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Polymers can exhibit a complex behaviour even in simple laminar velocity fields.
In particular, the dynamics of a polymer in a shear flow is dominated by an aperiodic end-over-end tumbling motion.
The phenomenon of tumbling is thus commonly associated with shear flows.
We address the question of whether tumbling can also exist in stretching-dominated velocity fields.
While the temporal dynamics of a system as elementary as a flexible dumbbell is trivial in an extensional flow,
we show that a rich dynamics is obtained by considering the simplest model of semi-flexible polymer,
namely the trumbbell model. This model consists of three beads joined by two rods and of an elastic hinge at the central bead.
The mere inclusion of one bending mode in the polymer model yields a random tumbling-through-folding
motion even in an extensional flow. The statistics of the tumbling times, however, has very different properties compared
to the shear-flow case; the typical tumbling time indeed grows exponentially as a function of the Weissenberg number.
We also study the statistics of the internal bending angle. In an extensional flow, this has similar
properties in two and in three dimensions. In contrast, in a turbulent flow the distribution of the bending angle shows a
strong dependence on the dimension of the flow. In two-dimensional isotropic turbulence, it is bimodal, i.e. polymers are
either found in a fully extended or in a fully folded configuration, and the latter configuration dominates for very strong turbulence.
In three-dimensional turbulence, the predominant configuration is the fully extended one.
These results are obtained by means of analytically solvable models and Lagrangian direct numerical simulations.
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