219 research outputs found
Transport of a dilute active suspension in pressure-driven channel flow
Confined suspensions of active particles show peculiar dynamics characterized
by wall accumulation, as well as upstream swimming, centerline depletion and
shear-trapping when a pressure-driven flow is imposed. We use theory and
numerical simulations to investigate the effects of confinement and non-uniform
shear on the dynamics of a dilute suspension of Brownian active swimmers by
incorporating a detailed treatment of boundary conditions within a simple
kinetic model where the configuration of the suspension is described using a
conservation equation for the probability distribution function of particle
positions and orientations, and where particle-particle and particle-wall
hydrodynamic interactions are neglected. Based on this model, we first
investigate the effects of confinement in the absence of flow, in which case
the dynamics is governed by a swimming Peclet number, or ratio of the
persistence length of particle trajectories over the channel width, and a
second swimmer-specific parameter whose inverse measures the strength of
propulsion. In the limit of weak and strong propulsion, asymptotic expressions
for the full distribution function are derived. For finite propulsion,
analytical expressions for the concentration and polarization profiles are also
obtained using a truncated moment expansion of the distribution function. In
agreement with experimental observations, the existence of a
concentration/polarization boundary layer in wide channels is reported and
characterized, suggesting that wall accumulation in active suspensions is
primarily a kinematic effect which does not require hydrodynamic interactions.
Next, we show that application of a pressure-driven Poiseuille flow leads to
net upstream swimming of the particles relative to the flow, and an analytical
expression for the mean upstream velocity is derived in the weak flow limit. In
stronger imposed flows .....
On the distribution and swim pressure of run-and-tumble particles in confinement
The spatial and orientational distribution in a dilute active suspension of
non-Brownian run-and-tumble spherical swimmers confined between two planar hard
walls is calculated theoretically. Using a kinetic model based on coupled
bulk/surface probability density functions, we demonstrate the existence of a
concentration wall boundary layer with thickness scaling with the run length,
the absence of polarization throughout the channel, and the presence of sharp
discontinuities in the bulk orientation distribution in the neighborhood of
orientations parallel to the wall in the near-wall region. Our model is also
applied to calculate the swim pressure in the system, which approaches the
previously proposed ideal-gas behavior in wide channels but is found to
decrease in narrow channels as a result of confinement. Monte-Carlo simulations
are also performed for validation and show excellent quantitative agreement
with our theoretical predictions
The sedimentation of flexible filaments
The dynamics of a flexible filament sedimenting in a viscous fluid are
explored analytically and numerically. Compared to the well-studied case of
sedimenting rigid rods, the introduction of filament compliance is shown to
cause a significant alteration in the long-time sedimentation orientation and
filament geometry. A model is developed by balancing viscous, elastic, and
gravitational forces in a slender-body theory for zero-Reynolds-number flows,
and the filament dynamics are characterized by a dimensionless
elasto-gravitation number. Filaments of both non-uniform and uniform
cross-sectional thickness are considered. In the weakly flexible regime, a
multiple-scale asymptotic expansion is used to obtain expressions for filament
translations, rotations, and shapes. These are shown to match excellently with
full numerical simulations. Furthermore, we show that trajectories of
sedimenting flexible filaments, unlike their rigid counterparts, are restricted
to a cloud whose envelope is determined by the elasto-gravitation number. In
the highly flexible regime we show that a filament sedimenting along its long
axis is susceptible to a buckling instability. A linear stability analysis
provides a dispersion relation, illustrating clearly the competing effects of
the compressive stress and the restoring elastic force in the buckling process.
The instability travels as a wave along the filament opposite the direction of
gravity as it grows and the predicted growth rates are shown to compare
favorably with numerical simulations. The linear eigenmodes of the governing
equation are also studied, which agree well with the finite-amplitude buckled
shapes arising in simulations
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