1,401 research outputs found
Apparent slip due to the motion of suspended particles in flows of electrolyte solutions
We consider pressure-driven flows of electrolyte solutions in small channels
or capillaries in which tracer particles are used to probe velocity profiles.
Under the assumption that the double layer is thin compared to the channel
dimensions, we show that the flow-induced streaming electric field can create
an apparent slip velocity for the motion of the particles, even if the flow
velocity still satisfies the no-slip boundary condition. In this case, tracking
of particle would lead to the wrong conclusion that the no-slip boundary
condition is violated. We evaluate the apparent slip length, compare with
experiments, and discuss the implications of these results
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
A note on the stability of slip channel flows
We consider the influence of slip boundary conditions on the modal and
non-modal stability of pressure-driven channel flows. In accordance with
previous results by Gersting (1974) (Phys. Fluids, 17) but in contradiction
with the recent investigation of Chu (2004) (C.R. Mecanique, 332), we show that
slip increases significantly the value of the critical Reynolds number for
linear instability. The non-modal stability analysis however reveals that the
slip has a very weak influence on the maximum transient energy growth of
perturbations at subcritical Reynolds numbers. Slip boundary conditions are
therefore not likely to have a significant effect on the transition to
turbulence in channel flows
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
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
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