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Fluid-structure interaction problems inspired by the nectar capture in bees

par Hua, Hoa Ai Béatrice
Président du jury Kozyreff, Gregory
Promoteur Brau, Fabian
Publication Non publié, 2023-07-04

Thèse de doctorat

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Résumé :

Capturing viscous fluid efficiently is a challenge that nectarivores overcame through thecourse of evolution to collect this primary source of energy. The understanding of theirdrinking mechanisms are sources of inspiration for biomimetic applications such ascontrolled fluid capture devices. The physical ingredients intervening in those processes areviscosity, capillarity, and elasticity. Viscosity has two antagonistic roles, it can hinder thefluid capture, during suction for example, whereas it can help increase the volume of fluidcaptured in a dipping process through a Landau-Levich-Derjaguin (LLD) mechanism. Formost nectarivores, capillarity dominates over gravity given their typical size. The surfacetension can induce a spontaneous rise of liquids and deformations when a soft solid is at anair-liquid interface. The elasticity of the tongues and of the various elements composing itcan thus also play a role in fluid capture. In this thesis, we aim to study bioinspired fluidcapture through elastocapillary and viscous effects.The various problems studied here are inspired by the nectar capture in bees and similarpollinators. Bees feed by dipping periodically their tongue in nectar at a constant frequency.The amount of fluid collected per unit time (ingestion rate) should thus increase with thenectar viscosity according to the LLD theory. However, a drop of the ingestion rate isobserved experimentally when the nectar viscosity exceed some threshold. This observationleads us to consider the fine structure of the tongue composed of a glossa decorated byslender papillae which open, as the hair of a paintbrush, when immersed in a liquid. Wethus propose to consider the relaxation dynamic of the papillae when they are immersed inthe nectar. To do so, we study the relaxation movement of a bent rod immersed in a viscousfluid. We use the linear beam equation supplemented by a viscous drag term varyingnonlinearly with the rod velocity. Different relaxation dynamics are identified according tothe magnitude of the viscosity (for a given bending stiffness of the rod). At high viscosity,the dynamics is overdamped and the rod relaxes to its straight equilibrium state withoutoscillation. In contrast, at low viscosity, the dynamics is underdamped and the rod oscillatesseveral times around its equilibrium position with a damped amplitude before reachingequilibrium. This viscoelastic theory describes satisfactorily the relaxation dynamicobserved experimentally with model systems and yields the characteristic relaxation timesas a function of the control parameters and in particular the fluid viscosity.Implementing the relaxation dynamic of the papillae in a simple capture model allowsto explain the drop in ingestion rate and to highlight the crucial role of the papillaeflexibility during the dipping process. At low viscosity, the papillae, which initially lie onthe glossa, have enough time to fully relax to their open position before the tongue retractsout of the liquid whereas, at high viscosity, they stay close to the glossa because theirrelaxation time is too large compared to the constant lapping time and the trapped volume isthus limited. Considering this physiological constraint and the fact that the sweetest nectarprovides the greatest energetic reward while being more viscous, we can predict an optimalsugar concentration. There is a good agreement between this optimal sugar concentrationfor most of the analyzed bee species and the natural sweetness of flower nectar.Another problem that is tackled in this thesis is the switching between two differentcapture mechanisms observed so far only for honeybees. Indeed, this species can switchbetween sucking and dipping to collect nectar whereas most animals stick to one drinking method. By developing physical models for both suction and dipping/lapping mechanisms,the transition between the two methods can be rationalized. A critical viscosity is derivedbelow which suction is energetically more efficient. Above it, lapping is a better strategy toingest more energy per unit of time. The predicted transition agrees with in vivo observations.The last work presented in this thesis addresses the problem of elastocapillarycoalescence in brushes which could occur when a bee’s tongue is removed from nectar. Todo so, we have considered a minimalist brush composed of two slender structuresquasi-statically withdrawn from a liquid bath. At the air-liquid interface, the menisci aroundthe structures interact and induce an attractive capillary force deflecting the flexiblestructures. As they are removed from the bath, their dry length increases and they becomeeasier to bend until the capillary force is strong enough to trigger contact. The transition tocoalescence is discontinuous (i.e. snapping) and occurs at a critical dry length. We observea subcritical bifurcation and the transition exhibits a large hysteresis loop between twostable states. Using the linear beam theory and the capillary force between two vertical rigidrods/lamellae, the bifurcation is characterized and an analytical coalescence criterion isderived agreeing with the experimental data. This is a first step for upcoming research onfluid capture by brushes through elastocapillary effects.