Andreas M. Menzel

Magnetorheological fluids consist of micrometer-sized magnetic particles in a carrier liquid. Sufficiently strong external magnetic fields lead to the formation of string-like particle aggregates. We demonstrate that hydrodynamic interactions, that is, mutual couplings via induced flows, play a substantial role during the structuring process. They support the formation of slender chains instead of more compact clusters in the absence of mutual hydrodynamic interactions between the particles. This fundamental insight is substantial from an application perspective, due to the enormous technical importance and potential of structured magnetorheological materials.

Magnetic elastomers, like magnetic fluids, consist of magnetizable particles in a carrier medium. In contrast to magnetic fluids, the carrier matrix is a soft elastic solid. Consequently, the particles are permanently held in place. Such positional fixation allows to use the structure of the spatial particle arrangement as a central degree of freedom to enhance the properties of the materials. Specifically, structural optimization can improve overall magnetostrictive and magnetorheological properties. Key questions concern the identification of optimized structures, their consequences on the overall material properties, and ways of transferring them into reality. Furthermore, to close the gap between pure fundamental and materials science on the one hand and education on the other hand, the contents are introduced into educational science and research. They provide a solid basis for context- and authenticity-based learning as well as related scientific investigations. We overview multiple challenges on this path, potential ways of solution, and we estimate further developments in the field. Clearly, this kind of challenge can only be addressed in an interdisciplinary and collaborative approach.

Magnetic elastomers couple magnetic interactions between enclosed magnetic microscopic particles to their overall shape and mechanical response. A genuine understanding links the underlying micro‐ and macroscopic scales. We overview a recent proof‐of‐concept approach that shows how analytical considerations and statistical simulations can outline a corresponding scale connection. Structural properties on the particle scale are linked to overall properties of a simple example system. Optimizing the particle arrangement within the elastomer can maximize the requested material response. Ongoing and future investigations serve to quantify more realistic systems and geometries, to understand processes of structure formation and particle aggregation on the microscopic scale during the production process, to elucidate means of generating desirable particle structures, and to understand and improve the process of disseminating the corresponding scientific results.

When swimming at low Reynolds numbers, inertial effects are negligible and reciprocal movements cannot induce net motion. Instead, symmetry breaking is necessary to achieve net propulsion. Directed swimming can be supported by magnetic fields, which simultaneously provide a versatile means of remote actuation. Thus, we analyze the motion of a straight microswimmer composed of three magnetizable beads connected by two elastic links. The swimming mechanism is based on oriented external magnetic fields that oscillate in magnitude. Through induced reversible hysteretic collapse of the two segments of the swimmer, the two pairs of beads jump into contact and separate nonreciprocally. Due to higher-order hydrodynamic interactions, net displacement results after each cycle. Different microswimmers can be tuned to different driving amplitudes and frequencies, allowing for simultaneous independent control by just one external magnetic field. The swimmer geometry and magnetic field shape are optimized for maximum swimming speed using an evolutionary optimization strategy. Thanks to the simple working principle, an experimental realization of such a microrobot seems feasible and may open new approaches for microinvasive medical interventions such as targeted drug delivery.

When a hole is introduced into an elastic material, it will usually act to reduce the overall mechanical stiffness. A general ambition is to investigate whether a stiff shell around the hole can act to maintain the overall mechanical properties. We consider this effect from a macroscopic continuum perspective down to atomistic scales. For this purpose, we focus on the basic continuum example situation of an isotropic, homogeneous, linearly elastic material loaded uniformly under compressive plane strain for low concentrations of holes. As we demonstrate, the thickness of the shell can be adjusted in a way to maintain the overall stiffness of the system. We derive a corresponding mathematical expression for the thickness of the shell that conceals the hole. Thus, one can work with given materials to mask the presence of the holes simply by adjusting the thickness of the surrounding shells, with no need to change the materials. Our predictions from linear elasticity continuum theory are extended to atomistic levels using molecular dynamics simulations of a model Lennard-Jones solid. These extensions attest the robustness of our predictions down to atomistic scales. Thus, they open a straightforward possibility to adjust the strategy of mechanical cloaking via atomistic manipulations. From both perspectives, the underlying concept is important in the context of light-weight construction.

Wedge-shaped geometries in low-Reynolds-number flows are of increasing importance, for instance, in the design of microfluidic devices. The corresponding Green's functions describing the induced flow in response to a locally applied force were derived some time ago. To achieve a complete characterization of particle motion at low Reynolds numbers, we derive the flow response to locally applied torques. This is accomplished through a direct calculation based on the Fourier-Kontorovich-Lebedev transform using the Papkovich-Neuber representation of the hydrodynamic fields. We then illustrate the resulting flow fields, highlighting their structure, key features, and dependence on the geometry and orientation of the applied torque. Based on these solutions, we compute the corresponding hydrodynamic mobility tensor that couples torque and motion. Owing to the broken spatial symmetry imposed by the wedge-shaped confinement, a particle subjected to a torque will experience not only rotational motion, but also translational motion. These results provide analytical tools relevant for predicting and controlling particle behavior in confined microfluidic environments.

One of the most important properties of soft functionalized magnetic composite materials in view of their technological potential is given by the magnetorheological effect. It describes the change in rheological properties such as the shear modulus by the application of external magnetic fields. We demonstrate how computational materials design can support in approximately doubling the magnitude of this important phenomenon for magnetic elastomers. The key is to work with two perpendicular magnetic field directions. We expect future practical relevance of our concept.

Soft matter is characterized by its relatively strong response to external and internal influences. A soft piece of rubber or biological tissue can be easily deformed between our fingers using muscle force, whereas a steel rod does not show visible deformations detectable by eye. We use theoretical calculations and computer simulations to investigate the properties of soft matter when it has additional functionalities. These can include magnetic or living components. We are particularly interested in how individual microscopic components contribute to the behavior and properties of the entire system. In the first case, we examine rubbers (elastomers) containing microscopic particles that become magnetized in an external magnetic field. Due to resulting magnetic forces between individual particles, the entire material can deform and change its stiffness. This allows deformations to be generated magnetically or the damping behavior of the materials to be externally adjusted, even during use. We have derived a mathematical relationship between the positions of the individual particles and the resulting overall deformation of the material, such as changes in volume or expansion along the external magnetic field. In a key step, we identified through an optimization process particle arrangements that lead to maximum deformations and maximum hardening or softening of the materials. As a second example, we investigate so-called active matter. It includes microscopic objects that move autonomously. We can think of microorganisms like bacteria in a liquid or in a soft solid. Viscoelastic media, which can both flow and exhibit temporary elastic responses, are likewise considered as enclosing materials. Interestingly, depending on the properties of the environment, the active particles can move in a disordered manner, collectively in one direction, organize into swarms with turbulent movement patterns, move in stripe patterns, or perform collective circular motions. Special flow properties of a carrier fluid can lead to regular structures. We have predicted the existence of several of these dynamic states. Many of these phenomena were derived for thin layers and films. We were able to generally expand the understanding of membrane elasticity and flow behavior in films, particularly regarding movements within the film plane. Additional examples of our work include the growth and spreading of bent bacteria on surfaces. In general, we will continue to work on how properties of artificially activated materials and active, living matter can be described and potentially complement each other.

It is frequent for active or living entities to find themselves embedded in a surrounding medium. Resulting composite systems are usually classified as either active fluids or active solids. Yet, in reality, particularly in the biological context, a broad spectrum of viscoelasticity exists in between these two limits. There, both viscous and elastic properties are combined. To bridge the gap between active fluids and active solids, we here systematically derive a unified continuum-theoretical framework. It covers regimes of viscous, viscoelastic, and elastic active behavior. Our continuum equations are obtained by coarse-graining a discrete, agent-based microscopic dynamic description. In our subsequent analysis, we mainly focus on thin active films on supporting substrates. Strength of activity and degree of elasticity are used as control parameters that control the overall behavior. We concentrate on the analysis of transitions between spatially uniform analytical solutions of collective migration. These include isotropic and polar, orientationally ordered states. A stationary polar solution of persistent directed collective motion is observed for rather fluidlike systems. It corresponds to the ubiquitous swarming state observed in various kinds of dry and wet active matter. With increasing elasticity, persistent motion in one direction is prevented by elastic anchoring and restoring forces. As a consequence, rotations of the spatially uniform migration direction and associated flow occur. Our unified description allows us to continuously tune the material behavior from a viscous active fluid, via a range of intermediate viscoelasticity, to dampened elastic active behavior by variation of a single parameter. Therefore, it allows us in the future to investigate the time evolution of complex systems and biomaterials such as biofilms within one framework.