Optimal feeding is optimal swimming for all P\'eclet numbers

Cells swimming in viscous fluids create flow fields which influence the transport of relevant nutrients, and therefore their feeding rate. We propose a modeling approach to the problem of optimal feeding at zero Reynolds number. We consider a simplified spherical swimmer deforming its shape tangentially in a steady fashion (so-called squirmer). Assuming that the nutrient is a passive scalar obeying an advection-diffusion equation, the optimal use of flow fields by the swimmer for feeding is determined by maximizing the diffusive flux at the organism surface for a fixed rate of energy dissipation in the fluid. The results are obtained through the use of an adjoint-based numerical optimization implemented by a Legendre polynomial spectral method. We show that, to within a negligible amount, the optimal feeding mechanism consists in putting all the energy expended by surface distortion into swimming - so-called treadmill motion - which is also the solution maximizing the swimming efficiency. Surprisingly, although the rate of feeding depends strongly on the value of the P\'eclet number, the optimal feeding stroke is shown to be essentially independent of it, which is confirmed by asymptotic analysis. Within the context of steady actuation, optimal feeding is therefore found to be equivalent to optimal swimming for all P\'eclet numbers.Comment: 14 pages, 6 figures, to appear in Physics of Fluid

Phoretic self-propulsion at finite P\'eclet numbers

Phoretic self-propulsion is a unique example of force- and torque-free motion on small scales. The classical framework describing the flow field around a particle swimming by self-diffusiophoresis neglects the advection of the solute field by the flow and assumes that the chemical interaction layer is thin compared to the particle size. In this paper we quantify and characterize the effect of solute advection on the phoretic swimming of a sphere. We first rigorously derive the regime of validity of the thin-interaction layer assumption at finite values of the P\'eclet number (Pe). Within this assumption, we solve computationally the flow around Janus phoretic particles and examine the impact of solute advection on propulsion and the flow created by the particle. We demonstrate that although advection always leads to a decrease of the swimming speed and flow stresslet at high values of the P\'eclet number, an increase can be obtained at intermediate values of Pe. This possible enhancement of swimming depends critically on the nature of the chemical interactions between the solute and the surface. We then derive an asymptotic analysis of the problem at small Pe allowing to rationalize our computational results. Our computational and theoretical analysis is accompanied by a parallel study of the role of reactive effects at the surface of the particle on swimming (Damk\"ohler number).Comment: 27 pages, 15 figures, to appear in J. Fluid Mec

Influence and optimization of the electrodes position in a piezoelectric energy harvesting flag

Fluttering piezoelectric plates may harvest energy from a fluid flow by converting the plate's mechanical deformation into electric energy in an output circuit. This work focuses on the influence of the arrangement of the piezoelectric electrodes along the plate's surface on the energy harvesting efficiency of the system, using a combination of experiments and numerical simulations. A weakly non-linear model of a plate in axial flow, equipped with a discrete number of piezoelectric patches is derived and confronted to experimental results. Numerical simulations are then used to optimize the position and dimensions of the piezoelectric electrodes. These optimal configurations can be understood physically in the limit of small and large electromechanical coupling.Comment: To appear in Journal of Sound and Vibratio

A space-averaged model of branched structures

Many biological systems and artificial structures are ramified, and present a high geometric complexity. In this work, we propose a space-averaged model of branched systems for conservation laws. From a one-dimensional description of the system, we show that the space-averaged problem is also one-dimensional, represented by characteristic curves, defined as streamlines of the space-averaged branch directions. The geometric complexity is then captured firstly by the characteristic curves, and secondly by an additional forcing term in the equations. This model is then applied to mass balance in a pipe network and momentum balance in a tree under wind loading.Comment: 10 pages, 11 figure

Stresslets Induced by Active Swimmers.

Active particles disturb the fluid around them as force dipoles, or stresslets, which govern their collective dynamics. Unlike swimming speeds, the stresslets of active particles are rarely determined due to the lack of a suitable theoretical framework for arbitrary geometry. We propose a general method, based on the reciprocal theorem of Stokes flows, to compute stresslets as integrals of the velocities on the particle's surface, which we illustrate for spheroidal chemically active particles. Our method will allow tuning the stresslet of artificial swimmers and tailoring their collective motion in complex environments.Funding from the EU (CIG to E. L.) and by the French Ministry of Defense (DGA to S. M.) is gratefully acknowledged.This is the author accepted manuscript. The final version is available from the American Physical Society via https://doi.org/10.1103/PhysRevLett.117.14800

Self-propulsion near the onset of Marangoni instability of deformable active droplets

International audienceExperimental observations indicate that chemically active droplets suspended in a surfactant-laden fluid can self-propel spontaneously. The onset of this motion is attributed to a symmetry-breaking Marangoni instability resulting from the nonlinear advective coupling of the distribution of surfactant to the hydrodynamic flow generated by Marangoni stresses at the droplet's surface. Here, we use weakly nonlinear analysis to characterize the self-propulsion near the instability threshold and the influence of the droplet's deformability. We report that in vicinity of the threshold, deformability enhances self-propulsion of viscous droplets, but hinders propulsion of drops that are roughly less viscous than the surrounding fluid. Our asymptotics further reveals that droplet deformability may alter the type of bifurcation leading to symmetry breaking: for moderately deformable droplets the onset of self-propulsion is transcritical and a regime of steady self-propulsion is stable; while in the case of highly deformable drops, no steady flows can be found within the asymptotic limit considered in this paper suggesting that the bifurcation is subcritical

Universal optimal geometry of minimal phoretic pumps

Abstract: Unlike pressure-driven flows, surface-mediated phoretic flows provide efficient means to drive fluid motion on very small scales. Colloidal particles covered with chemically-active patches with nonzero phoretic mobility (e.g. Janus particles) swim using self-generated gradients, and similar physics can be exploited to create phoretic pumps. Here we analyse in detail the design principles of phoretic pumps and show that for a minimal phoretic pump, consisting of 3 distinct chemical patches, the optimal arrangement of the patches maximizing the flow rate is universal and independent of chemistry

Drag Reduction, from Bending to Pruning

Most plants and benthic organisms have evolved efficient reconfiguration mechanisms to resist flow-induced loads. These mechanisms can be divided into bending, in which plants reduce their sail area through elastic deformation, and pruning, in which the loads are decreased through partial breakage of the structure. In this work, we show by using idealized models that these two mechanisms or, in fact, any combination of the two, are equally efficient to reduce the drag experienced by terrestrial and aquatic vegetation.Comment: 5 pages, 5 figure

Self-propulsion of pure water droplets by spontaneous Marangoni stress driven motion

We report spontaneous motion in a fully bio-compatible system consisting of pure water droplets in an oil-surfactant medium of squalane and monoolein. Water from the droplet is solubilized by the reverse micellar solution, creating a concentration gradient of swollen reverse micelles around each droplet. The strong advection and weak diffusion conditions allow for the first experimental realization of spontaneous motion in a system of isotropic particles at sufficiently large P\'eclet number according to a straightforward generalization of a recently proposed mechanism. Experiments with a highly concentrated solution of salt instead of water, and tetradecane instead of squalane, confirm the above mechanism. The present swimming droplets are able to carry external bodies such as large colloids, salt crystals, and even cells.Comment: 5 pages, 5 figure

Inductive effects on energy harvesting piezoelectric flag

National audienceInteraction between a flexible flag and a flow leads to a canonical fluid–structure instability whichproduces self-sustained vibrations, from which mechanical energy could be converted to electrical energythrough piezoelectric materials covering the flag and thus being deformed by its motion. We study thepossibility of harvesting this energy, especially the effect of an inductive circuit on the energy harvestingprocess. A destabilization of the coupled system is observed after adding an inductance. In the nonlinearcase, the harvesting efficiency increases significantly at lock–in between the frequencies of the flutteringflag and the electrical circuit.L'interaction d'un drapeau flexible avec un écoulement est connue pour donner lieu à une vibration auto-entretenue, dont l’énergie mécanique peut être convertie en énergie électrique par le biais des matériaux piézoélectriques qui couvrent le drapeau et ainsi se déforment avec celui-ci. On étudie la possibilité de récupérer cette énergie, et en particulier l'effet d'un circuit inductif sur le processus de récupération. Dans l’étude linéaire, une déstabilisation du système est observée par l'ajout d'une inductance. Une méthode numérique, basée sur une description explicite entre le couplage fluide–solide–électrique, est utilisée pour la simulation non-linéaire du système. En régime non-linéaire, l'efficacité de récupération augmente significativement lors de l'accrochage entre les fréquences de battement du drapeau et du circuit électrique