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Relaxation dynamics of a flexible rod in a fluid

par Draux, Ayrton;Hua, Hoa Ai Béatrice ;Damman, Pascal;Brau, Fabian
Référence Physical Review Fluids, 6, 11, 114102
Publication Publié, 2021-11-22

Article révisé par les pairs

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Résumé :

The relaxation dynamics of a bent rod immersed in a fluid is studied experimentally for various rod materials and sizes and fluid viscosities. One extremity of the rod is clamped while its free end is displaced from its equilibrium position by a controlled distance. For large bending stiffness or low viscosity, the dynamics is underdamped and the rod oscillates around its equilibrium position with a well-defined frequency and a damped amplitude. In contrast, for low bending stiffness or large viscosity, the dynamics is overdamped and the rod relaxes to its equilibrium position without oscillating. We show the existence of two overdamped regimes where the relaxation dynamics is characterized by two different polynomial decays showing that the viscous force is not proportional to the rod velocity. The system is modeled using the dynamical beam equation supplemented by the viscous force experienced by a rigid cylinder moving at a constant speed in a fluid. In spite of this approximation, the model describes the dynamics in good approximation and provides a simple explanation for the existence of two overdamped regimes which originate from a change of the viscous force behavior as the Reynolds number varies. The model is then used to characterize the overdamped relaxation dynamics of the papillae of the bee tongues observed during nectar feeding.We show that the papillae relaxation is not complete when the sugar concentration exceeds 30% which impacts the amount of nectar collected per lap and yields an optimal concentration around 55% for the energy intake rate.