Searcharxiv⌕ Search

arXiv subjects

Eric Lauga

Publications and source records attributed to Eric Lauga.

At least 145 records · Page 8Linked to original sources
arXiv2014

Stochastic dynamics of active swimmers in linear flows

Most classical work on the hydrodynamics of low-Reynolds-number swimming addresses deterministic locomotion in quiescent environments. Thermal fluctuations in fluids are known to lead to a Brownian loss of the swimming direction. As most cells or synthetic swimmers are immersed in external flows, we consider theoretically in this paper the stochastic dynamics of a model active particle (a self-propelled sphere) in a steady general linear flow. The stochasticity arises both from translational diffusion in physical space, and from a combination of rotary diffusion and run-and-tumble dynamics in orientation space. We begin by deriving a general formulation for all components of the long-time mean square displacement tensor for a swimmer with a time-dependent swimming velocity and whose orientation decorrelates due to rotary diffusion alone. This general framework is applied to obtain the convectively enhanced mean-squared displacements of a steadily-swimming particle in three canonical linear flows (extension, simple shear, and solid-body rotation). We then show how to extend our results to the case where the swimmer orientation also decorrelates on account of run-and-tumble dynamics. Self-propulsion in general leads to the same long-time temporal scalings as for passive particles in linear flows but with increased coefficients. In the particular case of solid-body rotation, the effective long-time diffusion is the same as that in a quiescent fluid, and we clarify the lack of flow-dependence by briefly examining the dynamics in elliptic linear flows. By comparing the new active terms with those obtained for passive particles we see that swimming can lead to an enhancement of the mean-square displacements by orders of magnitude, and could be relevant for biological organisms or synthetic swimming devices in fluctuating environmental or biological flows.

physics.flu-dyn↗
arXiv2014

Optimal propulsive flapping in Stokes flows

Swimming fish and flying insects use the flapping of fins and wings to generate thrust. In contrast, microscopic organisms typically deform their appendages in a wavelike fashion. Since a flapping motion with two degrees of freedom is able, in theory, to produce net forces from a time-periodic actuation at all Reynolds number, we compute in this paper the optimal flapping kinematics of a rigid spheroid in a Stokes flow. The hydrodynamics for the force generation and energetics of the flapping motion is solved exactly. We then compute analytically the gradient of a flapping efficiency in the space of all flapping gaits and employ it to derive numerically the optimal flapping kinematics as a function of the shape of the flapper and the amplitude of the motion. The kinematics of optimal flapping are observed to depend weakly on the flapper shape and are very similar to the figure-eight motion observed in the motion of insect wings. Our results suggest that flapping could be a exploited experimentally as a propulsion mechanism valid across the whole range of Reynolds numbers.

physics.flu-dyn↗
arXiv2014

Mixing by microorganisms in stratified fluids

We examine the vertical mixing induced by the swimming of microorganisms at low Reynolds and Péclet numbers in a stably stratified ocean, and show that the global contribution of oceanic microswimmers to vertical mixing is negligible. We propose two approaches to estimating the mixing efficiency, $η$, or the ratio of the rate of potential energy creation to the total rate-of-working on the ocean by microswimmers. The first is based on scaling arguments and estimates $η$ in terms of the ratio between the typical organism size, $a$, and an intrinsic length scale for the stratified flow, $\ell = \left ( νκ/ N^2 \right )^{1/4}$, where $ν$ is the kinematic viscosity, $κ$ the diffusivity, and $N$ the buoyancy frequency. In particular, for small organisms in the relevant oceanic limit, $a / \ell \ll 1$, we predict the scaling $η\sim (a / \ell)^3$. The second estimate of $η$ is formed by solving the full coupled flow-stratification problem by modeling the swimmer as a regularized force dipole, and computing the efficiency numerically. Our computational results, which are examined for all ratios $a/\ell$, validate the scaling arguments in the limit $a / \ell \ll 1$ and further predict $η\approx 1.2 \left ( a / \ell \right )^3$ for vertical swimming and $η\approx 0.15 \left ( a / \ell \right )^3$ for horizontal swimming. These results, relevant for any stratified fluid rich in biological activity, imply that the mixing efficiency of swimming microorganisms in the ocean is at very most 8\% and is likely smaller by at least two orders of magnitude.

physics.flu-dyn↗
arXiv2014

The Optimal Swimming Sheet

Propulsion at microscopic scales is often achieved through propagating traveling waves along hair-like organelles called flagella. Taylor's two-dimensional swimming sheet model is frequently used to provide insight into problems of flagellar propulsion. We derive numerically the large-amplitude waveform of the two-dimensional swimming sheet that yields optimum hydrodynamic efficiency; the ratio of the squared swimming speed to the rate-of-working of the sheet against the fluid. Using the boundary element method, we show the optimal waveform is a front-back symmetric regularized cusp that is 25% more efficient than the optimal sine-wave. This optimal two-dimensional shape is smooth, qualitatively different from the kinked form of Lighthill's optimal three-dimensional flagellum, not predicted by small-amplitude theory, and different from the smooth circular-arc-like shape of active elastic filaments.

physics.flu-dyn↗
arXiv2014

Viscous pumping inspired by flexible propulsion

Fluid-suspended microorganisms have evolved different swimming and feeding strategies in order to cope with an environment dominated by viscous effects. For instance ciliated organisms rely on the collective motion of flexible appendices to move and feed. By performing a non-reciprocal motion, flexible filaments can produce a net propulsive force, or pump fluid, in the absence of inertia. Inspired by such fundamental concept, we propose a strategy to produce macroscopic pumping and mixing in creeping flow. We measure experimentally the net motion of a Newtonian viscous fluid induced by the reciprocal motion of a flapper. When the flapper is rigid no net motion is induced. In contrast, when the flapper is made of a flexible material, a net fluid pumping is measured. We quantify the effectiveness of this pumping strategy and show that optimal pumping is achieved when the length of the flapper is on the same order as the elasto-hydrodynamic penetration length. We finally discuss the possible applications of flexible impellers in mixing operations at low Reynolds numbers.

physics.flu-dyn↗
arXiv2014

The geometry and wetting of capillary folding

Capillary forces are involved in a variety of natural phenomena, ranging from droplet breakup to the physics of clouds. The forces from surface tension can also be exploited in industrial application provided the length scales involved are small enough. Recent experimental investigations showed how to take advantage of capillarity to fold planar structures into three-dimensional configurations by selectively melting polymeric hinges joining otherwise rigid shapes. In this paper we use theoretical calculations to quantify the role of geometry and fluid wetting on the final folded state. Considering folding in two and three dimensions, studying both hydrophilic and hydrophobic situations with possible contact angle hysteresis, and addressing the shapes to be folded to be successively infinite, finite, curved, kinked, elastic, we are able to derive an overview of the geometrical parameter space available for capillary folding.

physics.flu-dyn↗
arXiv2014

Waving transport and propulsion in a generalized Newtonian fluid

Cilia and flagella are hair-like appendages that protrude from the surface of a variety of eukaryotic cells and deform in a wavelike fashion to transport fluids and propel cells. Motivated by the ubiquity of non-Newtonian fluids in biology, we address mathematically the role of shear-dependent viscosities on both the waving flagellar locomotion and ciliary transport by metachronal waves. Using a two-dimensional waving sheet as model for the kinematics of a flagellum or an array of cilia, and allowing for both normal and tangential deformation of the sheet, we calculate the flow field induced by a small-amplitude deformation of the sheet in a generalized Newtonian Carreau fluid up to order four in the dimensionless waving amplitude. Shear-thinning and shear-thickening fluids are seen to always induce opposite effects. When the fluid is shear-thinning, the rate of working of the sheet against the fluid is always smaller than in the Newtonian fluid, and the largest gain is obtained for antiplectic metachronal waves. Considering a variety of deformation kinematics for the sheet, we further show that in all cases transport by the sheet is more efficiency in a shear-thinning fluid, and in most cases the transport speed in the fluid is also increased. Comparing the order of magnitude of the shear-thinning contributions with past work on elastic effects as well as the magnitude of the Newtonian contributions, our theoretical results suggest that the impact of shear-dependent viscosities on transport could play a major biological role.

physics.flu-dyn↗
arXiv2014

Phoretic self-propulsion at finite Péclet 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 Péclet 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 Péclet 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 (Damköhler number).

physics.flu-dyn↗
arXiv2014

The wobbling-to-swimming transition of rotated helices

A growing body of work aims at designing and testing micron-scale synthetic swimmers. One method, inspired by the locomotion of flagellated bacteria, consists of applying a rotating magnetic field to a rigid, helically-shaped, propeller attached to a magnetic head. When the resulting device, termed an artificial bacteria flagellum, is aligned perpendicularly to the applied field, the helix rotates and the swimmer moves forward. Experimental investigation of artificial bacteria flagella shows that at low frequency of the applied field, the axis of the helix does not align perpendicularly to the field but wobbles around the helix, with an angle increasing as the inverse of the field frequency. By numerical computations and asymptotic analysis, we provide a theoretical explanation for this wobbling behavior. We numerically demonstrate the wobbling-to-swimming transition as a function of the helix geometry and the dimensionless Mason number which quantifies the ratio of viscous to magnetic torques. We then employ an asymptotic expansion for near-straight helices to derive an analytical estimate for the wobbling angle allowing to rationalize our computations and past experimental results. These results can help guide future design of artificial helical swimmers.

physics.flu-dyn↗
arXiv2014

Generalized squirming motion of a sphere

A number of swimming microorganisms such as ciliates ($\textit{Opalina}$) and multicellular colonies of flagellates ($\textit{Volvox}$) are approximately spherical in shape and swim using beating arrays of cilia or short flagella covering their surfaces. Their physical actuation on the fluid may be mathematically modeled as the generation of surface velocities on a continuous spherical surface -- a model known in the literature as squirming, which has been used to address various aspects of the biological physics of locomotion. Previous analyses of squirming assumed axisymmetric fluid motion and hence restricted all swimming kinematics to take place along a line. In this paper we generalize squirming to three spatial dimensions. We derive analytically the flow field surrounding a spherical squirmer with arbitrary surface motion, and use it to derive its three-dimensional translational and rotational swimming kinematics. We then use our results to physically interpret the flow field induced by the swimmer in terms of fundamental flow singularities up to terms decaying spatially as $\sim 1/r^3$. Our results will enable to develop new models in biological physics, in particular in the area of hydrodynamic interactions and collective locomotion.

physics.flu-dyn↗
arXiv2013

Spontaneous autophoretic motion of isotropic particles

Suspended colloidal particles interacting chemically with a solute are able to self-propel by autophoretic motion when they are asymmetrically patterned (Janus colloids). Here we demonstrate that the chemical anisotropy is not a necessary condition to achieve locomotion. The non linear interplay between surface osmotic flows and solute advection can produce spontaneous, and self-sustained motion of isotropic particles. We solve, for a spherical particle, the classical nonlinear autophoretic theoretical framework at arbitrary Péclet number. For a given set of material parameters, there exists a critical particle size, or equivalently a critical Peclet number, above which spontaneous autophoretic motion occurs. The flow induced by the particle further displays a hierarchy of instabilities associated with quantized critical Peclet numbers. Using numerical solutions of the full (unsteady) diffusiophoretic problem we confirm our analytical predictions and show that, above the instability threshold, the isotropic particles reach a steady swimming state with broken front-back symmetry in the concentration field and the hydrodynamic signature of a "pusher" swimmer. This instability to propulsion could be relevant to the high-throughput production of self-propelled particles.

cond-mat.soft↗
arXiv2013

Shape of optimal active flagella

Many eukaryotic cells use the active waving motion of flexible flagella to self-propel in viscous fluids. However, the criteria governing the selection of particular flagellar waveforms among all possible shapes has proved elusive so far. To address this question, we derive computationally the optimal shape of an internally-forced periodic planar flagellum deforming as a travelling wave. The optimum is here defined as the shape leading to a given swimming speed with minimum energetic cost. To calculate the energetic cost though, we consider the irreversible internal power expanded by the molecular motors forcing the flagellum, only a portion of which ending up dissipated in the fluid. This optimisation approach allows us to derive a family of shapes depending on a single dimensionless number quantifying the relative importance of elastic to viscous effects: the Sperm number. The computed optimal shapes are found to agree with the waveforms observed on spermatozoon of marine organisms, thus suggesting that these eukaryotic flagella might have evolved to be mechanically optimal.

physics.bio-ph↗
arXiv2013

Low-Reynolds number swimming in a capillary tube

We use the boundary element method to study the low-Reynolds number locomotion of a spherical model microorganism in a circular tube. The swimmer propels itself by tangen- tial or normal surface motion in a tube whose radius is on the order of the swimmer size. Hydrodynamic interactions with the tube walls significantly affect the average swimming speed and power consumption of the model microorganism. In the case of swimming parallel to the tube axis, the locomotion speed is always reduced (resp. increased) for swimmers with tangential (resp. normal) deformation. In all cases, the rate of work nec- essary for swimming is increased by confinement. Swimmers with no force-dipoles in the far field generally follow helical trajectories, solely induced by hydrodynamic interactions with the tube walls, and in qualitative agreement with recent experimental observations for Paramecium. Swimmers of the puller type always display stable locomotion at a lo- cation which depends on the strength of their force dipoles: swimmers with weak dipoles (small α) swim in the centre of the tube while those with strong dipoles (large α) swim near the walls. In contrast, pusher swimmers and those employing normal deformation are unstable and end up crashing into the walls of the tube. Similar dynamics is observed for swimming into a curved tube. These results could be relevant for the future design of artificial microswimmers in confined geometries.

physics.flu-dyn↗
arXiv2013

Fluid elasticity increases the locomotion of flexible swimmers

We conduct experiments with flexible swimmers to address the impact of fluid viscoelasticity on their locomotion. The swimmers are composed of a magnetic head actuated in rotation by a frequency-controlled magnetic field and a flexible tail whose deformation leads to forward propulsion. We consider both viscous Newtonian and glucose-based Boger fluids with similar viscosities. We find that the elasticity of the fluid systematically enhances the locomotion speed of the swimmer, and that this enhancement increases with Deborah number. Using Particle Image Velocimetry to visualize the flow field, we find a significant difference in the amount of shear between the rear and leading parts of the swimmer head. We conjecture that viscoelastic normal stresses lead to a net elastic forces in the swimming direction and thus a faster swimming speed.

physics.flu-dyn↗
arXiv2013

Crawling scallop: Friction-based locomotion with one degree of freedom

Fluid-based locomotion at low Reynolds number is subject to the constraints of the scallop theorem, which dictate that body kinematics identical under a time-reversal symmetry (in particular, those with a single degree of freedom) cannot display locomotion on average. The implications of the theorem naturally compel one to ask whether similar symmetry constraints exist for locomotion in different environments. In this work we consider locomotion along a surface where forces are described by isotropic Coulomb friction. To address whether motions with a single degree of freedom can lead to transport, we analyze a model system consisting of two bodies whose separation distance undergoes periodic time variations. The behavior of the two-body system is entirely determined by the kinematic specification of their separation, the friction forces, and the mass of each body. We show that the constraints of the scallop theorem can be escaped in frictional media if two asymmetry conditions are met at the same time: the frictional forces of each body against the surface must be distinct and the time-variation of the body-body separation must vary asymmetrically in time (so quick-slow or slow-quick in the extension-contraction phases). Our results are demonstrated numerically and interpreted using asymptotic expansions.

physics.bio-ph↗
arXiv2013

Micropropulsion and microrheology in complex fluids via symmetry breaking

Many biological fluids have polymeric microstructures and display non-Newtonian rheology. We take advantage of such nonlinear fluid behavior and combine it with geometrical symmetry-breaking to design a novel small-scale propeller able to move only in complex fluids. Its propulsion characteristics are explored numerically in an Oldroyd-B fluid for finite Deborah numbers while the small Deborah number limit is investigated analytically using a second-order fluid model. We then derive expressions relating the propulsion speed to the rheological properties of the complex fluid, allowing thus to infer the normal stress coefficients in the fluid from the locomotion of the propeller. Our simple mechanism can therefore be used either as a non-Newtonian micro-propeller or as a micro-rheometer.

physics.flu-dyn↗
arXiv2013

Taylor's swimming sheet: Analysis and improvement of the perturbation series

In G.I. Taylor's historic paper on swimming microorganisms, a two dimensional sheet was proposed as a model for flagellated cells passing traveling waves as a means of locomotion. Using a perturbation series, Taylor computed swimming speeds up to fourth order in amplitude. Here we systematize that expansion so that it can be carried out formally to arbitrarily high order. The resultant series diverges for an order one value of the wave amplitude, but may be transformed into series with much improved convergence properties and which yield results comparing favorably to those obtained numerically via a boundary integral method for moderate and large values of the wave amplitudes.

physics.flu-dyn↗