  A polymer in a turbulent flow undergoes the coil-stretch transition when the
Weissenberg number, i.e. the product of the Lyapunov exponent of the flow and
the relaxation time of the polymer, surpasses a critical value. The effect of
internal friction on the transition is studied by means of Brownian dynamics
simulations of the elastic dumbbell model in a homogeneous and isotropic,
incompressible, turbulent flow and analytical calculations for a stochastic
velocity gradient. The results are explained by adapting the large deviations
theory of Balkovsky et al. [Phys. Rev. Lett., 2000, 84, 4765] to an elastic
dumbbell with internal viscosity. In turbulent flows, a distinctive feature of
the probability distribution of polymer extensions is its power-law behaviour
for extensions greater than the equilibrium length and smaller than the contour
length. It is shown that although internal friction does not modify the
critical Weissenberg number for the coil-stretch transition, it makes the slope
of the probability distribution steeper, thus rendering the transition sharper.
Internal friction therefore provides a possible explanation for the steepness
of the distribution of polymer extensions observed in experiments at large
Weissenberg numbers.
