Optimal turbulent transport in microswimmer suspensions

Reinken, Henning; Klapp, Sabine H. L.; Wilczek, Michael

doi:10.1103/physrevfluids.7.084501

Cited by 6 publications

(6 citation statements)

References 64 publications

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“…Performing additional numerical calculations for different values of a, we determine the hysteresis region in a-λ-space, which is shown as the area shaded in green in figure 4. We obtained similar results for the lower limit of the hysteresis from numerical calculations starting from an initially isotropic state with small random perturbations [62]. Due to the random initial values, the development of a disordered, turbulent state is favored.…”

Section: Hysteretic Behaviorsupporting

confidence: 69%

“…A final answer would require an analysis going beyond the scope of this work. Meanwhile, numerically solving the full dynamic equation (1), we not only observe a square vortex lattice for λ = 0 [62], but also for small values of λ below the threshold to turbulence. In fact, the numerical calculations show that λ has no impact on the observed patterns (including the lattice constant) in this stationary regime whatsoever, see appendix C.…”

Section: Stationary Pattern Selectionmentioning

confidence: 91%

“…This term has a negative sign and, thus, leads to the saturation of the emerging patterns. Note that in most studies [23,31,37,40,[57][58][59][60][61][62], there is an additional positive coefficient in front of the cubic term. However, this coefficient can be scaled out by an appropriate rescaling of v and λ.…”

Section: Modelmentioning

confidence: 99%

“…In the stationary vortex lattice, v rms can be calculated analytically, which yields v rms = 2A s . In the turbulent state, v rms is generally smaller because the nonlinear advection term leads to energy transfer between scales and subsequent dissipation, which comes on top of the amplitude saturation via the cubic term in equation ( 1) [58,62].…”

Section: Hysteretic Behaviormentioning

confidence: 99%

“…Recently, the model was substantiated by a derivation from a generic microscopic theory [55,56]. Although there are a large number of follow-up studies using the model [31,37,40,[57][58][59][60][61][62], it is still unclear how mesoscale turbulence emerges from the underlying regular structures that the model supports. To answer this question, we here focus on the stability of possible structures, which include stripe patterns, as well as square, triangular and hexagonal lattices of vortices.…”

Section: Introductionmentioning

confidence: 99%

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

Reinken,

Heidenreich,

Bär

et al. 2024

New J. Phys.

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Active fluids, such as suspensions of microswimmers, are well 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, stationary 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 a critical advection or alignment strength, above which the square vortex lattice becomes unstable. 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 such as Rayleigh–Bénard convection experiments and corresponding models such as the Swift–Hohenberg equation. 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.

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Section: Hysteretic Behaviorsupporting

confidence: 69%

Section: Stationary Pattern Selectionmentioning

confidence: 91%

Section: Modelmentioning

confidence: 99%

Section: Hysteretic Behaviormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Reinken,

Heidenreich,

Bär

et al. 2024

New J. Phys.

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Unconstrained Mesoscale Turbulence

Reinken

2024

Springer Theses

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Anomalous dynamics of a passive droplet in active turbulence

Singh,

Chaudhuri

2024

Nat Commun

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Motion of a passive deformable object in an active environment serves as a representative of both in-vivo systems such as intracellular particle motion in Acanthamoeba castellanii, or in-vitro systems such as suspension of beads inside dense swarms of Escherichia coli. Theoretical modeling of such systems is challenging due to the requirement of well resolved hydrodynamics which can explore the spatiotemporal correlations around the suspended passive object in the active fluid. We address this critical lack of understanding using coupled hydrodynamic equations for nematic liquid crystals with finite active stress to model the active bath, and a suspended nematic droplet with zero activity. The droplet undergoes deformation fluctuations and its movement shows periods of “runs” and “stays”. At relatively low interfacial tension, the droplet begins to break and mix with the outer active bath. We establish that the motion of the droplet is influenced by the interplay of spatial correlations of the flow and the size of the droplet. The mean square displacement shows a transition from ballistic to normal diffusion which depends on the droplet size. We discuss this transition in relation to spatiotemporal scales associated with velocity correlations of the active bath and the droplet.

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Optimal turbulent transport in microswimmer suspensions

Cited by 6 publications

References 64 publications

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

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

Unconstrained Mesoscale Turbulence

Anomalous dynamics of a passive droplet in active turbulence

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