Ising-like Critical Behavior of Vortex Lattices in an Active Fluid

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

“…A stable vortex lattice could also be realized experimentally by introducing a periodic array of small obstacles into a bacterial suspensions that exhibits active turbulence [39]. This phenomenon could be reproduced with simulations in a model of an active polar fluid [40,41]. More recently, several numerical studies have suggested control schemes to tame and control turbulence in active nematics [42,43].…”

“…In three-dimensional channels several experimental and theoretical studies with active nematics have shown that widening the smallest extension of the channel can lead to a transition between coherent patterns and apparently turbulent flows [50][51][52]. For the polar active fluid, simulations of the transition between turbulent states and regular vortex patterns, which are externally stabilized by small obstacles in the flow, have been shown to exhibit features of a non-equilibrium phase transition in the Ising universality class [41]. The latter study has utilized a model for suspensions of microswimmers (such as Bacillus Subtilis) that supports regular structures even in the absence of external stabilization, as well as turbulent states [40].…”

Optimal turbulent transport in microswimmer suspensions

“…where q is a pressure-like quantity that ensures the incompressibility condition ∇ • v = 0. The dynamics can be characterized as a competition between gradient dynamics determined by the functional F and nonlinear advection (λv•∇v), where λ is the advection strength, which can be related to mesoscopic parameters such as the self-propulsion speed [20,50]. For high activity, i.e., 0 < a < 1, the minimum of F is a vortex pattern with square lattice symmetry characterized by two perpendicular modes with characteristic wavelength Λ = 2π [21].…”

“…However, it is largely unexplored how the complex emerging large-scale flow patterns, which are typical for such microswimmer suspensions, impact the mixing and transport properties of these non-equilibrium systems. Here, we quantify active fluid transport in the framework of an experimentally validated model for polar active fluids, which enables a precise control of the flow states ranging from vortex lattices [16][17][18][19][20][21][22] to active turbulence [21][22][23][24][25][26], either externally, e.g. through obstacles [17,19,20,27,28], or by changing the fluid parameters [18,21,22].…”

“…Here, we quantify active fluid transport in the framework of an experimentally validated model for polar active fluids, which enables a precise control of the flow states ranging from vortex lattices [16][17][18][19][20][21][22] to active turbulence [21][22][23][24][25][26], either externally, e.g. through obstacles [17,19,20,27,28], or by changing the fluid parameters [18,21,22].…”