1,028 research outputs found
Persistent correlation of constrained colloidal motion
We have investigated the motion of a single optically trapped colloidal
particle close to a limiting wall at time scales where the inertia of the
surrounding fluid plays a significant role. The velocity autocorrelation
function exhibits a complex interplay due to the momentum relaxation of the
particle, the vortex diffusion in the fluid, the obstruction of flow close to
the interface, and the harmonic restoring forces due to the optical trap. We
show that already a weak trapping force has a significant impact on the
velocity autocorrelation function C(t)= at times where the
hydrodynamic memory leads to an algebraic decay. The long-time behavior for the
motion parallel and perpendicular to the wall is derived analytically and
compared to numerical results. Then, we discuss the power spectral densities of
the displacement and provide simple interpolation formulas. The theoretical
predictions are finally compared to recent experimental observations.Comment: 12 pages, 6 figure
Lubrication approximation for micro-particles moving along parallel walls
Lubrication expressions for the friction coefficients of a spherical particle
moving in a fluid between and along two parallel solid walls are explicitly
evaluated in the low-Reynolds-number regime. They are used to determine
lubrication expression for the particle free motion under an ambient Poiseuille
flow. The range of validity and the accuracy of the lubrication approximation
is determined by comparing with the corresponding results of the accurate
multipole procedure. The results are applicable for thin, wide and long
microchannels, or quasi-two-dimensional systems.Comment: 4 pages, 5 figure
Lattice-Boltzmann simulations of the drag force on a sphere approaching a superhydrophobic striped plane
By means of lattice-Boltzmann simulations the drag force on a sphere of
radius R approaching a superhydrophobic striped wall has been investigated as a
function of arbitrary separation h. Superhydrophobic (perfect-slip vs. no-slip)
stripes are characterized by a texture period L and a fraction of the gas area
. For very large values of h/R we recover the macroscopic formulae for a
sphere moving towards a hydrophilic no-slip plane. For h/R=O(1) and smaller the
drag force is smaller than predicted by classical theories for hydrophilic
no-slip surfaces, but larger than expected for a sphere interacting with a
uniform perfectly slipping wall. At a thinner gap, the force reduction
compared to a classical result becomes more pronounced, and is maximized by
increasing . In the limit of very small separations our simulation data
are in quantitative agreement with an asymptotic equation, which relates a
correction to a force for superhydrophobic slip to texture parameters. In
addition, we examine the flow and pressure field and observe their oscillatory
character in the transverse direction in the vicinity of the wall, which
reflects the influence of the heterogeneity and anisotropy of the striped
texture. Finally, we investigate the lateral force on the sphere, which is
detectable in case of very small separations and is maximized by stripes with
.Comment: 9 pages, 7 figure
Hydrodynamic orienting of asymmetric microobjects under gravity
It is shown that nonsymmetric microobjects orient while settling under
gravity in a viscous fluid. To analyze this process, a simple shape is chosen:
a non-deformable `chain'. The chain consists of two straight arms, made of
touching solid spheres. In the absence of external torques, the spheres are
free to spin along the arms. The motion of the chain is evaluated by solving
the Stokes equations with the use of the multipole method. It is demonstrated
that the spinning beads speed up sedimentation by a small amount, and increase
the orientation rate significantly in comparison to the corresponding rigid
chain. It is shown that chains orient towards the V-shaped stable stationary
configuration. In contrast, rods and star-shaped microobjects do not rotate.
The hydrodynamic orienting is relevant for efficient swimming of non-symmetric
microobjects, and for sedimenting suspensions.Comment: 9 page
Acoustic radiation- and streaming-induced microparticle velocities determined by micro-PIV in an ultrasound symmetry plane
We present micro-PIV measurements of suspended microparticles of diameters
from 0.6 um to 10 um undergoing acoustophoresis in an ultrasound symmetry plane
in a microchannel. The motion of the smallest particles are dominated by the
Stokes drag from the induced acoustic streaming flow, while the motion of the
largest particles are dominated by the acoustic radiation force. For all
particle sizes we predict theoretically how much of the particle velocity is
due to radiation and streaming, respectively. These predictions include
corrections for particle-wall interactions and ultrasonic thermoviscous
effects, and they match our measurements within the experimental uncertainty.
Finally, we predict theoretically and confirm experimentally that the ratio
between the acoustic radiation- and streaming-induced particle velocities is
proportional to the square of the particle size, the actuation frequency and
the acoustic contrast factor, while it is inversely proportional to the
kinematic viscosity.Comment: 11 pages, 9 figures, RevTex 4-
Brownian motion in a non-homogeneous force field and photonic force microscope
The Photonic Force Microscope (PFM) is an opto-mechanical technique based on
an optical trap that can be assumed to probe forces in microscopic systems.
This technique has been used to measure forces in the range of pico- and
femto-Newton, assessing the mechanical properties of biomolecules as well as of
other microscopic systems. For a correct use of the PFM, the force field to
measure has to be invariable (homogeneous) on the scale of the Brownian motion
of the trapped probe. This condition implicates that the force field must be
conservative, excluding the possibility of a rotational component. However,
there are cases where these assumptions are not fulfilled Here, we show how to
improve the PFM technique in order to be able to deal with these cases. We
introduce the theory of this enhanced PFM and we propose a concrete analysis
workflow to reconstruct the force field from the experimental time-series of
the probe position. Furthermore, we experimentally verify some particularly
important cases, namely the case of a conservative or rotational force-field
Symmetric three-particle motion in Stokes flow: equilibrium for heavy spheres in contrast to "end-of-world" for point forces
A stationary stable solution of the Stokes equations for three identical
heavy solid spheres falling in a vertical plane is found. It has no analog in
the point-particle approximation. Three spheres aligned horizontally at equal
distances evolve towards the equilibrium relative configuration while the point
particles collapse onto a single point in a finite time.Comment: 4 pages, 7 figure
Non-equilibrium hydrodynamics of a rotating filament
The nonlinear dynamics of an elastic filament that is forced to rotate at its
base is studied by hydrodynamic simulation techniques; coupling between
stretch, bend, twist elasticity and thermal fluctuations is included. The
twirling-overwhirling transition is located and found to be strongly
discontinuous. For finite bend and twist persistence length, thermal
fluctuations lower the threshold rotational frequency, for infinite persistence
length the threshold agrees with previous analytical predictions
First-order virial expansion of short-time diffusion and sedimentation coefficients of permeable particles suspensions
For suspensions of permeable particles, the short-time translational and
rotational self-diffusion coefficients, and collective diffusion and
sedimentation coefficients are evaluated theoretically. An individual particle
is modeled as a uniformly permeable sphere of a given permeability, with the
internal solvent flow described by the Debye-Bueche-Brinkman equation. The
particles are assumed to interact non-hydrodynamically by their excluded
volumes. The virial expansion of the transport properties in powers of the
volume fraction is performed up to the two-particle level. The first-order
virial coefficients corresponding to two-body hydrodynamic interactions are
evaluated with very high accuracy by the series expansion in inverse powers of
the inter-particle distance. Results are obtained and discussed for a wide
range of the ratio, x, of the particle radius to the hydrodynamic screening
length inside a permeable sphere. It is shown that for x >= 10, the virial
coefficients of the transport properties are well-approximated by the
hydrodynamic radius (annulus) model developed by us earlier for the effective
viscosity of porous-particle suspensions
Faxen relations in solids - a generalized approach to particle motion in elasticity and viscoelasticity
A movable inclusion in an elastic material oscillates as a rigid body with
six degrees of freedom. Displacement/rotation and force/moment tensors which
express the motion of the inclusion in terms of the displacement and force at
arbitrary exterior points are introduced. Using reciprocity arguments two
general identities are derived relating these tensors. Applications of the
identities to spherical particles provide several new results, including simple
expressions for the force and moment on the particle due to plane wave
excitation.Comment: 11 pages, 4 figure
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