We study properties of dilute polymer solutions. The probability density function (PDF) of polymer end-to-end extensions R in turbulent flows is examined. We show that if the value of the Lyapunov exponent λ is smaller than the inverse molecular relaxation time 1/τ then the PDF has a strong peak at the equilibrium size R0 and a power tail at R>>R0. This confirms and extends the results of J. L. Lumley [Symp. Math. 9, 315 (1972)]. There is no essential influence of polymers on the flow in this regime. At λτ>1 the majority of molecules is stretched to the linear size Rop>>R0, which can be much smaller than the maximal length of the molecules due to their back reaction.
Physical Review Letters
- Pub Date:
- May 2000
- Nonlinear Sciences - Chaotic Dynamics;
- Condensed Matter;
- Physics - Fluid Dynamics
- 4 pages, revtex. Submitted to Phys. Rev. Lett. Revised after referee reports