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C7 (N):Dense active suspensions in the chaotic regime

The goal of the project is to investigate active particle motion in a soluble medium (bacteria or active colloids) in the chaotic flow regime (“turbulence”) on an essentially two-dimensional manifold. We employ three differ-ent methods bridging the scales from microscopic particle motion to the continuum. On the smallest scale, we conduct (i) direct numerical simulations. This will be the basis for the construction of a (ii) mixture model founded on the Eulerian spatial averaging leading to an effective flow model. Built on this, a (iii) probability density function description and, in turn, its group theoretical properties will be the final goal to understand the complete and detailed statistics of the problem.

Funding for this project has started in July 2018.

Probability theory of active suspensions
B. Deußen, M. Oberlack, Y. Wang
Physics of Fluids33 (6),061902 (2021);

Vorticity Determines the Force on Bodies Immersed in Active Fluids
Thomas Speck, Ashreya Jayaram
Physical Review Letters126 (13), (2021);

When immersed into a fluid of active Brownian particles, passive bodies might start to undergo linear or angular directed motion depending on their shape. Here we exploit the divergence theorem to relate the forces responsible for this motion to the density and current induced by—but far away from—the body. In general, the force is composed of two contributions: due to the strength of the dipolar field component and due to particles leaving the boundary, generating a nonvanishing vorticity of the polarization. We derive and numerically corroborate results for periodic systems, which are fundamentally different from unbounded systems with forces that scale with the area of the system. We demonstrate that vorticity is localized close to the body and to points at which the local curvature changes, enabling the rational design of particle shapes with desired propulsion properties.

High-order simulation scheme for active particles driven by stress boundary conditions
B Deußen, A Jayaram, F Kummer, Y Wang, T Speck, M Oberlack
Journal of Physics: Condensed Matter33 (24),244004 (2021);

We study the dynamics and interactions of elliptic active particles in a two dimensional solvent. The particles are self-propelled through prescribing a fluid stress at one half of the fluid-particle boundary. The fluid is treated explicitly solving the Stokes equation through a discontinuous Galerkin scheme, which allows to simulate strictly incompressible fluids. We present numerical results for a single particle and give an outlook on how to treat suspensions of interacting active particles.

Quorum-sensing active particles with discontinuous motility
Andreas Fischer, Friederike Schmid, Thomas Speck
Physical Review E101 (1),012601 (2020);

We develop a dynamic mean-field theory for polar active particles that interact through a self-generated field, in particular one generated through emitting a chemical signal. While being a form of chemotactic response, it is different from conventional chemotaxis in that particles discontinuously change their motility when the local concentration surpasses a threshold. The resulting coupled equations for density and polarization are linear and can be solved analytically for simple geometries, yielding inhomogeneous density profiles. Specifically, here we consider a planar and circular interface. Our theory thus explains the observed coexistence of dense aggregates with an active gas. There are, however, differences from the more conventional picture of liquid-gas coexistence based on a free energy, most notably the absence of a critical point. We corroborate our analytical predictions by numerical simulations of active particles under confinement and interacting through volume exclusion. Excellent quantitative agreement is reached through an effective translational diffusion coefficient. We finally show that an additional response to the chemical gradient direction is sufficient to induce vortex clusters. Our results pave the way to engineer motility responses in order to achieve aggregation and collective behavior even at unfavorable conditions.

From scalar to polar active matter: Connecting simulations with mean-field theory
Ashreya Jayaram, Andreas Fischer, Thomas Speck
Physical Review E101 (2), (2020);

We study numerically the phase behavior of self-propelled elliptical particles interacting through the “hard” repulsive Gay-Berne potential at infinite Péclet number. Changing a single parameter, the aspect ratio, allows us to continuously go from discoid active Brownian particles to elongated polar rods. Discoids show phase separation, which changes to a cluster state of polar domains, which then form polar bands as the aspect ratio is increased. From the simulations, we identify and extract the two effective parameters entering the mean-field description: the force imbalance coefficient and the effective coupling to the local polarization. These two coefficients are sufficient to obtain a complete and consistent picture, unifying the paradigms of scalar and polar active matter.

Statistical theory of helical turbulence
B. Deußen, D. Dierkes, and M. Oberlack
Physics of Fluids32 (6),065109 (2020);

A statistical theory for homogeneous helical turbulence is developed under the condition of strong symmetry. The latter describes reflectional symmetry in planes through and normal to the helical unit vector eξ, which can be achieved by demanding that the mean velocity is zero. The two-point velocity correlation, the pressure–velocity correlation, and the two-point triple correlation are expressed by scalar functions in the helical unit vector system. By introducing the continuity equation for the correlations, the number of unknown functions can be reduced to such an extent that ultimately, a single scalar transport equation remains. Furthermore, a two-point Poisson equation is derived to express the pressure–velocity correlation in terms of the triple correlation. From the two-point version of the transport equation, the single-point limit is derived. Using the single-point equation, it can be shown that all velocity components are generally non-zero. Therefore, it is concluded that the phenomenon of vortex stretching is present in the helical coordinate system. Finally, the theory of axisymmetric turbulence is derived as a limiting case of helical turbulence to show consistency with former work.


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