Abstract
The constitutive (rheological) equation of state, relating local stress to the rate-of-strain tensor, is derived consistently within the kinetic theory approximation for a dilute solution of elastic polymers in a strong flow. Microscopic polymer parameters (i.e. nonlinear elastic potential and the equilibrium polymer length) enter explicitly this coarse-grained description. This theory describes recent experiments by Groisman and Steinberg [1] on pure elastic turbulence (i.e. a steady state, realized at very low Re number, which is characterized by a non-smooth small-scale velocity distribution). The measured temporal spectra of velocity fluctuations are theoretically explained. A coarse-grained hydrodynamic description of pure elastic turbulence is given by a nonlinear diffusion equation for the velocity gradient tensor. Nonlinear elastic dissipation (originating from the anharmonic polymer elasticity) plays a key role in the emergence of the small scale turbulence.
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Chertkov, M. (2001). Turbulence in Polymer Solutions. In: Kambe, T., Nakano, T., Miyauchi, T. (eds) IUTAM Symposium on Geometry and Statistics of Turbulence. Fluid Mechanics and Its Applications, vol 59. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9638-1_40
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DOI: https://doi.org/10.1007/978-94-015-9638-1_40
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