332 research outputs found
Hydrodynamic interactions betweem many spheres
This paper is an introductory guide to many-particle hydrodynamic
interactions. Basic concepts of the fluid dynamics are assumed to be known.
Experience in the Stokes equations is useful but not necessary. The study is
estimated to fit five sessions about three hours each.Comment: Latex, 17 page
A class of periodic and quasi-periodic trajectories of particles settling under gravity in a viscous fluid
We investigate regular configurations of a small number of particles settling
under gravity in a viscous fluid. The particles do not touch each other and can
move relative to each other. The dynamics is analyzed in the point-particle
approximation. A family of regular configurations is found with periodic
oscillations of all the settling particles. The oscillations are shown to be
robust under some out-of-phase rearrangements of the particles. In the presence
of an additional particle above such a regular configuration, the particle
periodic trajectories are horizontally repelled from the symmetry axis, and
flattened vertically. The results are used to propose a mechanism how a
spherical cloud, made of a large number of particles distributed at random,
evolves and destabilizes.Comment: 11 pages, 16 figure
Stable Configurations Of Charged Sedimenting Particles
The qualitative behavior of charged particles in a vacuum is given by
Earnshaw's Theorem which states that there is no steady configuration of
charged particles in a vacuum which is asymptotically stable to perturbations.
In a viscous fluid, examples of stationary configurations of sedimenting
uncharged particles are known, but they are unstable or neutrally stable - they
are not attractors. In this paper, it is shown by example that two charged
particles settling in a fluid may have a configuration which is asymptotically
stable to perturbations, for a wide range of charges, radii and densities. The
existence of such "bound states" is essential from a fundamental point of view
and it can be significant for dilute charged particulate systems in various
biological, medical and industrial contexts.Comment: 5 pages, 2 figures, supplemental materia
Translational and rotational Brownian displacements of colloidal particles of complex shapes
The exact analytical expressions for the time-dependent cross-correlations of
the translational and rotational Brownian displacements of a particle with
arbitrary shape were derived by us in [J. Chem. Phys. 142, 214902 (2015) and
144, 076101 (2016)]. They are in this work applied to construct a method to
analyze Brownian motion of a particle of an arbitrary shape, and to extract
accurately the self-diffusion matrix from the measurements of the
cross-correlations, which in turn allows to gain some information on the
particle structure. As an example, we apply our new method to analyze the
experimental results of D. J. Kraft et al. for the micrometer-sized aggregates
of the beads [Phys. Rev. E 88, 050301 (R) (2013)]. We explicitly demonstrate
that our procedure, based on the measurements of the time-dependent
cross-correlations in the whole range of times, allows to determine the self
diffusion (or alternatively the friction matrix) with a much higher precision
than the method based only on their initial slopes. Therefore, the analytical
time-dependence of the cross-correlations serves as a useful tool to extract
information about particle structure from trajectory measurements.Comment: 4 pages, 2 figure
Dynamics of elastic dumbbells sedimenting in a viscous fluid: oscillations and hydrodynamic repulsion
Hydrodynamic interactions between two identical elastic dumbbells settling
under gravity in a viscous fluid at low-Reynolds-number are investigated within
the point-particle model. Evolution of a benchmark initial configuration is
studied, in which the dumbbells are vertical and their centres are aligned
horizontally. Rigid dumbbells and pairs of separate beads starting from the
same positions tumble periodically while settling down. We find that elasticity
(which breaks time-reversal symmetry of the motion) significantly affects the
system's dynamics. This is remarkable taking into account that elastic forces
are always much smaller than gravity. We observe oscillating motion of the
elastic dumbbells, which tumble and change their length non-periodically.
Independently of the value of the spring constant, a horizontal hydrodynamic
repulsion appears between the dumbbells - their centres of mass move apart from
each other horizontally. The shift is fast for moderate values of the spring
constant k, and slows down when k tends to zero or to infinity; in these
limiting cases we recover the periodic dynamics reported in the literature. For
moderate values of the spring constant, and different initial configurations,
we observe the existence of a universal time-dependent solution to which the
system converges after an initial relaxation phase. The tumbling time and the
width of the trajectories in the centre-of-mass frame increase with time. In
addition to its fundamental significance, the benchmark solution presented here
is important to understand general features of systems with larger number of
elastic particles, at regular and random configurations.Comment: 12 pages, 7 figure
Note: Brownian motion of colloidal particles of arbitrary shape
The analytical expressions for the time-dependent cross-correlations of the
translational and rotational Brownian displacements of a particle with
arbitrary shape are derived. The reference center is arbitrary, and the
reference frame is such that the rotational-rotational diffusion tensor is
diagonal.Comment: 2 page
Brownian motion of a particle with arbitrary shape
Brownian motion of a particle with an arbitrary shape is investigated
theoretically. Analytical expressions for the time-dependent cross-correlations
of the Brownian translational and rotational displacements are derived from the
Smoluchowski equation. The role of the particle mobility center is determined
and discussed.Comment: 11 page
Periodic and quasiperiodic motions of many particles falling in a viscous fluid
Dynamics of regular clusters of many non-touching particles falling under
gravity in a viscous fluid at low Reynolds number are analysed within the
point-particle model. Evolution of two families of particle configurations is
determined: 2 or 4 regular horizontal polygons (called `rings') centred above
or below each other. Two rings fall together and periodically oscillate. Four
rings usually separate from each other with chaotic scattering. For hundreds of
thousands of initial configurations, a map of the cluster lifetime is
evaluated, where the long-lasting clusters are centred around periodic
solutions for the relative motions, and surrounded by regions of the chaotic
scattering,in a similar way as it was observed by Janosi et al. (1997) for
three particles only. These findings suggest to consider the existence of
periodic orbits as a possible physical mechanism of the existence of unstable
clusters of particles falling under gravity in a viscous fluid.Comment: 11 pages, 10 figure
Hydrodynamic radius approximation for spherical particles suspended in a viscous fluid: influence of particle internal structure and boundary
Systems of spherical particles moving in Stokes flow are studied for a
different particle internal structure and boundaries, including the Navier-slip
model. It is shown that their hydrodynamic interactions are well described by
treating them as solid spheres of smaller hydrodynamic radii, which can be
determined from measured single-particle diffusion or intrinsic viscosity
coefficients. Effective dynamics of suspensions made of such particles is quite
accurately described by mobility coefficients of the solid particles with the
hydrodynamic radii, averaged with the unchanged direct interactions between the
particles.Comment: 7 pages, 2 figure
Dynamics of flexible fibers in shear flow
Dynamics of flexible non-Brownian fibers in shear flow at low-Reynolds-number
are analyzed numerically for a wide range of the ratios A of the fiber bending
force to the viscous drag force. Initially, the fibers are aligned with the
flow, and later they move in the plane perpendicular to the flow vorticity. A
surprisingly rich spectrum of different modes is observed when the value of A
is systematically changed, with sharp transitions between coiled and
straightening out modes, period-doubling bifurcations from periodic to
migrating solutions, irregular dynamics and chaos.Comment: 5 pages, 7 figure
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