Turbulence of polymer solutions

Abstract

We investigate high-Reynolds number turbulence in dilute polymer solutions. We show the existence of a critical value of the Reynolds number which separates two different regimes. In the first regime, below the transition, the influence of the polymer molecules on the flow is negligible and they can be regarded as passively embedded in the flow. This case admits a detailed investigation of the statistics of the polymer elongations. The second state is realized when the Reynolds number is larger than the critical value. This regime is characterized by the strong back reaction of polymers on the flow. We establish some properties of the statistics of the stress and velocity in this regime and discuss its relation to the drag reduction phenomenon.PACS numbers 83.50. Ws, 61.25.Hq,

Polymer Transport in Random Flow

“…Asymptotic results for this model were already obtained in refs. [5,6,12,13]. The study of the δ-correlated flow allows a complete analytical treatment and the derivation of the exact pdf of polymer elongation.…”

“…This means that a stationary pdf does not exist: most of the molecules are highly stretched and the passive approach is no longer appropriate for the Hookean dumbbell model. Thus, q = 0 (Wi = 1) is the threshold for the coil-stretch transition [5][6][7].…”

“…[9]). The passive approach, however, is justified when the stress due to polymers is much smaller than the viscous stress, which can be estimated as ν v λ, ν v being the kinematic viscosity of the fluid [5,6].…”

Passive Fields and Particles in Chaotic Flows

“…If the gradients and thus the Lyapunov exponents were constant, the thermal fluctuations would give rise to a Gaussian distribution. However, in the presence of fluctuations in the Lyapunov exponent a power law distribution of the size of the polymers follows (Balkovsky et al, 2000;Balkovsky et al, 2001;Chertkov, 2000). A corresponding result in a more general context of multiplicative stochastic processes with a reflecting barrier is given in (Sornette and Cont, 1997).…”

“…The passive dynamics of polymers in a prescribed flow field then is a first step towards a description of the polymer dynamics in a turbulent flow. It is also a nice example of how the presence of both additive and multiplicative fluctuating forces can give rise to a power law probability distribution (Balkovsky et al, 2000;Balkovsky et al, 2001;Chertkov, 2000;Sornette and Cont, 1997).…”