Friction Scaling Laws for Transport in Bacterial Turbulence

Abstract

Understanding the role of frictional drag in diffusive transport is an important problem in the field of active turbulence. Using a continuum model that applies well to bacterial suspensions, we investigate the role of Ekmann friction on the transport of passive (Lagrangian) tracers that go with the local flow. We find that the crossover from ballistic to diffusive regime happens at a time scale ${\tau }_c$ that attains a minimum at zero friction, meaning that both injection and dissipation of energy delay the relaxation of tracers. We explain this by proposing that ${\tau }_c\sim 2{\ell }^{\ast }/u_{\text{rms}}$, where ${\ell }^{\ast }$ is a dominant length scale extracted from energy spectrum peak, and $u_{\text{rms}}$ is a velocity scale that sets the kinetic energy at steady state, both scales monotonically decrease with friction. Finally, we predict robust scaling laws for ${\ell }^{\ast }$, $u_{\text{rms}}$ and the diffusion coefficient $\mathcal{D}\sim {\ell }^{\ast }{u}_{\text{rms}}/2$, that are valid over a wide range of fluid friction. Our findings might be relevant to transport phenomena in a generic active fluid.

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Cited by in corpus (11)

• Active Turbulence
• Anomalous diffusion and Lévy walks distinguish active from inertial turbulence
• Intermittency, fluctuations and maximal chaos in an emergent universal state of active turbulence
• Scaling regimes of active turbulence with external dissipation
• Lagrangian Manifestation of Anomalies in Active Turbulence
• Dynamics of a Passive Droplet in Active Turbulence
• Onset of Intermittency and Multiscaling in Active Turbulence
• Flocking turbulence of microswimmers in confined domains
• Self-sustained patchy turbulence in shear-thinning active fluids
• Emergence of Local Ordering and Mesoscale Giant Number Fluctuations in Active Turbulence
• Optimal Turbulent Transport in Microswimmer Suspensions