arXiv subjects

Andreas M. Menzel

Publications and source records attributed to Andreas M. Menzel.

At least 37 records · Page 2Linked to original sources

arXiv2024

Analytical expressions for the two basic modes of surface displacement and overall deformation of a free-standing or elastically embedded sphere

Calculating by analytical theory the deformation of finite-sized elastic bodies in response to internally applied forces is a challenge. Here, we derive explicit analytical expressions for the amplitudes of modes of surface deformation of a homogeneous, isotropic, linearly elastic sphere. The modes under consideration correspond to overall changes in volume and to relative uniaxial elongation or contraction. Both situations of an elastic sphere embedded under no-slip conditions in a linearly elastic, homogeneous, isotropic, infinitely extended background medium and of a free-standing elastic sphere are considered. For example, our analytical expressions are important as a basis for computational material optimization in the context of spherical soft actuators.

cond-mat.soft↗

arXiv2024

Hydrodynamics of a disk in a thin film of weakly nematic fluid subject to linear friction

To make progress towards the development of a theory on the motion of inclusions in thin structured films and membranes, we here consider as an initial step a circular disk in a two-dimensional, uniaxially anisotropic fluid layer. We assume overdamped dynamics, incompressibility of the fluid, and global alignment of the axis of anisotropy. Motion within this layer is affected by additional linear friction with the environment, for instance, a supporting substrate. We investigate the induced flows in the fluid when the disk is translated parallel or perpendicular to the direction of anisotropy. Moreover, expressions for corresponding mobilities and resistance coefficients of the disk are derived. Our results are obtained within the framework of a perturbative expansion in the parameters that quantify the anisotropy of the fluid. Good agreement is found for moderate anisotropy when compared to associated results from finite-element simulations. At pronounced anisotropy, the induced flow fields are still predicted qualitatively correctly by the perturbative theory, although quantitative deviations arise. We hope to stimulate with our investigations corresponding experimental analyses, for example, concerning fluid flows in anisotropic thin films on uniaxially rubbed supporting substrates.

cond-mat.soft↗

arXiv2024

Internal sites of actuation and activation in thin elastic films and membranes of finite thickness

Functionalized thin elastic films and membranes frequently feature internal sites of net forces or stresses. These are, for instance, active sites of actuation, or rigid inclusions in a strained membrane that induce counterstress upon externally imposed deformations. We theoretically analyze the geometry of isotropic, flat, thin, linearly elastic films or membranes of finite thickness, laterally extended to infinity. At the mathematical core of such characterizations are the fundamental solutions for localized force and stress singularities associated with corresponding Green's functions. We derive such solutions in three dimensions and place them into the context of previous two-dimensional calculations. To this end, we consider both no-slip and stress-free conditions at the top and/or bottom surfaces. We provide an understanding for why the fully free-standing thin elastic membrane leads to diverging solutions in most geometries and compare these situations to the truly two-dimensional case. A no-slip support of at least one of the surfaces stabilizes the solution, which illustrates that the divergences in the fully free-standing case are connected to global deformations. Within the mentioned framework, our results are important for associated theoretical characterizations of thin elastic films, whether supported or free-standing, and of membranes subject to internal or external forces or stresses.

cond-mat.soft↗

arXiv2024

Vortex pattern stabilization in thin films resulting from shear thickening of active suspensions

The need for structuring on micrometer scales is abundant, for example, in view of phononic applications. We here outline a novel approach based on the phenomenon of active turbulence on the mesoscale. As we demonstrate, a shear-thickening carrier fluid of active microswimmers intrinsically stabilizes regular vortex patterns of otherwise turbulent active suspensions. The fluid self-organizes into a periodically structured nonequilibrium state. Introducing additional passive particles of intermediate size leads to regular spatial organization of these objects. Our approach opens a new path towards functionalization through patterning of thin films and membranes.

cond-mat.soft↗

arXiv2023

Magnetic elastomers as specific soft actuators -- predicting particular modes of deformation from selected configurations of magnetizable inclusions

Amongst the various fascinating types of material behavior featured by magnetic gels and elastomers are magnetostrictive effects. That is, deformations in shape or changes in volume are induced from outside by external magnetic fields. Application of the materials as soft actuators is therefore conceivable. Mostly, straight contraction or extension of the materials along a certain direction is discussed and investigated in this context. Here, we demonstrate that various further, different, higher modes of deformation can be excited. To this end, different spatial arrangements of the magnetizable particles enclosed by the soft elastic matrix, which constitute the materials, need to be controlled and realized. We address various different types of spatial configurations of the particles and evaluate resulting types of deformation using theoretical tools developed for this purpose. Examples are sheet-like arrangements of particles, circular or star-shaped arrangements of chain-like aggregates, or actual three-dimensional star-like particle configurations. We hope to stimulate with our work the development of experimental design and engineering methods so that selected spatial particle arrangements in magnetic gels and elastomers can be put to reality. Overall, we in this way wish to promote the transfer of these promising class of materials to real-world applications.

cond-mat.soft↗

arXiv2023

Stochastic motion under nonlinear friction representing shear thinning

We study stochastic motion under a nonlinear frictional force that levels off with increasing velocity. Specifically, our frictional force is of the so-called Coulomb-tanh type. At small speed, it increases approximately linearly with velocity, while at large speed it approaches a constant magnitude, similarly to solid (dry, Coulomb) friction. In one spatial dimension, a formal analogy between the associated Fokker-Planck equation and the Schrödinger equation for a quantum-mechanical oscillator in a nonharmonic Pöschl-Teller potential is revealed. Then, the stationary velocity statistics can be treated analytically. From such analytical considerations, we determine associated diffusion coefficients, which we confirm by agent-based simulations. Moreover, from such simulations and from numerically solving the associated Fokker-Planck equation, we find that the spatial distribution function, starting from an initial Gaussian shape, develops tails that appear exponential at intermediate time scales. At small magnitudes of stochastic driving, the velocity distribution resembles the case of linear friction, while at large magnitudes it rather approaches the case of solid (dry, Coulomb) friction. The same is true for diffusion coefficients. In a certain sense, thus interpolating between the two extreme cases of linear friction and solid (dry, Coulomb) friction, our approach should be useful to describe several cases of practical relevance. For instance, a reduced increase in friction with increasing relative speed is typical of shear-thinning behavior. Therefore, driven motion in shear-thinning environments is one specific example to which our description may be applied.

cond-mat.stat-mech↗

arXiv2022

Circular motion subject to external alignment under active driving: nonlinear dynamics and the circle map

Hardly any real self-propelling or actively driven object is perfect. Thus, undisturbed motion will generally not follow straight lines but rather circular trajectories. We here address self-propelled or actively driven objects that move in discrete steps and additionally tempt to migrate towards a certain direction by discrete angular adjustment. Overreaction in the angular alignment is possible. This competition implies pronounced nonlinear dynamics including period doubling and chaotic behavior in a broad parameter regime. Such behavior directly affects the appearance of the trajectories, also during collective motion under spatial self-concentration.

cond-mat.soft↗

arXiv2022

The role of boundaries for displacements and motion in two-dimensional fluid or elastic films and membranes

Thin fluid or elastic films and membranes are found in nature and technology, for instance, as confinements of living cells or in loudspeakers. When applying a net force, resulting flows in an unbounded two-dimensional incompressible low-Reynolds-number fluid or displacements in a two-dimensional linearly elastic solid seem to diverge logarithmically with the distance from the force center, which has led to some debate. Recently, we have demonstrated that such divergences cancel when the total (net) force vanishes. Here, we illustrate that, if a net force is present, the boundaries play a prominent role. Already a single no-slip boundary regulates the flow and displacement fields and leads to their decay to leading order inversely in distance from a force center and the boundary. In other words, it is the boundary that stabilizes the system in this situation, unlike the three-dimensional case, where an unbounded medium by itself is able to absorb a net force. We quantify the mobility and displaceability of an inclusion as a function of the distance from the boundary, as well as interactions between different inclusions. In the case of free-slip boundary conditions, a kinked boundary is necessary to achieve stabilization.

cond-mat.soft↗

arXiv2022

Density functional approach to elastic properties of three-dimensional dipole-spring models for magnetic gels

Magnetic gels are composite materials, consisting of a polymer matrix and embedded magnetic particles. Those are mechanically coupled to each other, giving rise to the magnetostrictive effects as well as to a controllable overall elasticity responsive to external magnetic fields. Due to their inherent composite and thereby multiscale nature, a theoretical framework bridging different levels of description is indispensable for understanding the magnetomechanical properties of magnetic gels. In this study, we extend a recently developed density functional approach from two spatial dimensions to more realistic three-dimensional systems. Along these lines, we connect a mesoscopic characterization resolving the discrete structure of the magnetic particles, to macroscopic continuum parameters of magnetic gels. In particular, we incorporate the long-range nature of the magnetic dipole-dipole interaction, and consider the approximate incompressibility of the embedding media, and relative rotations with respect to an external magnetic field breaking rotational symmetry. We then probe the shape of the model system in its reference state, confirming the dependence of magnetostrictive effects on the configuration of the magnetic particles and on the shape of the considered sample. Moreover, calculating the elastic and rotational coefficients on the basis of our mesoscopic approach, we examine how the macroscopic types of behavior are related to the mesoscopic properties. Implications for real systems of random particle configurations are also discussed.

cond-mat.soft↗

arXiv2022

A group theoretical approach to elasticity under constraints and predeformations

Respecting deformational constraints and predeformations poses a substantial challenge in the description of nonlinear elasticity. We here outline how group theory can play a beneficial role to overcome this challenge. Specifically, group theory guides us to generalized definitions of nonlinear shear deformation gradients and expressions of generalized elastic moduli in the nonlinear regime. Particularly, such achievements become important in the context of larger deformations under constraints and additional deformations on top of predeformations.

cond-mat.soft↗

arXiv2022

Statistics for an object actively driven by spontaneous symmetry breaking into reversible directions

Propulsion of otherwise passive objects is achieved by mechanisms of active driving. We concentrate on cases in which the direction of active drive is subject to spontaneous symmetry breaking. In our case, this direction will be maintained, until a large enough impulse by an additional stochastic force reverses it. Examples may be provided by self-propelled droplets, gliding bacteria stochastically reversing their propulsion direction, or nonpolar vibrated hoppers. The magnitude of active forcing is regarded as constant, and we include the effect of inertial contributions. Interestingly, this situation can formally be mapped to stochastic motion under (dry, solid) Coulomb friction, however, with a negative friction parameter. Diffusion coefficients are calculated by formal mapping to the situation of a quantum-mechanical harmonic oscillator exposed to an additional repulsive delta-potential. Results comprise a ditched or double-peaked velocity distribution and spatial statistics showing outward propagating maxima when starting from initially concentrated arrangements.

physics.bio-ph↗

arXiv2022

Elastic deformations of loaded core-shell systems

Macroscopic elastic core-shell systems can be generated as toy models to be deformed and haptically studied by hand. On the mesoscale, colloidal core-shell particles and microgels are fabricated and investigated by different types of microscopy. We analyse, using linear elasticity theory, the response of spherical core-shell systems under the influence of a line density of force that is oriented radially and acts along the equator of the outer surface. Interestingly, deformational coupling of the shell to the core can determine the resulting overall appearance in response to the forces. We address various combinations of radii, stiffness, and Poisson ratio of core and shell and illustrate the resulting deformations. Macroscopically, the situation could be realized by wrapping a cord around the equator of a macroscopic model system and pulling it tight. On the mesoscale, colloidal microgel particles symmetrically confined to the interface between two immiscible fluids are pulled radially outward by surface tension.

cond-mat.soft↗

arXiv2022

Mediated interactions between rigid inclusions in two-dimensional elastic or fluid films

Interactions between rigid inclusions in continuous three-dimensional linearly elastic solids and low-Reynolds-number viscous fluids have largely been quantified during the past. Prime example systems are given by functionalized elastic composite materials or fluid colloidal suspensions. Here, we address the significantly less frequently studied situation of rigid inclusions in two-dimensional elastic or low-Reynolds-number fluid films. We concentrate on the situation in which disk-like inclusions remain well separated from each other and do not get into contact. Specifically, we demonstrate and explain that the logarithmic divergence of the associated Green's function is removed in the absence of net external forces on the inclusions, in line with physical intuition. For instance, this situation applies when only pairwise mutual interactions between the inclusions prevail. Our results will support, for example, investigations on membranes functionalized by appropriate inclusions, both of technical or biological origin, or the dynamics of active microswimmers in appropriately prepared thin films.

cond-mat.soft↗

arXiv2021

Steady azimuthal flow field induced by a rotating sphere near a rigid disk or inside a gap between two coaxially positioned rigid disks

Geometric confinements play an important role in many physical and biological processes and significantly affect the rheology and behavior of colloidal suspensions at low Reynolds numbers. On the basis of the linear Stokes equations, we investigate theoretically and computationally the viscous azimuthal flow induced by the slow rotation of a small spherical particle located in the vicinity of a rigid no-slip disk or inside a gap between two coaxially positioned rigid no-slip disks of the same radius. We formulate the solution of the hydrodynamic problem as a mixed-boundary-value problem in the whole fluid domain, which we subsequently transform into a system of dual integral equations. Near a stationary disk, we show that the resulting integral equation can be reduced into an elementary Abel integral equation that admits a unique analytical solution. Between two coaxially positioned stationary disks, we demonstrate that the flow problem can be transformed into a system of two Fredholm integral equations of the first kind. The latter are solved by means of numerical approaches. Using our solution, we further investigate the effect of the disks on the slow rotational motion of a colloidal particle and provide expressions of the hydrodynamic mobility as a function of the system geometry. We compare our results with corresponding finite-element simulations and observe very good agreement.

physics.flu-dyn↗

arXiv2021

Stimuli-responsive twist actuators made from soft elastic composite materials -- linking mesoscopic and macroscopic descriptions

Very recently, the construction of twist actuators from magnetorheological gels and elastomers has been suggested. These materials consist of magnetizable colloidal particles embedded in a soft elastic polymeric environment. The twist actuation is enabled by a net chirality of the internal particle arrangement. Upon magnetization by a homogeneous external magnetic field, the systems feature an overall torsional deformation around the magnetization direction. Starting from a discrete minimal mesoscopic model set-up we work towards a macroscopic characterization. The two scales are linked by identifying expressions for the macroscopic system parameters as functions of the mesoscopic model parameters. In this way, the observed behavior of a macroscopic system can in principle be mapped to and illustratively be understood from an appropriate mesoscopic picture. Our results apply equally well to corresponding soft electrorheological gels and elastomers.

cond-mat.soft↗

arXiv2020

Dynamical Crystallites of Active Chiral Particles

One of the intrinsic characteristics of far-from-equilibrium systems is the nonrelaxational nature of the system dynamics, which leads to novel properties that cannot be understood and described by conventional pathways based on thermodynamic potentials. Of particular interest are the formation and evolution of ordered patterns composed of active particles that exhibit collective behavior. Here we examine such a type of nonpotential active system, focusing on effects of coupling and competition between chiral particle self-propulsion and self-spinning. It leads to the transition between three bulk dynamical regimes dominated by collective translative motion, spinning-induced structural arrest, and dynamical frustration. In addition, a persistently dynamical state of self-rotating crystallites is identified as a result of a localized-delocalized transition induced by the crystal-melt interface. The mechanism for the breaking of localized bulk states can also be utilized to achieve self-shearing or self-flow of active crystalline layers.

cond-mat.soft↗

arXiv2020

Towards an analytical description of active microswimmers in clean and in surfactant-covered drops

Geometric confinements are frequently encountered in the biological world and strongly affect the stability, topology, and transport properties of active suspensions in viscous flow. Based on a far-field analytical model, the low-Reynolds-number locomotion of a self-propelled microswimmer moving inside a clean viscous drop or a drop covered with a homogeneously distributed surfactant, is theoretically examined. The interfacial viscous stresses induced by the surfactant are described by the well-established Boussinesq-Scriven constitutive rheological model. Moreover, the active agent is represented by a force dipole and the resulting fluid-mediated hydrodynamic couplings between the swimmer and the confining drop are investigated. We find that the presence of the surfactant significantly alters the dynamics of the encapsulated swimmer by enhancing its reorientation. Exact solutions for the velocity images for the Stokeslet and dipolar flow singularities inside the drop are introduced and expressed in terms of infinite series of harmonic components. Our results offer useful insights into guiding principles for the control of confined active matter systems and support the objective of utilizing synthetic microswimmers to drive drops for targeted drug delivery applications.

physics.flu-dyn↗

arXiv2020

Magnetically induced elastic deformations of magnetic gels and elastomers containing particles of mixed size

Soft elastic composite materials can serve as actuators when they transform changes in external fields into mechanical deformation. Here, we address the corresponding deformational behavior of magnetic gels and elastomers, consisting of magnetizable colloidal particles in a soft polymeric matrix and exposed to external magnetic fields. Since many practical realizations of such materials involve particulate inclusions of polydisperse size distributions, we concentrate on the effect that mixed particle sizes have on the overall deformational response. To perform a systematic study, our focus is on binary size distributions. We systematically vary the fraction of larger particles relative to smaller ones and characterize the resulting magnetostrictive behavior. The consequences for systems of various different spatial particle arrangements and different degrees of compressibility of the elastic matrix are evaluated. In parts, we observe a qualitative change in the overall response for selected systems of mixed particle sizes. Specifically, overall changes in volume and relative elongations or contractions in response to an induced magnetization can be reversed into the opposite types of behavior. Our results should apply to the characteristics of other soft elastic composite materials like electrorheological gels and elastomers when exposed to external electric fields as well. Overall, we hope to stimulate the further investigation on the purposeful use of mixed particle sizes as a means to design tailored requested material behavior.

cond-mat.soft↗