arXiv subjects

Eric Lauga

Publications and source records attributed to Eric Lauga.

At least 181 records · Page 10Linked to original sources

arXiv2011

Enhanced diffusion by reciprocal swimming

Purcell's scallop theorem states that swimmers deforming their shapes in a time-reversible manner ("reciprocal" motion) cannot swim. Using numerical simulations and theoretical calculations we show here that in a fluctuating environment, reciprocal swimmers undergo, on time scales larger than that of their rotational diffusion, diffusive dynamics with enhanced diffusivities, possibly by orders of magnitude, above normal translational diffusion. Reciprocal actuation does therefore lead to a significant advantage over non-motile behavior for small organisms such as marine bacteria.

cond-mat.soft↗

arXiv2011

Comparative hydrodynamics of bacterial polymorphism

Most bacteria swim through fluids by rotating helical flagella which can take one of twelve distinct polymorphic shapes. The most common helical waveform is the "normal" form, used during forward swimming runs. To shed light on the prevalence of the normal form in locomotion, we gather all available experimental measurements of the various polymorphic forms and compute their intrinsic hydrodynamic efficiencies. The normal helical form is found to be the most hydrodynamically efficient of the twelve polymorphic forms by a significant margin - a conclusion valid for both the peritrichous and polar flagellar families, and robust to a change in the effective flagellum diameter or length. The hydrodynamic optimality of the normal polymorph suggests that, although energetic costs of locomotion are small for bacteria, fluid mechanical forces may have played a significant role in the evolution of the flagellum.

physics.bio-ph↗

arXiv2010

Life around the scallop theorem

Locomotion on small scales is dominated by the effects of viscous forces and, as a result, is subject to strong physical and mathematical constraints. Following Purcell's statement of the scallop theorem which delimitates the types of swimmer designs which are not effective on small scales, we review the different ways the constraints of the theorem can be escaped for locomotion purposes.

physics.bio-ph↗

arXiv2010

Propulsion by passive filaments and active flagella near boundaries

Confinement and wall effects are known to affect the kinematics and propulsive characteristics of swimming microorganisms. When a solid body is dragged through a viscous fluid at constant velocity, the presence of a wall increases fluid drag, and thus the net force required to maintain speed has to increase. In contrast, recent optical trapping experiments have revealed that the propulsive force generated by human spermatozoa is decreased by the presence of boundaries. Here, we use a series of simple models to analytically elucidate the propulsive effects of a solid boundary on passively actuated filaments and model flagella. For passive flexible filaments actuated periodically at one end, the presence of the wall is shown to increase the propulsive forces generated by the filaments in the case of displacement-driven actuation, while it decreases the force in the case of force-driven actuation. In the case of active filaments as models for eukaryotic flagella, we demonstrate that the manner in which a solid wall affects propulsion cannot be known a priori, but is instead a nontrivial function of the flagellum frequency, wavelength, its material characteristics, the manner in which the molecular motors self-organize to produce oscillations (prescribed activity model or self-organized axonemal beating model), and the boundary conditions applied experimentally to the tethered flagellum. In particular, we show that in some cases, the increase in fluid friction induced by the wall can lead to a change in the waveform expressed by the flagella which results in a decrease in their propulsive force.

physics.bio-ph↗

arXiv2010

Passive hydrodynamic synchronization of two-dimensional swimming cells

Spermatozoa flagella are known to synchronize when swimming in close proximity. We use a model consisting of two-dimensional sheets propagating transverse waves of displacement to demonstrate that fluid forces lead to such synchronization passively. Using two distinct asymptotic descriptions (small amplitude and long wavelength), we derive the synchronizing dynamics analytically for ar- bitrarily shaped waveforms in Newtonian fluids, and show that phase locking will always occur for sufficiently asymmetric shapes. We characterize the effect of the geometry of the waveforms and the separation between the swimmers on the synchronizing dynamics, the final stable conformations, and the energy dissipated by the cells. For two closely-swimming cells, synchronization always oc- curs at the in-phase or opposite-phase conformation, depending solely on the geometry of the cells. In contrast, the work done by the swimmers is always minimized at the in-phase conformation. As the swimmers get further apart, additional fixed points arise at intermediate values of the relative phase. In addition, computations for large-amplitude waves using the boundary integral method reveal that the two asymptotic limits capture all the relevant physics of the problem. Our results provide a theoretical framework to address other hydrodynamic interactions phenomena relevant to populations of self-propelled organisms.

physics.flu-dyn↗

arXiv2010

Efficiency optimization and symmetry-breaking in a model of ciliary locomotion

A variety of swimming microorganisms, called ciliates, exploit the bending of a large number of small and densely-packed organelles, termed cilia, in order to propel themselves in a viscous fluid. We consider a spherical envelope model for such ciliary locomotion where the dynamics of the individual cilia are replaced by that of a continuous overlaying surface allowed to deform tangentially to itself. Employing a variational approach, we determine numerically the time-periodic deformation of such surface which leads to low-Reynolds locomotion with minimum rate of energy dissipation (maximum efficiency). Employing both Lagrangian and Eulerian points of views, we show that in the optimal swimming stroke, individual cilia display weak asymmetric beating, but that a significant symmetry-breaking occurs at the organism level, with the whole surface deforming in a wave-like fashion reminiscent of metachronal waves of biological cilia. This wave motion is analyzed using a formal modal decomposition, is found to occur in the same direction as the swimming direction, and is interpreted as due to a spatial distribution of phase-differences in the kinematics of individual cilia. Using additional constrained optimizations, as well as a constructed analytical ansatz, we derive a complete optimization diagram where all swimming efficiencies, swimming speeds, and amplitude of surface deformation can be reached, with the mathematically optimal swimmer, of efficiency one half, being a singular limit. Biologically, our work suggests therefore that metachronal waves may allow cilia to propel cells forward while reducing the energy dissipated in the surrounding fluid.

physics.flu-dyn↗

arXiv2010

Hydrodynamic friction of fakir-like super-hydrophobic surfaces

A fluid droplet located on a super-hydrophobic surface makes contact with the surface only at small isolated regions, and is mostly in contact with the surrounding air. As a result, a fluid in motion near such a surface experiences very low friction, and super-hydrophobic surfaces display strong drag-reduction in the laminar regime. Here we consider theoretically a super-hydrophobic surface composed of circular posts (so called fakir geometry) located on a planar rectangular lattice. Using a superposition of point forces with suitably spatially-dependent strength, we derive the effective surface slip length for a planar shear flow on such a fakir surface as the solution to an infinite series of linear equations. In the asymptotic limit of small surface coverage by the posts, the series can be interpreted as Riemann sums, and the slip length can be obtained analytically. For posts on a square lattice, our analytical results are in excellent quantitative agreement with previous numerical computations.

physics.flu-dyn↗

arXiv2010

Jet propulsion without inertia

A body immersed in a highly viscous fluid can locomote by drawing in and expelling fluid through pores at its surface. We consider this mechanism of jet propulsion without inertia in the case of spheroidal bodies, and derive both the swimming velocity and the hydrodynamic efficiency. Elementary examples are presented, and exact axisymmetric solutions for spherical, prolate spheroidal, and oblate spheroidal body shapes are provided. In each case, entirely and partially porous (i.e. jetting) surfaces are considered, and the optimal jetting flow profiles at the surface for maximizing the hydrodynamic efficiency are determined computationally. The maximal efficiency which may be achieved by a sphere using such jet propulsion is 12.5%, a significant improvement upon traditional flagella-based means of locomotion at zero Reynolds number. Unlike other swimming mechanisms which rely on the presentation of a small cross section in the direction of motion, the efficiency of a jetting body at low Reynolds number increases as the body becomes more oblate, and limits to approximately 162% in the case of a flat plate swimming along its axis of symmetry. Our results are discussed in the light of slime extrusion mechanisms occurring in many cyanobacteria.

physics.flu-dyn↗

arXiv2010

A two-dimensional model of low-Reynolds number swimming beneath a free surface

Biological organisms swimming at low Reynolds number are often influenced by the presence of rigid boundaries and soft interfaces. In this paper we present an analysis of locomotion near a free surface with surface tension. Using a simplified two-dimensional singularity model, and combining a complex variable approach with conformal mapping techniques, we demonstrate that the deformation of a free surface can be harnessed to produce steady locomotion parallel to the interface. The crucial physical ingredient lies in the nonlinear hydrodynamic coupling between the disturbance flow created by the swimmer and the free boundary problem at the fluid surface.

physics.flu-dyn↗

arXiv2010

Pumping by flapping in a viscoelastic fluid

In a world without inertia, Purcell's scallop theorem states that in a Newtonian fluid a time-reversible motion cannot produce any net force or net flow. Here we consider the extent to which the nonlinear rheological behavior of viscoelastic fluids can be exploited to break the constraints of the scallop theorem in the context of fluid pumping. By building on previous work focusing on force generation, we consider a simple, biologically-inspired geometrical example of a flapper in a polymeric (Oldroyd-B) fluid, and calculate asymptotically the time-average net fluid flow produced by the reciprocal flapping motion. The net flow occurs at fourth order in the flapping amplitude, and suggests the possibility of transporting polymeric fluids using reciprocal motion in simple geometries even in the absence of inertia. The induced flow field and pumping performance are characterized and optimized analytically. Our results may be useful in the design of micro-pumps handling complex fluids.

physics.flu-dyn↗

arXiv2010

Stokesian jellyfish: Viscous locomotion of bilayer vesicles

Motivated by recent advances in vesicle engineering, we consider theoretically the locomotion of shape-changing bilayer vesicles at low Reynolds number. By modulating their volume and membrane composition, the vesicles can be made to change shape quasi-statically in thermal equilibrium. When the control parameters are tuned appropriately to yield periodic shape changes which are not time-reversible, the result is a net swimming motion over one cycle of shape deformation. For two classical vesicle models (spontaneous curvature and bilayer coupling), we determine numerically the sequence of vesicle shapes through an enthalpy minimization, as well as the fluid-body interactions by solving a boundary integral formulation of the Stokes equations. For both models, net locomotion can be obtained either by continuously modulating fore-aft asymmetric vesicle shapes, or by crossing a continuous shape-transition region and alternating between fore-aft asymmetric and fore-aft symmetric shapes. The obtained hydrodynamic efficiencies are similar to that of other low Reynolds number biological swimmers, and suggest that shape-changing vesicles might provide an alternative to flagella-based synthetic microswimmers.

physics.bio-ph↗

arXiv2009

The long-time dynamics of two hydrodynamically-coupled swimming cells

Swimming micro-organisms such as bacteria or spermatozoa are typically found in dense suspensions, and exhibit collective modes of locomotion qualitatively different from that displayed by isolated cells. In the dilute limit where fluid-mediated interactions can be treated rigorously, the long-time hydrodynamics of a collection of cells result from interactions with many other cells, and as such typically eludes an analytical approach. Here we consider the only case where such problem can be treated rigorously analytically, namely when the cells have spatially confined trajectories, such as the spermatozoa of some marine invertebrates. We consider two spherical cells swimming, when isolated, with arbitrary circular trajectories, and derive the long-time kinematics of their relative locomotion. We show that in the dilute limit where the cells are much further away than their size, and the size of their circular motion, a separation of time scale occurs between a fast (intrinsic) swimming time, and a slow time where hydrodynamic interactions lead to change in the relative position and orientation of the swimmers. We perform a multiple-scale analysis and derive the effective dynamical system - of dimension two - describing the long-time behavior of the pair of cells. We show that the system displays one type of equilibrium, and two types of rotational equilibrium, all of which are found to be unstable. A detailed mathematical analysis of the dynamical systems further allows us to show that only two cell-cell behaviors are possible in the limit of $t\to\infty$, either the cells are attracted to each other (possibly monotonically), or they are repelled (possibly monotonically as well), which we confirm with numerical computations.

physics.bio-ph↗

arXiv2009

Two-dimensional flagellar synchronization in viscoelastic fluids

Experimental studies have demonstrated that spermatozoa synchronize their flagella when swimming in close proximity. In a Newtonian fluid, it was shown theoretically that such synchronization arises passively due to hydrodynamic forces between the two swimmers if their waveforms exhibit a front-back geometrical asymmetry. Motivated by the fact that most biological fluids possess a polymeric microstructure, we address here synchronization in a viscoelastic fluid analytically. Using a two-dimensional infinite sheet model we show that the presence of polymeric stresses removes the geometrical asymmetry constraint, and therefore even symmetric swimmers synchronize. Such synchronization occurs on asymptotically faster time scales than in a Newtonian fluid, and the swimmers are seen to be driven into a stable in-phase conformation minimizing the energy dissipated in the surrounding fluid.

physics.flu-dyn↗

arXiv2009

The transient swimming of a waving sheet

Small-scale locomotion plays an important role in biology. Different modelling approaches have been proposed in the past. The simplest model is an infinite inextensible two-dimensional waving sheet, {originally introduced by Taylor}, which serves as an idealized geometrical model for both spermatozoa locomotion and ciliary transport in Stokes flow. Here we complement classic steady-state calculations by deriving the transient low-Reynolds number swimming speed of such a waving sheet when starting from rest (small-amplitude initial-value problem). We also determine the transient fluid flow in the `pumping' setup where the sheet is not free to move but instead generates a net fluid flow around it. The time scales for these two problems, which in general govern transient effects in transport and locomotion at low Reynolds numbers, are also derived using physical arguments.

physics.flu-dyn↗

arXiv2009

Shaking-induced motility in suspensions of soft active particles

We investigate theoretically the collective dynamics of soft active particles living in a viscous fluid. We focus on a minimal model for active but non-motile particles consisting of $N>1$ elastic dimers deformed by active stresses and interacting hydrodynamically. We first derive a set of effective equations of motion for the positions of the particles. We then exploit these equations in two experimentally-relevant cases: uncorrelated random internal stresses, and uniform monochromatic external shaking. In both cases, we show that small groups of intrinsically non-motile particles can display non-trivial modes of locomotion resulting from the hydrodynamic correlations between the particle-conformation fluctuations. In addition, we demonstrate that a coherent shaking yields spatial ordering in suspension of soft particles interacting solely through the fluid.

cond-mat.soft↗

arXiv2009

The friction of a mesh-like super-hydrophobic surface

When a liquid droplet is located above a super-hydrophobic surface, it only barely touches the solid portion of the surface, and therefore slides very easily on it. More generally, super-hydrophobic surfaces have been shown to lead to significant reduction of viscous friction in the laminar regime, so it is of interest to quantify their effective slipping properties as a function of their geometric characteristics. Most previous studies have considered flows bounded by arrays of either long grooves, or isolated solid pillars on an otherwise flat solid substrate, and for which therefore the surrounding air constitutes the continuous phase. Here we consider instead the case where the super-hydrophobic surface is made of isolated holes in an otherwise continuous no-slip surface, and specifically focus on the mesh-like geometry recently achieved experimentally. We present an analytical method to calculate the friction of such a surface in the case where the mesh is thin. The results for the effective slip length of the surface are computed, compared to simple estimates, and a practical fit is proposed displaying a logarithmic dependance on the area fraction of the solid surface.

physics.flu-dyn↗

arXiv2009

The optimal elastic flagellum

Motile eukaryotic cells propel themselves in viscous fluids by passing waves of bending deformation down their flagella. An infinitely long flagellum achieves a hydrodynamically optimal low-Reynolds number locomotion when the angle between its local tangent and the swimming direction remains constant along its length. Optimal flagella therefore adopt the shape of a helix in three dimensions (smooth) and that of a sawtooth in two dimensions (non-smooth). Physically, biological organisms (or engineered micro-swimmers) must expend internal energy in order to produce the waves of deformation responsible for the motion. Here we propose a physically-motivated derivation of the optimal flagellum shape. We determine analytically and numerically the shape of the flagellar wave which leads to the fastest swimming while minimizing an appropriately-defined energetic expenditure. Our novel approach is to define an energy which includes not only the work against the surrounding fluid, but also (1) the energy stored elastically in the bending of the flagellum, (2) the energy stored elastically in the internal sliding of the polymeric filaments which are responsible for the generation of the bending waves (microtubules), and (3) the viscous dissipation due to the presence of an internal fluid. This approach regularizes the optimal sawtooth shape for two-dimensional deformation at the expense of a small loss in hydrodynamic efficiency. The optimal waveforms of finite-size flagella are shown to depend upon a competition between rotational motions and bending costs, and we observe a surprising bias towards half-integer wave-numbers. Their final hydrodynamic efficiencies are above 6%, significantly larger than those of swimming cells, therefore indicating available room for further biological tuning.

physics.bio-ph↗

arXiv2009

Hydrodynamic phase-locking of swimming microorganisms

Some microorganisms, such as spermatozoa, synchronize their flagella when swimming in close proximity. Using a simplified model (two infinite, parallel, two-dimensional waving sheets), we show that phase-locking arises from hydrodynamics forces alone, and has its origin in the front-back asymmetry of the geometry of their flagellar waveform. The time-evolution of the phase difference between co-swimming cells depends only on the nature of this geometrical asymmetry, and microorganisms can phase-lock into conformations which minimize or maximize energy dissipation.

physics.bio-ph↗