Onset of meso-scale turbulence in active nematics

Abstract

Meso-scale turbulence is an innate phenomenon, distinct from inertial turbulence, that spontaneously occurs at low Reynolds number in fluidized biological systems. This spatiotemporal disordered flow radically changes nutrient and molecular transport in living fluids and can strongly affect the collective behaviour in prominent biological processes, including biofilm formation, morphogenesis and cancer invasion. Despite its crucial role in such physiological processes, understanding meso-scale turbulence and any relation to classical inertial turbulence remains obscure. Here we show how the motion of active matter along a micro-channel transitions to meso-scale turbulence through the evolution of locally disordered patches (active puffs) from an ordered vortex-lattice flow state. We demonstrate that the stationary critical exponents of this transition to meso-scale turbulence in a channel coincide with the directed percolation universality class. This finding bridges our understanding of the onset of low-Reynolds-number meso-scale turbulence and traditional scale-invariant turbulence in confinement.

Aerodynamics and Percolation: Unfolding Laminar Separation Bubble on Airfoils

“…We also see that the quality of our results is comparable with that of other groups, like the work on directed percolation in a channel flow [13]. Other experimental studies on DP [11,20] suffer from similar shortcomings, such as the continuous onset of turbulence and truncated scaling ranges. By establishing an adapted DP model, we are able to trace these shortcomings back to typical experimental constraints, such as noisy control parameters and experimental coarse graining.…”

“…Since Pomeau's work, several simulations have supported his conjecture; however, only in the last few years has it been possible to provide experimental evidence [4] because of the novel possibilities of extracting accurate measurements from a turbulent flow with sufficient spatial and temporal resolution. Recent studies approached transition from different angles by means of low-order models [5][6][7] and sophisticated simulations [8][9][10][11], as well as experiments [12][13][14]. They concordantly indicate nonequilibrium phase transition occurring in basic shear flows, i.e., pipe, channel, and Couette flows.…”

Active matter invasion

“…In addition to the bulk dynamics, the interaction with walls or obstacles of different shape can add further complexity. Theoretically, using the active nematohydrodynamics framework, a transition to spontaneous flows in channels has been predicted [49,50], as well as more complex states with intricate interplay of defects and vortices, and a transition to active turbulence [51,52,53].…”

“…The activity-induced length-scale Λ ζ = K Q /ζ emerges from the competition between the activity driving the dynamics and the elastic resistance against deformations in the director field [28,61,62], while the capillary width d imposes an upper limit for hydrodynamic interactions across the capillary. The activity number A relates these two length-scales [51,52].…”

“…As the activity is increased further, the initial spontaneous transition to flows is followed by the generation of counter-rotating vortices along the capillary. As the active phase grows and advances through the capillary, a lattice of vortices is formed behind the interface, reminiscent of vortex-lattices in a nongrowing confined active matter [52,64], which appear when the activity-induced vorticity length scale becomes comparable to the capillary width. Interestingly, however, in this growing active matter, the orientation of the vortex closest to the interface also determines the parity of the interface.…”