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Modelling active fluids

Especially interesting for
  • fundamental research
  • materials sciences

An active fluid consists of a large quantity of microswimmers (e.g. bacteria) which move in the water. Such a fluid exhibits a very specific flow behaviour. PTB, together with Cambridge University, UK, has developed a theoretical model which can calculate such movements.

Velocity field of the active fluid represented as a two-dimensional view of a three-dimensional volume. T he colour coding shows the strength and direction of the eddies.

An active fluid behaves surprisingly differently from a usual liquid: where the latter exhibits a laminar flow (i.e. flows without any disturbance), chaotic currents and eddies appear in the bacterial suspension, i.e. the flow dynamics is totally different. Whereas a conventional fluid is moved by external influences, in the case of a bacterial fluid, the propulsion comes from deep within the bacterial fluid itself, namely from the bacteria's flagella.

To model such a fluid, the Navier-Stokes equation was extended by an instability which is known from the pattern formation. The equation then describes flow patterns where there is no external propulsion. In a detailed turbulence analysis, direct numerical simulations were compared with flow structures from the experiments performed in Cambridge with bacillus subtilis bacteria. Although the suggested equation has a relatively simple structure, the results are in very good quantitative agreement. The chaotic structures encountered, however, differ qualitatively from those found in usual turbulence due to the fact that eddies occur with a characteristic size. For the simulations, a pseudospectral algorithm with anti-aliasing was developed at PTB which converts the partial differential equations into a system of conventional, non-linear differential equations. This was solved by means of an operatorsplitting method which treats the linear part exactly. The flow field of the bacteria was recorded for 1 min for each measurement, whereas the corresponding simulation on PTB's computer cluster took several days.

In this way, it was possible for the first time to compare a model of the turbulence in a bacterial suspension directly with experimental data and model parameters. With the aid of the new model, also physical quantities which are difficult to measure – such as, e.g., elasticity or anisotropic viscosity of the active fluid – can be determined.

Scientific publication

J. Dunkel, S. Heidenreich, K. Drescher, H. H. Wensink, M. Bär, R. E. Goldstein: Fluid dynamics of bacterial turbulence. Phys. Rev. Lett. 110, 228102 (2013)