2,910 research outputs found
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
Autophoretic locomotion from geometric asymmetry
Among the few methods which have been proposed to create small-scale
swimmers, those relying on self-phoretic mechanisms present an interesting
design challenge in that chemical gradients are required to generate net
propulsion. Building on recent work, we propose that asymmetries in geometry
are sufficient to induce chemical gradients and swimming. We illustrate this
idea using two different calculations. We first calculate exactly the
self-propulsion speed of a system composed of two spheres of unequal sizes but
identically chemically homogeneous. We then consider arbitrary,
small-amplitude, shape deformations of a chemically-homogeneous sphere, and
calculate asymptotically the self-propulsion velocity induced by the shape
asymmetries. Our results demonstrate how geometric asymmetries can be tuned to
induce large locomotion speeds without the need of chemical patterning.Comment: 17 pages, 10 figure
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
Unsteady feeding and optimal strokes of model ciliates
The flow field created by swimming microorganisms not only enables their
locomotion but also leads to advective transport of nutrients. In this paper we
address analytically and computationally the link between unsteady feeding and
unsteady swimming on a model microorganism, the spherical squirmer, actuating
the fluid in a time-periodic manner. We start by performing asymptotic
calculations at low P\'eclet number (Pe) on the advection-diffusion problem for
the nutrients. We show that the mean rate of feeding as well as its
fluctuations in time depend only on the swimming modes of the squirmer up to
order Pe^(3/2), even when no swimming occurs on average, while the influence of
non-swimming modes comes in only at order Pe^2. We also show that generically
we expect a phase delay between feeding and swimming of 1/8th of a period.
Numerical computations for illustrative strokes at finite Pe confirm
quantitatively our analytical results linking swimming and feeding. We finally
derive, and use, an adjoint-based optimization algorithm to determine the
optimal unsteady strokes maximizing feeding rate for a fixed energy budget. The
overall optimal feeder is always the optimal steady swimmer. Within the set of
time-periodic strokes, the optimal feeding strokes are found to be equivalent
to those optimizing periodic swimming for all values of the P\'eclet number,
and correspond to a regularization of the overall steady optimal.Comment: 26 pages, 11 figures, to appear in Journal of Fluid Mechanic
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.Comment: 29 pages, 20 figure
Electro-hydrodynamic synchronization of piezoelectric flags
Hydrodynamic coupling of flexible flags in axial flows may profoundly
influence their flapping dynamics, in particular driving their synchronization.
This work investigates the effect of such coupling on the harvesting efficiency
of coupled piezoelectric flags, that convert their periodic deformation into an
electrical current. Considering two flags connected to a single output circuit,
we investigate using numerical simulations the relative importance of
hydrodynamic coupling to electrodynamic coupling of the flags through the
output circuit due to the inverse piezoelectric effect. It is shown that
electrodynamic coupling is dominant beyond a critical distance, and induces a
synchronization of the flags' motion resulting in enhanced energy harvesting
performance. We further show that this electrodynamic coupling can be
strengthened using resonant harvesting circuits.Comment: 14 pages, 10 figures, to appear in J. Fluids Struc
Fluid-solid-electric lock-in of energy-harvesting piezoelectric flags
The spontaneous flapping of a flag in a steady flow can be used to power an
output circuit using piezoelectric elements positioned at its surface. Here, we
study numerically the effect of inductive circuits on the dynamics of this
fluid-solid-electric system and on its energy harvesting efficiency. In
particular, a destabilization of the system is identified leading to energy
harvesting at lower flow velocities. Also, a frequency lock-in between the flag
and the circuit is shown to significantly enhance the system's harvesting
efficiency. These results suggest promising efficiency enhancements of such
flow energy harvesters through the output circuit optimization.Comment: 8 pages, 8 figures, to appear in Physical Review Applie
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
Synchronized flutter of two slender flags
The interactions and synchronization of two parallel and slender flags in a
uniform axial flow are studied in the present paper by generalizing Lighthill's
Elongated Body Theory (EBT) and Lighthill's Large Amplitude Elongated Body
Theory (LAEBT) to account for the hydrodynamic coupling between flags. The
proposed method consists in two successive steps, namely the reconstruction of
the flow created by a flapping flag within the LAEBT framework and the
computation of the fluid force generated by this nonuniform flow on the second
flag. In the limit of slender flags in close proximity, we show that the effect
of the wakes have little influence on the long time coupled-dynamics and can be
neglected in the modeling. This provides a simplified framework extending LAEBT
to the coupled dynamics of two flags. Using this simplified model, both linear
and large amplitude results are reported to explore the selection of the
flapping regime as well as the dynamical properties of two side-by-side slender
flags. Hydrodynamic coupling of the two flags is observed to destabilize the
flags for most parameters, and to induce a long-term synchronization of the
flags, either in-phase or out-of-phase.Comment: 14 pages, 10 figures, to appear in J. Fluid Mec
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