273 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
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
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
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