arXiv subjects

Henning Reinken

Publications and source records attributed to Henning Reinken.

12 recordsLinked to original sources

arXiv2026

Hydrodynamics substantially affects induced structure formation in magnetic fluids

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.

cond-mat.soft↗

arXiv2025

Oscillatory collective motion in viscoelastic and elastic active fluids and solids under circular confinement

In an inspiring recent study, Xu et al. [Nat. Phys. 19, 46 (2023)] observed for a living active biofilm under circular confinement two emergent dynamic modes of collective motion in the film. One corresponds to global rotational motion of oscillating sense of rotation, the other one to uniformly translating motion of rotating migration direction. The authors reproduced these features in a discretized theoretical model for elastic active solids. We here demonstrate that the discovered fundamental phenomena are generic and emerge abundantly for a broad range of viscoelastic fluids and solids. Elastic solids represent only one limiting case.

cond-mat.soft↗

arXiv2025

Rheologically tuned modes of collective transport in active viscoelastic films

While many living biological media combine both viscous and elastic properties, most theoretical studies employ either purely fluid- or solid-like descriptions. We here use a unified framework for active films on substrates capable of describing a broad range of viscoelastic behavior to explore the interplay between activity and rheology. The core of the study is a comprehensive state diagram showing a rich world of spatiotemporal dynamic states. Our results demonstrate the potential of tunable rheology to realize modes of controlled active transport on the microscale.

cond-mat.soft↗

arXiv2025

Unified description of viscous, viscoelastic, or elastic thin active films on substrates

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 viscous, viscoelastic, and elastic active materials. 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 fluid-like 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 to continuously tune the material behavior from viscous, via viscoelastic, to elastic active behavior by variation of a single parameter. Therefore, it allows in the future to investigate the time evolution of complex systems and biomaterials such as biofilms within one framework.

cond-mat.soft↗

arXiv2024

Self-sustained patchy turbulence in shear-thinning active fluids

Bacterial suspensions and other active fluids are known to develop highly dynamical vortex states, denoted as active or mesoscale turbulence. We reveal the pronounced effect of non-Newtonian rheological conditions on these turbulent states, concentrating on shear thinning. A self-sustained heterogeneous state of coexisting turbulent and quiescent areas develops, which results in anomalous velocity statistics. The heterogeneous state emerges in a hysteretic transition when varying activity. We provide an extensive numerical analysis and observe features consistent with a directed percolation transition. Our results are important, for instance, when addressing active objects in biological media with complex rheological properties.

cond-mat.soft↗

arXiv2024

Pattern selection and the route to turbulence in incompressible polar active fluids

Active fluids, such as suspensions of microswimmers, are known to self-organize into complex spatio-temporal flow patterns. An intriguing example is mesoscale turbulence, a state of dynamic vortex structures exhibiting a characteristic length scale. Here, we employ a minimal model for the effective microswimmer velocity field to explore how the turbulent state develops from regular vortex patterns when the strength of activity resp. related parameters such as nonlinear advection or polar alignment strength - is increased. First, we demonstrate analytically that the system, without any spatial constraints, develops a stationary square vortex lattice in the absence of nonlinear advection. Subsequently, we perform an extended stability analysis of this nonuniform "ground state" and uncover a linear instability, which follows from the mutual excitement and simultaneous growth of multiple perturbative modes. This extended analysis is based on linearization around an approximation of the analytical vortex lattice solution and allows us to calculate critical activity parameters. Above these critical values, the vortex lattice develops into mesoscale turbulence in numerical simulations. Utilizing the numerical approach, we uncover an extended region of hysteresis where both patterns are possible depending on the initial condition. Here, we find that turbulence persists below the instability of the vortex lattice. We further determine the stability of square vortex patterns as a function of their wavenumber and represent the results analogous to the well-known Busse balloons known from classical pattern-forming systems. Here, the region of stable periodic patterns shrinks and eventually disappears with increasing activity parameters. Our results show that the strength of activity plays a similar role for active turbulence as the Reynolds number does in driven flow exhibiting inertial turbulence.

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↗

arXiv2022

Optimal Turbulent Transport in Microswimmer Suspensions

Microswimmer suspensions self-organize into complex spatio-temporal flow patterns, including vortex lattices and mesoscale turbulence. Here we explore the consequences for the motion of passive tracers, based on a continuum model for the microswimmer velocity field. We observe two qualitatively different regimes distinguished via the dimensionless Kubo number $K$. At advection strengths right above the transition to turbulence, the flow field evolves very slowly ($K \gg 1$) and the spatial vortex structures lead to dominant trapping effects. In contrast, deep in the turbulent state, much faster dynamics ($K \ll 1$) consistent with the so-called sweeping hypothesis leads to transport properties completely determined by the temporal correlations. In between ($K \approx 1$), we observe a regime of optimal transport, signaled by a maximum of the diffusion coefficient.

physics.flu-dyn↗

arXiv2022

Ising-like critical behavior of vortex lattices in an active fluid

Turbulent vortex structures emerging in bacterial active fluids can be organized into regular vortex lattices by weak geometrical constraints such as obstacles. Here we show, using a continuum-theoretical approach, that the formation and destruction of these patterns exhibit features of a continuous second-order equilibrium phase transition, including long-range correlations, divergent susceptibility, and critical slowing down. The emerging vorticity field can be mapped onto a two-dimensional (2D) Ising model with antiferromagnetic nearest-neighbor interactions by coarse-graining. The resulting effective temperature is found to be proportional to the strength of the nonlinear advection in the continuum model.

cond-mat.soft↗

arXiv2018

Asymmetric pattern formation in microswimmer suspensions induced by orienting fields

This paper studies the influence of orienting external fields on pattern formation, particularly mesoscale turbulence, in microswimmer suspensions. To this end, we apply a hydrodynamic theory that can be derived from a microscopic microswimmer model [Phys. Rev. E 97, 022613 (2018)]. The theory combines a dynamic equation for the polar order parameter with a modified Stokes equation for the solvent flow. Here, we extend the model by including an external field that exerts an aligning torque on the swimmers (mimicking the situation in chemo-, photo-, magneto- or gravitaxis). Compared to the field-free case, the external field breaks the rotational symmetry of the vortex dynamics and leads instead to strongly asymmetric, traveling stripe patterns, as demonstrated by numerical solution and linear stability analysis. We further analyze the emerging structures using a reduced model which involves only an (effective) microswimmer velocity field. This model is significantly easier to handle analytically, but still preserves the main features of the asymmetric pattern formation. We observe an underlying transition between a square vortex lattice and a traveling stripe pattern. These structures can be well described in the framework of weakly nonlinear analysis, provided the strength of nonlinear advection is sufficiently weak.

cond-mat.soft↗

arXiv2018

Derivation of a hydrodynamic theory for mesoscale dynamics in microswimmer suspensions

In this paper we systematically derive a fourth-order continuum theory capable of reproducing mesoscale turbulence in a three-dimensional suspension of microswimmers. We start from overdamped Langevin equations for a generic microscopic model (pushers or pullers), which include hydrodynamic interactions on both, small length scales (polar alignment of neighboring swimmers) and large length scales, where the solvent flow interacts with the order parameter field. The flow field is determined via the Stokes equation supplemented by an ansatz for the stress tensor. In addition to hydrodynamic interactions, we allow for nematic pair interactions stemming from excluded-volume effects. The results here substantially extend and generalize earlier findings [Phys. Rev. E 94, 020601(R) (2016)], in which we derived a two-dimensional hydrodynamic theory. From the corresponding mean-field Fokker-Planck equation combined with a self-consistent closure scheme, we derive nonlinear field equations for the polar and the nematic order parameter, involving gradient terms of up to fourth order. We find that the effective microswimmer dynamics depends on the coupling between solvent flow and orientational order. For very weak coupling corresponding to a high viscosity of the suspension, the dynamics of mesoscale turbulence can be described by a simplified model containing only an effective microswimmer velocity.

cond-mat.soft↗

arXiv2016

Shear banding in nematogenic fluids with oscillating orientational dynamics

We investigate the occurrence of shear banding in nematogenic fluids under planar Couette flow, based on mesoscopic dynamical equations for the orientational order parameter and the shear stress. We focus on parameter values where the sheared homogeneous system exhibits regular oscillatory orientational dynamics, whereas the equilibrium system is either isotropic (albeit close to the isotropic--nematic transition) or deep in its nematic phase. The numerical calculations are restricted to spatial variations in shear gradient direction. We find several new types of shear banded states characterized by regions with regular oscillatory orientational dynamics. In all cases shear banding is accompanied by a non--monotonicity of the flow curve of the homogeneous system; however, only in the case of the initially isotropic system this curve has the typical $S$--like shape. We also analyze the influence of different orientational boundary conditions and of the spatial correlation length.

cond-mat.soft↗