arXiv subjects

Andreas M. Menzel

Publications and source records attributed to Andreas M. Menzel.

At least 55 records · Page 3Linked to original sources

arXiv2020

Towards a soft magnetoelastic twist actuator

Soft actuators allow to transform external stimuli to mechanical deformations. Because of their deformational response to external magnetic fields, magnetic gels and elastomers represent ideal candidates for such tasks. Mostly, linear magnetostrictive deformations, that is, elongations or contractions along straight axes are discussed in this context. In contrast to that, we here suggest to realize a twist actuator that responds by torsional deformations around the axis of the applied magnetic field. For this purpose, we theoretically investigate the overall mechanical response of a basic model system containing discrete magnetizable particles in a soft elastic matrix. Two different types of discrete particle arrangements are used as starting conditions in the nonmagnetized state. These contain globally twisted anisotropic particle arrangements on the one hand, and groups of discrete helical-like particle structures positioned side by side on the other hand. Besides the resulting twist upon magnetization, we also evaluate different other modes of deformation. Our analysis supports the construction of magnetically orientable and actuatable torsional mixing devices in fluidic applications or other types of soft actuators that initiate relative rotations between different components.

cond-mat.soft↗

arXiv2020

Dynamics of a microswimmer-microplatelet composite

Guiding active microswimmers by external fields to requested target locations is a promising strategy to realize complex transport on the microscale. To this end, one possibility consists of attaching the microswimmers to orientable passive components. Accordingly, we analyze theoretically, using a minimal model, the dynamics of a microswimmer when rigidly attached tangentially to a (significantly larger) microplatelet, here represented by a thin circular disk. On this way, we determine the flow field in the whole space induced by a Stokeslet that is located above the center of a spatially fixed rigid disk of no-slip surface conditions. Finally, we determine and analyze possible trajectories of the overall composite. To this end, the platelet is additionally endowed with a permanent magnetic moment, which allows to steer the motion of the whole composite by a homogeneous external magnetic field. As previous experimental studies suggest, related setups may be helpful to guide sperm cells to requested targets or for the purpose of coordinated drug delivery.

physics.flu-dyn↗

arXiv2019

Magnetostriction in magnetic gels and elastomers as a function of the internal structure and particle distribution

Magnetic gels and elastomers are promising candidates to construct reversibly excitable soft actuators, triggered from outside by magnetic fields. These magnetic fields induce or alter the magnetic interactions between discrete rigid particles embedded in a soft elastic polymeric matrix, leading to overall deformations. It is a major challenge in theory to correctly predict from the discrete particle configuration the type of deformation resulting for a finite-sized system. Considering an elastic sphere, we here present such an approach. The method is in principle exact, at least within the framework of linear elasticity theory and for large enough interparticle distances. Different particle arrangements are considered. We find, for instance, that regular simple cubic configurations show elongation of the sphere along the magnetization if oriented along a face or space diagonal of the cubic unit cell. Contrariwise, with the magnetization along the edge of the cubic unit cell, they contract. The opposite is true in this geometry for body- and face-centered configurations. Remarkably, for the latter configurations but the magnetization along a face or space diagonal of the unit cell, contraction was observed to revert to expansion with decreasing Poisson ratio of the elastic material. Randomized configurations were considered as well. They show a tendency of elongating the sphere along the magnetization, which is more pronounced for compressible systems. Our results can be tested against actual experiments for spherical samples. Moreover, our approach shall support the search of optimal particle distributions for a maximized effect of actuation.

cond-mat.soft↗

arXiv2019

Theory of active particle penetration through a planar elastic membrane

With the rapid advent of biomedical and biotechnological innovations, a deep understanding of the nature of interaction between nanomaterials and cell membranes, tissues, and organs, has become increasingly important. Active penetration of nanoparticles through cell membranes is a fascinating phenomenon that may have important implications in various biomedical and clinical applications. Using a fully analytical theory supplemented by particle-based computer simulations, the penetration process of an active particle through a planar two-dimensional elastic membrane is studied. The membrane is modeled as a self-assembled sheet of particles, uniformly arranged on a square lattice. A coarse-grained model is introduced to describe the mutual interactions between the membrane particles. The active penetrating particle is assumed to interact sterically with the membrane particles. State diagrams are presented to fully characterize the system behavior as functions of the relevant control parameters governing the transition between different dynamical states. Three distinct scenarios are identified. These compromise trapping of the active particle, penetration through the membrane with subsequent self-healing, in addition to penetration with permanent disruption of the membrane. The latter scenario is accompanied by a partial fragmentation of the membrane and creation of a hole of a size exceeding the interaction range of the membrane components. Our analytical theory is based on a combination of a perturbative expansion technique and a discrete-to-continuum formulation. Our approach might be helpful for the prediction of the transition threshold between the trapping and penetration in real-space experiments involving motile swimming bacteria or artificial active particles.

cond-mat.soft↗

arXiv2019

Frequency-dependent higher-order Stokes singularities near a planar elastic boundary: implications for the hydrodynamics of an active microswimmer near an elastic interface

The emerging field of self-driven active particles in fluid environments has recently created significant interest in the biophysics and bioengineering communities owing to their promising future biomedical and technological applications. These microswimmers move autonomously through aqueous media where under realistic situations they encounter a plethora of external stimuli and confining surfaces with peculiar elastic properties. Based on a far-field hydrodynamic model, we present an analytical theory to describe the physical interaction and hydrodynamic couplings between a self-propelled active microswimmer and an elastic interface that features resistance toward shear and bending. We model the active agent as a superposition of higher-order Stokes singularities and elucidate the associated translational and rotational velocities induced by the nearby elastic boundary. Our results show that the velocities can be decomposed in shear and bending related contributions which approach the velocities of active agents close to a no-slip rigid wall in the steady limit. The transient dynamics predict that contributions to the velocities of the microswimmer due to bending resistance are generally more pronounced than to shear resistance. Our results provide insight into the control and guidance of artificial and synthetic self-propelling active microswimmers near elastic confinements.

physics.flu-dyn↗

arXiv2019

Creeping motion of a solid particle inside a spherical elastic cavity. II. Asymmetric motion

An analytical method is proposed for computing the low-Reynolds-number hydrodynamic mobility function of a small colloidal particle asymmetrically moving inside a large spherical elastic cavity, the membrane of which is endowed with resistance toward shear and bending. In conjunction with the results obtained in the first part [Daddi-Moussa-Ider, Löwen, and Gekle, Eur. Phys. J. E 41, 104 (2018)], in which the axisymmetric motion normal to the surface of an elastic cavity is investigated, the general motion for an arbitrary force direction can be addressed. The elastohydrodynamic problem is formulated and solved using the classic method of images through expressing the hydrodynamic flow fields as a multipole expansion involving higher-order derivatives of the free-space Green's function. In the quasi-steady limit, we demonstrate that the particle self-mobility function of a particle moving tangent to the surface of the cavity is larger than that predicted inside a rigid stationary cavity of equal size. This difference is justified by the fact that a stationary rigid cavity introduces additional hindrance to the translational motion of the encapsulated particle, resulting in a reduction of its hydrodynamic mobility. Furthermore, the motion of the cavity is investigated, revealing that the translational pair (composite) mobility, which linearly couples the velocity of the elastic cavity to the force exerted on the solid particle, is solely determined by membrane shear properties. Our analytical predictions are favorably compared with fully-resolved computer simulations based on a completed-double-layer boundary integral method.

physics.flu-dyn↗

arXiv2019

Multi-species dynamical density functional theory for microswimmers: derivation, orientational ordering, trapping potentials, and shear cells

Microswimmers typically operate in complex environments. In biological systems, often diverse species are simultaneously present and interact with each other. Here, we derive a (time-dependent) particle-scale statistical description, namely a dynamical density functional theory, for such multi-species systems, extending existing works on one-component microswimmer suspensions. In particular, our theory incorporates the effect of external potentials, but also steric and hydrodynamic interactions between swimmers. For the latter, a previously introduced force-dipole-based minimal (pusher or puller) microswimmer model is used. As a limiting case of our theory, mixtures of hydrodynamically interacting active and passive particles are captured as well. After deriving the theory, we apply it to different planar swimmer configurations. First, these are binary pusher--puller mixtures in external traps. In the considered situations, we find that the majority species imposes its behavior on the minority species. Second, for unconfined binary pusher--puller mixtures, the linear stability of an orientationally disordered state against the emergence of global polar orientational order (and thus emergent collective motion) is tested analytically. Our statistical approach predicts, qualitatively in line with previous particle-based computer simulations, a threshold for the fraction of pullers and for their propulsion strength that lets overall collective motion arise. Third, we let driven passive colloidal particles form the boundaries of a shear cell, with confined active microswimmers on their inside. Driving the passive particles then effectively imposes shear flows, which persistently acts on the inside microswimmers. Their resulting behavior reminds of the one of circle swimmers, though with varying swimming radii.

cond-mat.soft↗

arXiv2019

Binary pusher-puller mixtures of active microswimmers and their collective behavior

Microswimmers are active particles of microscopic size that self-propel by setting the surrounding fluid into motion. According to the kind of far-field fluid flow that they induce, they are classified into pushers and pullers. Many studies have explored similarities and differences between suspensions of either pushers or pullers, but the behavior of mixtures of the two is still to be investigated. Here, we rely on a minimal discrete microswimmer model, particle-resolved, including hydrodynamic interactions, to examine the orientational ordering in such binary pusher-puller mixtures. In agreement with existing literature, we find that our monodisperse suspensions of pushers do not show alignment, whereas those of solely pullers spontaneously develop ordered collective motion. By continuously varying the composition of the binary mixtures, starting from pure puller systems, we find that ordered collective motion is largely maintained up to pusher-puller composition ratios of about 1:2. Surprisingly, pushers when surrounded by a majority of pullers are more tightly aligned than indicated by the average overall orientational order in the system. Our study outlines how orientational order can be tuned in active microswimmer suspensions to a requested degree by doping with other species.

cond-mat.soft↗

arXiv2019

Classical density functional theory for a two-dimensional isotropic ferrogel model with labeled particles

In this study, we formulate a density functional theory (DFT) for systems of labeled particles, considering a two-dimensional bead-spring lattice with a magnetic dipole on every bead as a model for ferrogels. On the one hand, DFT has been widely studied to investigate fluid-like states of materials, in which constituent particles are not labeled as they can exchange their positions without energy cost. On the other hand, in ferrogels consisting of magnetic particles embedded in elastic polymer matrices, the particles are labeled by their positions as their neighbors do not change over time. We resolve such an issue of particle labeling, introducing a mapping of the elastic interaction mediated by the springs onto a pairwise additive interaction (pseudo-springs) between unlabeled particles. We further investigate magnetostriction and changes in the elastic constants under altered magnetic interactions employing the pseudo-spring potential. It is revealed that there are two different response scenarios in the mechanical properties of the dipole-spring systems: while systems at low packing fractions are hardened as the magnetic moments increase in magnitude, at high packing fractions softening due to diminishing effects from the steric force, associated with increases in the volume, is observed. Validity of the theory is also verified by Monte-Carlo simulations with both real and pseudo-springs. We expect that our DFT approach may shed light on an understanding of materials with particle inclusions.

cond-mat.soft↗

arXiv2019

Displacement field around a rigid sphere in a compressible elastic environment, corresponding higher-order Faxén relations, as well as higher-order displaceability and rotateability matrices

An efficient route to the displacement field around a rigid spherical inclusion in an infinitely extended homogeneous elastic medium is presented in a slightly alternative way when compared to some common textbook methods. Moreover, two Faxén relations of next-higher order beyond the stresslet are calculated explicitly for compressible media. They quantify higher-order moments involving the force distribution on rigid particles in a deformed elastic medium. Additionally, the displaceability and rotateability matrices are calculated up to (including) sixth order in inverse particle separation distance. These matrices describe the interactions mediated between the rigid embedded particles by the elastic environment. All methods and results can formally be transferred to the corresponding case of incompressible hydrodynamic low-Reynolds-number Stokes flow by considering the limit of an incompressible environment. The roles of compressibility of the embedding medium and of the here additionally derived higher-order contributions are highlighted by some selected example configurations.

cond-mat.soft↗

arXiv2019

Membrane penetration and trapping of an active particle

The interaction between nano- or micro-sized particles and cell membranes is of crucial importance in many biological and biomedical applications such as drug and gene delivery to cells and tissues. During their cellular uptake, the particles can pass through cell membranes via passive endocytosis or by active penetration to reach a target cellular compartment or organelle. In this manuscript, we develop a simple model to describe the interaction of a self-driven spherical particle (moving through an effective constant active force) with a minimal membrane system, allowing for both penetration and trapping. We numerically calculate the state diagram of this system, the membrane shape, and its dynamics. In this context, we show that the active particle may either get trapped near the membrane or penetrates through it, where the membrane can either be permanently destroyed or recover its initial shape by self-healing. Additionally, we systematically derive a continuum description allowing to accurately predict most of our results analytically. This analytical theory helps identifying the generic aspects of our model, suggesting that most of its ingredients should apply to a broad range of membranes, from simple model systems composed of magnetic microparticles to lipid bilayers. Our results might be useful to predict mechanical properties of synthetic minimal membranes.

cond-mat.soft↗

arXiv2018

Particle-scale statistical theory for hydrodynamically induced polar ordering in microswimmer suspensions

Previous particle-based computer simulations have revealed a significantly more pronounced tendency of spontaneous global polar ordering in puller (contractile) microswimmer suspensions than in pusher (extensile) suspensions. We here evaluate a microscopic statistical theory to investigate the emergence of such order through a linear instability of the disordered state. For this purpose, input concerning the orientation-dependent pair-distribution function is needed, and we discuss corresponding approaches, particularly a heuristic variant of the Percus test-particle method applied to active systems. Our theory identifies an inherent evolution of polar order in planar systems of puller microswimmers, if mutual alignment due to hydrodynamic interactions overcomes the thermal dealignment by rotational diffusion. In the theory, the cause of orientational ordering can be traced back to the actively induced hydrodynamic rotation--translation coupling between the swimmers. Conversely, disordered pusher suspensions remain linearly stable against homogeneous polar orientational ordering. We expect that our results can be confirmed in experiments on (semi-)dilute active microswimmer suspensions, based, for instance, on biological pusher- and puller-type swimmers.

cond-mat.soft↗

arXiv2018

Reversible magnetomechanical collapse: virtual touching and detachment of rigid inclusions in a soft elastic matrix

Soft elastic composite materials containing particulate rigid inclusions in a soft elastic matrix are candidates for developing soft actuators or tunable damping devices. The possibility to reversibly drive the rigid inclusions within such a composite together to a close-to-touching state by an external stimulus would offer important benefits. Then, a significant tuning of the mechanical properties could be achieved due to the resulting mechanical hardening. For a long time, it has been argued whether a virtual touching of the embedded magnetic particles with subsequent detachment can actually be observed in real materials, and if so, whether the process is reversible. Here, we present experimental results that demonstrate this phenomenon in reality. Our system consists of two paramagnetic nickel particles embedded at finite initial distance in a soft elastic polymeric gel matrix. Magnetization in an external magnetic field tunes the magnetic attraction between the particles and drives the process. We quantify the scenario by different theoretical tools, i.e., explicit analytical calculations in the framework of linear elasticity theory, a projection onto simplified dipole-spring models, as well as detailed finite-element simulations. From these different approaches, we conclude that in our case the cycle of virtual touching and detachment shows hysteretic behavior due to the mutual magnetization between the paramagnetic particles. Our results are important for the design and construction of reversibly tunable mechanical damping devices. Moreover, our projection on dipole-spring models allows the formal connection of our description to various related systems, e.g., magnetosome filaments in magnetotactic bacteria.

cond-mat.soft↗

arXiv2018

Memory-based mediated interactions between rigid particulate inclusions in viscoelastic environments

Many practically relevant materials combine properties of viscous fluids and elastic solids to viscoelastic behavior. Our focus is on the induced dynamic behavior of damped finite-sized particulate inclusions in such substances. We explicitly describe history-dependent interactions that emerge between the embedded particles. These interactions are mediated by the viscoelastic surroundings. They result from the flows and distortions of the viscoelastic medium when induced by the rigid inclusions. Both, viscoelastic environments of terminal fluid-like flow or of completely reversible damped elastic behavior, are covered. For illustration and to highlight the role of the formalism in potential applications, we briefly address the relevant examples of dragging a rigid sphere through a viscoelastic environment together with subsequent relaxation dynamics, the switching dynamics of magnetic fillers in elastic gel matrices, and the swimming behavior of active microswimmers in viscoelastic solutions. The approach provides a basis for more quantitative and extended investigations of these and related systems in the future.

cond-mat.soft↗

arXiv2018

Dynamics of a simple model microswimmer in an anisotropic fluid: implications for alignment behavior and active transport in a nematic liquid crystal

Several recent experiments investigate the orientational and transport behavior of self-driven bacteria and colloidal particles in nematic liquid crystals. Correspondingly, we study theoretically the dynamics of a minimal model microswimmer in a uniaxially anisotropic fluid. As a first step, the hydrodynamic Green's function providing the resulting fluid flow in response to a localized force acting on the anisotropic fluid is derived analytically. On this basis, the behavior of both puller- and pusher-type microswimmers in the anisotropic fluid is analyzed. Depending on the propulsion mechanism and the relative magnitude of different involved viscosities, we find alignment of the swimmers parallel or perpendicular to the anisotropy axis. Particularly, also an oblique alignment is identified under certain circumstances. The observed swimmer reorientation results from the hydrodynamic coupling between the self-induced fluid flow and the anisotropy of the surrounding fluid, which distorts the self-generated flow field. We support parts of our results by a simplified linear stability analysis. Our theoretical predictions are in qualitative agreement with recent experimental observations on swimming bacteria in nematic liquid crystals. They support the objective of utilizing the, possibly switchable, anisotropy of a host fluid to guide individual microswimmers and active particles along a requested path, enabling controlled active transport.

cond-mat.soft↗

arXiv2018

Dynamical density functional theory for circle swimmers

The majority of studies on self-propelled particles and microswimmers concentrates on objects that do not feature a deterministic bending of their trajectory. However, perfect axial symmetry is hardly found in reality, and shape-asymmetric active microswimmers tend to show a persistent curvature of their trajectories. Consequently, we here present a particle-scale statistical approach of circle-swimmer suspensions in terms of a dynamical density functional theory. It is based on a minimal microswimmer model and, particularly, includes hydrodynamic interactions between the swimmers. After deriving the theory, we numerically investigate a planar example situation of confining the swimmers in a circularly symmetric potential trap. There, we find that increasing curvature of the swimming trajectories can reverse the qualitative effect of active drive. More precisely, with increasing curvature, the swimmers less effectively push outwards against the confinement, but instead form high-density patches in the center of the trap. We conclude that the circular motion of the individual swimmers has a localizing effect, also in the presence of hydrodynamic interactions. Parts of our results could be confirmed experimentally, for instance, using suspensions of L-shaped circle swimmers of different aspect ratio.

cond-mat.stat-mech↗

arXiv2018

Hydrodynamic coupling and rotational mobilities near planar elastic membranes

We study theoretically and numerically the coupling and rotational hydrodynamic interactions between spherical particles near a planar elastic membrane that exhibits resistance towards shear and bending. Using a combination of the multipole expansion and Faxen's theorems, we express the frequency-dependent hydrodynamic mobility functions as a power series of the ratio of the particle radius to the distance from the membrane for the self mobilities, and as a power series of the ratio of the radius to the interparticle distance for the pair mobilities. In the quasi-steady limit of zero frequency, we find that the shear- and bending-related contributions to the particle mobilities may have additive or suppressive effects depending on the membrane properties in addition to the geometric configuration of the interacting particles relative to the confining membrane. To elucidate the effect and role of the change of sign observed in the particle self and pair mobilities, we consider an example involving a torque-free doublet of counterrotating particles near an elastic membrane. We find that the induced rotation rate of the doublet around its center of mass may differ in magnitude and direction depending on the membrane shear and bending properties. Near a membrane of only energetic resistance toward shear deformation, such as that of a certain type of elastic capsules, the doublet undergoes rotation of the same sense as observed near a no-slip wall. Near a membrane of only energetic resistance toward bending, such as that of a fluid vesicle, we find a reversed sense of rotation. Our analytical predictions are supplemented and compared with fully resolved boundary integral simulations where a very good agreement is obtained over the whole range of applied frequencies.

physics.flu-dyn↗

arXiv2018

State diagram of a three-sphere microswimmer in a channel

Geometric confinements are frequently encountered in soft matter systems and in particular significantly alter the dynamics of swimming microorganisms in viscous media. Surface-related effects on the motility of microswimmers can lead to important consequences in a large number of biological systems, such as biofilm formation, bacterial adhesion and microbial activity. On the basis of low-Reynolds-number hydrodynamics, we explore the state diagram of a three-sphere microswimmer under channel confinement in a slit geometry and fully characterize the swimming behavior and trajectories for neutral swimmers, puller- and pusher-type swimmers. While pushers always end up trapped at the channel walls, neutral swimmers and pullers may further perform a gliding motion and maintain a stable navigation along the channel. We find that the resulting dynamical system exhibits a supercritical pitchfork bifurcation in which swimming in the mid-plane becomes unstable beyond a transition channel height while two new stable limit cycles or fixed points that are symmetrically disposed with respect to the channel mid-height emerge. Additionally, we show that an accurate description of the averaged swimming velocity and rotation rate in a channel can be captured analytically using the method of hydrodynamic images, provided that the swimmer size is much smaller than the channel height.

physics.flu-dyn↗