The properties of elastic turbulence in semi-dilute polymer solutions (original) (raw)

Turbulence of polymer solutions

Physical review. E, Statistical, nonlinear, and soft matter physics, 2001

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, so 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.

Turbulence in dilute polymer solutions

Physics of Fluids, 2005

We investigate turbulence in dilute polymer solutions when polymers are strongly stretched by the flow. We establish power-law spectrum of velocity, which is not associated with a flux of a conserved quantity, in two cases. The first case is the elastic waves range of high Reynolds number turbulence of polymer solutions above the coil-stretch transition. The second case is the elastic turbulence, where chaotic flow is excited due to elastic instabilities at small Reynolds numbers.

Elastic turbulence in a polymer solution flow

Arxiv preprint nlin/0104052, 2001

Turbulence is one of the most fascinating phenomena in nature and one of the biggest challenges for modern physics. It is common knowledge that a flow of a simple, Newtonian fluid is likely to be turbulent, when velocity is high, viscosity is low and size of the tank is large [1,2]. Solutions of flexible longchain polymers are known as visco-elastic fluids [3]. In our experiments we show, that flow of a polymer solution with large enough elasticity can become quite irregular even at low velocity, high viscosity and in a small tank. The fluid motion is excited in a broad range of spatial and temporal scales. The flow resistance increases by a factor of about twenty. So, while the Reynolds number, Re, may be arbitrary low, the observed flow has all main features of developed turbulence, and can be compared to turbulent flow in a pipe at Re ≃ 10 5 [1,2]. 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. Motion of simple, low molecular, Newtonian fluids is governed by the Navier-Stokes equation [1,2]. This equation has a non-linear term, which is inertial in its nature. The ratio between the non-linearity and viscous dissipation is given by the Reynolds number, Re = V L/ν,where V is velocity, L is characteristic size and ν is kinematic viscosity of the fluid. When Re is high, non-linear effects are strong and the flow is likely to be turbulent. So, turbulence is a paradigm for a strongly non-linear phenomenon [1,2].

Turbulent mixing in dilute polymer solutions

Chemical Engineering Science, 1993

Addition of polymer molecules to solvents influences the turbulence characteristics and in turn it influences the macromixing and micromixing behaviour in such flows in a profound way. The mixing lengths in pipe flows of dilute polymer solutions are known to be several times larger than those for Newtonian flows. A simple phenomenological model of polymer-turbulence interaction is developed to evaluate the reduction in friction factor and it is then used for analysing mixing in one-dimensional turbulent flows. The extent of mixing in dilute polymer solutions is then predicted quantitatively. The limited experimental data available show that the model simulates mixing in flows of Newtonian fluids as well as in mildly viscoelastic drag-reducing fluids very well.