392 research outputs found
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
Particles held by springs in a linear shear flow exhibit oscillatory motion
The dynamics of small spheres, which are held by linear springs in a low
Reynolds number shear flow at neighboring locations is investigated. The flow
elongates the beads and the interplay of the shear gradient with the nonlinear
behavior of the hydrodynamic interaction among the spheres causes in a large
range of parameters a bifurcation to a surprising oscillatory bead motion. The
parameter ranges, wherein this bifurcation is either super- or subcritical, are
determined.Comment: 4 pages, 5 figure
The Effect of the Third Dimension on Rough Surfaces Formed by Sedimenting Particles in Quasi-Two-Dimensions
The roughness exponent of surfaces obtained by dispersing silica spheres into
a quasi-two-dimensional cell is examined. The cell consists of two glass plates
separated by a gap, which is comparable in size to the diameter of the beads.
Previous work has shown that the quasi-one-dimensional surfaces formed have two
distinct roughness exponents in two well-defined length scales, which have a
crossover length about 1cm. We have studied the effect of changing the gap
between the plates to a limit of about twice the diameter of the beads.Comment: 4 pages, 4 figures, submitted to IJMP
Stick boundary conditions and rotational velocity auto-correlation functions for colloidal particles in a coarse-grained representation of the solvent
We show how to implement stick boundary conditions for a spherical colloid in
a solvent that is coarse-grained by the method of stochastic rotation dynamics.
This allows us to measure colloidal rotational velocity auto-correlation
functions by direct computer simulation. We find quantitative agreement with
Enskog theory for short times and with hydrodynamic mode-coupling theory for
longer times. For aqueous colloidal suspensions, the Enskog contribution to the
rotational friction is larger than the hydrodynamic one when the colloidal
radius drops below 35nm.Comment: new version with some minor change
Wetting and particle adsorption in nanoflows
Molecular dynamics simulations are used to study the behavior of
closely-fitting spherical and ellipsoidal particles moving through a
fluid-filled cylinder at nanometer scales. The particle, the cylinder wall and
the fluid solvent are all treated as atomic systems, and special attention is
given to the effects of varying the wetting properties of the fluid. Although
the modification of the solid-fluid interaction leads to significant changes in
the microstructure of the fluid, its transport properties are found to be the
same as in bulk. Independently of the shape and relative size of the particle,
we find two distinct regimes as a function of the degree of wetting, with a
sharp transition between them. In the case of a highly-wetting suspending
fluid, the particle moves through the cylinder with an average axial velocity
in agreement with that obtained from the solution of the continuum Stokes
equations. In contrast, in the case of less-wetting fluids, only the early-time
motion of the particle is consistent with continuum dynamics. At later times,
the particle is eventually adsorbed onto the wall and subsequently executes an
intermittent stick-slip motion.We show that van der Walls forces are the
dominant contribution to the particle adsorption phenomenon and that depletion
forces are weak enough to allow, in the highly-wetting situation, an initially
adsorbed particle to spontaneously desorb
Hydrodynamic interactions and Brownian forces in colloidal suspensions: Coarse-graining over time and length-scales
We describe in detail how to implement a coarse-grained hybrid Molecular
Dynamics and Stochastic Rotation Dynamics simulation technique that captures
the combined effects of Brownian and hydrodynamic forces in colloidal
suspensions. The importance of carefully tuning the simulation parameters to
correctly resolve the multiple time and length-scales of this problem is
emphasized. We systematically analyze how our coarse-graining scheme resolves
dimensionless hydrodynamic numbers such as the Reynolds number, the Schmidt
number, the Mach number, the Knudsen number, and the Peclet number. The many
Brownian and hydrodynamic time-scales can be telescoped together to maximize
computational efficiency while still correctly resolving the physically
relevant physical processes. We also show how to control a number of numerical
artifacts, such as finite size effects and solvent induced attractive depletion
interactions. When all these considerations are properly taken into account,
the measured colloidal velocity auto-correlation functions and related self
diffusion and friction coefficients compare quantitatively with theoretical
calculations. By contrast, these calculations demonstrate that, notwithstanding
its seductive simplicity, the basic Langevin equation does a remarkably poor
job of capturing the decay rate of the velocity auto-correlation function in
the colloidal regime, strongly underestimating it at short times and strongly
overestimating it at long times. Finally, we discuss in detail how to map the
parameters of our method onto physical systems, and from this extract more
general lessons that may be relevant for other coarse-graining schemes such as
Lattice Boltzmann or Dissipative Particle Dynamics.Comment: 31 pages, 14 figure
Active particles in periodic lattices
Both natural and artificial small-scale swimmers may often self-propel in
environments subject to complex geometrical constraints. While most past
theoretical work on low-Reynolds number locomotion addressed idealised
geometrical situations, not much is known on the motion of swimmers in
heterogeneous environments. As a first theoretical model, we investigate
numerically the behaviour of a single spherical micro-swimmer located in an
infinite, periodic body-centred cubic lattice consisting of rigid inert spheres
of the same size as the swimmer. Running a large number of simulations we
uncover the phase diagram of possible trajectories as a function of the
strength of the swimming actuation and the packing density of the lattice. We
then use hydrodynamic theory to rationalise our computational results and show
in particular how the far-field nature of the swimmer (pusher vs. puller)
governs even the behaviour at high volume fractions
Cluster algebras in algebraic Lie theory
We survey some recent constructions of cluster algebra structures on
coordinate rings of unipotent subgroups and unipotent cells of Kac-Moody
groups. We also review a quantized version of these results.Comment: Invited survey; to appear in Transformation Group
Simulating (electro)hydrodynamic effects in colloidal dispersions: smoothed profile method
Previously, we have proposed a direct simulation scheme for colloidal
dispersions in a Newtonian solvent [Phys.Rev.E 71,036707 (2005)]. An improved
formulation called the ``Smoothed Profile (SP) method'' is presented here in
which simultaneous time-marching is used for the host fluid and colloids. The
SP method is a direct numerical simulation of particulate flows and provides a
coupling scheme between the continuum fluid dynamics and rigid-body dynamics
through utilization of a smoothed profile for the colloidal particles.
Moreover, the improved formulation includes an extension to incorporate
multi-component fluids, allowing systems such as charged colloids in
electrolyte solutions to be studied. The dynamics of the colloidal dispersions
are solved with the same computational cost as required for solving
non-particulate flows. Numerical results which assess the hydrodynamic
interactions of colloidal dispersions are presented to validate the SP method.
The SP method is not restricted to particular constitutive models of the host
fluids and can hence be applied to colloidal dispersions in complex fluids
- …