62 research outputs found
Intrinsic viscosity of a suspension of weakly Brownian ellipsoids in shear
We analyze the angular dynamics of triaxial ellipsoids in a shear flow
subject to weak thermal noise. By numerically integrating an overdamped angular
Langevin equation, we find the steady angular probability distribution for a
range of triaxial particle shapes. From this distribution we compute the
intrinsic viscosity of a dilute suspension of triaxial particles. We determine
how the viscosity depends on particle shape in the limit of weak thermal noise.
While the deterministic angular dynamics depends very sensitively on particle
shape, we find that the shape dependence of the intrinsic viscosity is weaker,
in general, and that suspensions of rod-like particles are the most sensitive
to breaking of axisymmetry. The intrinsic viscosity of a dilute suspension of
triaxial particles is smaller than that of a suspension of axisymmetric
particles with the same volume, and the same ratio of major to minor axis
lengths.Comment: 14 pages, 6 figures, 1 table, revised versio
Effect of weak fluid inertia upon Jeffery orbits
We consider the rotation of small neutrally buoyant axisymmetric particles in
a viscous steady shear flow. When inertial effects are negligible the problem
exhibits infinitely many periodic solutions, the "Jeffery orbits". We compute
how inertial effects lift their degeneracy by perturbatively solving the
coupled particle-flow equations. We obtain an equation of motion valid at small
shear Reynolds numbers, for spheroidal particles with arbitrary aspect ratios.
We analyse how the linear stability of the \lq log-rolling\rq{} orbit depends
on particle shape and find it to be unstable for prolate spheroids. This
resolves a puzzle in the interpretation of direct numerical simulations of the
problem. In general both unsteady and non-linear terms in the Navier-Stokes
equations are important.Comment: 5 pages, 2 figure
Rotation of a spheroid in a simple shear at small Reynolds number
We derive an effective equation of motion for the orientational dynamics of a
neutrally buoyant spheroid suspended in a simple shear flow, valid for
arbitrary particle aspect ratios and to linear order in the shear Reynolds
number. We show how inertial effects lift the degeneracy of the Jeffery orbits
and determine the stabilities of the log-rolling and tumbling orbits at
infinitesimal shear Reynolds numbers. For prolate spheroids we find stable
tumbling in the shear plane, log-rolling is unstable. For oblate particles, by
contrast, log-rolling is stable and tumbling is unstable provided that the
aspect ratio is larger than a critical value. When the aspect ratio is smaller
than this value tumbling turns stable, and an unstable limit cycle is born.Comment: 25 pages, 5 figure
Aperiodic tumbling of microrods advected in a microchannel flow
We report on an experimental investigation of the tumbling of microrods in
the shear flow of a microchannel (40 x 2.5 x 0.4 mm). The rods are 20 to 30
microns long and their diameters are of the order of 1 micron. Images of the
centre-of-mass motion and the orientational dynamics of the rods are recorded
using a microscope equipped with a CCD camera. A motorised microscope stage is
used to track individual rods as they move along the channel. Automated image
analysis determines the position and orientation of a tracked rods in each
video frame. We find different behaviours, depending on the particle shape, its
initial position, and orientation. First, we observe periodic as well as
aperiodic tumbling. Second, the data show that different tumbling trajectories
exhibit different sensitivities to external perturbations. These observations
can be explained by slight asymmetries of the rods. Third we observe that after
some time, initially periodic trajectories lose their phase. We attribute this
to drift of the centre of mass of the rod from one to another stream line of
the channel flow.Comment: 14 pages, 8 figures, as accepted for publicatio
Superconducting transition temperatures and coherence length in non s-wave pairing materials correlated with spin-fluctuation mediated interaction
Following earlier work on electron or hole liquids flowing through assemblies
with magnetic fluctuations, we have recently exposed a marked correlation of
the superconducting temperature Tc, for non s-wave pairing materials, with
coherence length xi and effective mass m*. The very recent study of Abanov et
al. [Europhys. Lett. 54, 488 (2001)] and the prior investigation of Monthoux
and Lonzarich [Phys. Rev. B 59, 14598 (1999)] have each focussed on the concept
of a spin-fluctuation temperature T_sf, which again is intimately related to
Tc. For the d-wave pairing via antiferromagnetic spin fluctuations in the
cuprates, these studies are brought into close contact with our own work, and
the result is that k_B T_sf ~ hbar^2 / m* xi^2. This demonstrates that xi is
also determined by such antiferromagnetic spin-fluctuation mediated pair
interaction. The coherence length in units of the lattice spacing is then
essentially given in the cuprates as the square root of the ratio of two
characteristic energies, namely: the kinetic energy of localization of a charge
carrier of mass m* in a specified magnetic correlation length to the hopping
energy. The quasi-2D ruthenate Sr_2RuO_4, with Tc ~ 1.3 K, has p-wave
spin-triplet pairing and so is also briefly discussed here.Comment: Accepted for publication in Phys. Rev.
The role of inertia for the rotation of a nearly spherical particle in a general linear flow
We analyse the angular dynamics of a neutrally buoyant nearly spherical
particle immersed in a steady general linear flow. The hydrodynamic torque
acting on the particle is obtained by means of a reciprocal theorem, regular
perturbation theory exploiting the small eccentricity of the nearly spherical
particle, and assuming that inertial effects are small, but finite.Comment: 7 pages, 1 figur
- …