Elastic turbulence: random flow of visco-elastic fluid without

Elastic turbulence: random flow of visco-elastic fluid without inertia.

Victor Steinberg

Department of Physics of Complex Systems,

Weizmann Institute of Science, Rehovot, 76100 Israel

As we showed recently a flow of a visco-elastic polymer solution can become quite irregular even at low velocity, high viscosity, and in a small vessel. The fluid motion is excited in a broad range of spatial and temporal scales. The flow resistance increases by a factor of about twenty, and can be compared to turbulent flow in a pipe at Re=105. While the Reynolds number may be arbitrary low, the observed flow shows main features of developed turbulence. This elastic turbulence is accompanied by significant stretching of the polymer molecules, and the resulting increase of the elastic stresses can reach two orders of magnitude. We also show that very viscous liquids can be mixed rather efficiently at very low Re in a curved channel at polymer concentration as low as 0.001%.

We further investigate this phenomenon in von Karman swirling flow between two disks. Role of elastic stress in statistical and scaling properties of elastic turbulence in a flow of a polymer solution between two disks is discussed. Analogy with a small scale fast dynamo in magneto-hydrodynamics and with a passive scalar turbulent advection in the Batchelor regime is used to explain the experimentally observed statistical properties, flow structure, and scaling of elastic turbulence. Stretching of a polymer and coil-stretch transition in a random flow as a source of the elastic stress is also studied in detail.