Abstract
Self-sustained turbulent structures have been observed in a wide range of living fluids, yet no quantitative theory exists to explain their properties. We report experiments on active turbulence in highly concentrated 3D suspensions of Bacillus subtilis and compare them with a minimal fourth-order vector-field theory for incompressible bacterial dynamics. Velocimetry of bacteria and surrounding fluid, determined by imaging cells and tracking colloidal tracers, yields consistent results for velocity statistics and correlations over 2 orders of magnitude in kinetic energy, revealing a decrease of fluid memory with increasing swimming activity and linear scaling between kinetic energy and enstrophy. The best-fit model allows for quantitative agreement with experimental data.
Highlights
Self-sustained turbulent structures have been observed in a wide range of living fluids, yet no quantitative theory exists to explain their properties
We report experiments on active turbulence in highly concentrated 3D suspensions of Bacillus subtilis and compare them with a minimal fourth-order vector-field theory for incompressible bacterial dynamics
Very different in size and composition, these systems are often jointly termed ‘‘active’’ fluids, for which there is a range of continuum theories [12,14,15,16,17,18,19,20,21,22,23,24]. From these have come important qualitative insights into instability mechanisms [13,14,15,16,21,25] driving dynamical pattern formation, but a quantitative picture remains inchoate; even for the simplest active suspensions uncertainty remains about which hydrodynamic equations and transport coefficients [26,27] provide an adequate minimal description, due in large part to the inability of existing data to constrain the manifold parameters in these models
Summary
One approach to remedy this problem is to characterize collective turbulent dynamics of bacteria [17,18] and other low Reynolds number swimmers, just as in high Reynolds number fluid turbulence, in terms of kinetic energy, mean squared vorticity (enstrophy) and spatiotemporal correlation functions, and to compare with an appropriate longwavelength theory (i.e., Navier-Stokes-type equations) We present such an analysis here, measuring collective behavior in dense suspensions of the bacterium Bacillus subtilis in comparison to predictions of a (fourth-order) continuum model for bacterial flow [7,28]. The inlet and outlet of the device were sealed with vacuum grease, and images were acquired in the (xy) midplane of the chambers, % 40 m above the bottom, using a
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