixture of small and large beads can lead to segregation where the large beads either accumulate at the top of the sample, the so-called Brazil nut effect (BNE), or at the bottom, the reverse Brazil nut effect (RBNE). Here we demonstrate experimentally a sharp transition from the RBNE to the BNE when the particle coefficient of friction increases due to aging of the particles. This result can be explained by the two competing mechanisms of buoyancy and sidewall-driven convection, where the latter is assumed to grow in strength with increasing friction.

Physik in unserer Zeit **38**, 266

(2007)

Granulare Medien, wie Sand, Salz, Kohle oder Kaffeebohnen, lassen sich durch vertikales Schütteln entmischen. In Abhängigkeit von der Schüttelamplitude sammeln sich die größeren Teilchen entweder an der Oberfläche (der sogenannte Paranuss-Effekt), oder sie sinken nach unten (inverser Paranuss-Effekt). Mit Experimenten, Computersimulationen und Theorie ist es jüngst gelungen, die zu diesem Verhalten führenden Mechanismen zu identifizieren.

Physical Review E **74**, 011307

(2006)

A granular mixture of particles of two sizes that is shaken vertically will in most cases segregate. If the larger particles accumulate at the top of the sample, this is called the Brazil-nut effect (BNE); if they accumulate at the bottom, it is called the reverse Brazil-nut effect (RBNE). While this process is of great industrial importance in the handling of bulk solids, it is not well understood. In recent years ten different mechanisms have been suggested to explain when each type of segregation is observed. However, the dependence of the mechanisms on driving conditions and material parameters and hence their relative importance is largely unknown. In this paper we present experiments and simulations where both types of particles are made from the same material and shaken under low air pressure, which reduces the number of mechanisms to be considered to seven. We observe both BNE and RBNE by varying systematically the driving frequency and amplitude, diameter ratio, ratio of total volume of small to large particles, and overall sample volume. All our results can be explained by a combination of three mechanisms: a geometrical mechanism called void filling, transport of particles in sidewall-driven convection rolls, and thermal diffusion, a mechanism predicted by kinetic theory.

Physical Review E **71**, 030301(R)

(2005)

A statistical description of static granular material requires ergodic sampling of the phase space spanned by the different configurations of the particles. We periodically fluidize a column of glass beads and find that the sequence of volume fractions *ϕ* of postfluidized states is history independent and Gaussian distributed about a stationary state. The standard deviation of *ϕ* exhibits, as a function of *ϕ*, a minimum corresponding to a maximum in the number of statistically independent regions. Measurements of the fluctuations enable us to determine the compactivity *X*, a temperaturelike state variable introduced in the statistical theory of Edwards and Oakeshott Physica A 157 1080 (1989).

phdthesis, Otto-von-Guericke Universität Magdeburg

(2003)

Recently a fingering morphology, resembling the hydrodynamic Saffman-Taylor instability, was identified in the quasi-two-dimensional electrodeposition of copper by M. Lòpez-Salvans et al. [Phys. Rev. Lett. 76, 4062 (1996)]. This thesis tries to elucidate the underlying mechanism by measuring the dispersion relation of the growing front.

The instability is accompanied by gravity-driven convection rolls at the electrodes, which are examined using particle image velocimetry. While at the anode the theory presented by Chazalviel et al. [J. Electroanal. Chem. 407, 61 (1996)] describes the convection roll, the flow field at the cathode is more complicated because of the growing deposit. In particular, the analysis of the orientation of the velocity vectors reveals some lag of the development of the convection roll compared to the finger envelope.

In thin-layer electrodeposition the dissipated electrical energy leads to a substantial heating of the ion solution. Measurements of the resulting temperature field by means of an infrared camera indicate, that its properties correspond closely with the development of the concentration field. In particular, we find that the thermal gradients at the electrodes act similar to a weak additional driving force to the convection rolls driven by concentration gradients.

Physical Review E **65**, 041607

(2002)

Recently a fingering morphology, resembling the hydrodynamic Saffman-Taylor instability, was identified in the quasi-two-dimensional electrodeposition of copper. We present here measurements of the dispersion relation of the growing front. The instability is accompanied by gravity-driven convection rolls at the electrodes, which are examined using particle image velocimetry. While at the anode the theory presented by Chazalviel et al. [J. Electroanal. Chem. 407, 61 (1996)] describes the convection roll, the flow field at the cathode is more complicated because of the growing deposit. In particular, the analysis of the orientation of the velocity vectors reveals some lag of the development of the convection roll compared to the finger envelope.

Physical Review E **66**, 026307

(2002)

In thin-layer electrodeposition the dissipated electrical energy leads to a substantial heating of the ion solution. We measured the resulting temperature field by means of an infrared camera. The properties of the temperature field correspond closely with the development of the concentration field. In particular, we find that the thermal gradients at the electrodes act similar to a weak additional driving force to the convection rolls driven by concentration gradients.

Physics Reports **337**, 117

(2000)

The temporal evolution of a water–sand interface driven by gravity is experimentally investigated. By means of a Fourier analysis of the evolving interface the growth rates are determined for the different modes appearing in the developing front. To model the observed behavior we apply the idea of the Rayleigh–Taylor instability for two stratified fluids. Carrying out a linear stability analysis we calculate the growth rates from the corresponding dispersion relations for finite and infinite cell sizes and compose those results with the experimental data. Alternatively, the situation of the sedimenting sand can be modeled by a two-dimensional cellular automaton. A qualitative similarity between that model and the experimental situation is obtained.

European Physical Journal **4**, 475

(1998)

Evolution of Spontaneous Structures in Dissipative Continuous Systems (Busse, Friedrich H. and Müller, Stefan C.) **495**, Springer Verlag, Berlin

(1998)