3,081 research outputs found
Lattice Boltzmann simulations of a viscoelastic shear-thinning fluid
We present a hybrid lattice Boltzmann algorithm for the simulation of flow
glass-forming fluids, characterized by slow structural relaxation, at the level
of the Navier-Stokes equation. The fluid is described in terms of a nonlinear
integral constitutive equation, relating the stress tensor locally to the
history of flow. As an application, we present results for an integral
nonlinear Maxwell model that combines the effects of (linear) viscoelasticity
and (nonlinear) shear thinning. We discuss the transient dynamics of
velocities, shear stresses, and normal stress differences in planar
pressure-driven channel flow, after switching on (startup) and off (cessation)
of the driving pressure. This transient dynamics depends nontrivially on the
channel width due to an interplay between hydrodynamic momentum diffusion and
slow structural relaxation
Universality Class of the Reversible-Irreversible Transition in Sheared Suspensions
Collections of non-Brownian particles suspended in a viscous fluid and
subjected to oscillatory shear at very low Reynolds number have recently been
shown to exhibit a remarkable dynamical phase transition separating reversible
from irreversible behaviour as the strain amplitude or volume fraction are
increased. We present a simple model for this phenomenon, based on which we
argue that this transition lies in the universality class of the conserved DP
models or, equivalently, the Manna model. This leads to predictions for the
scaling behaviour of a large number of experimental observables. Non-Brownian
suspensions under oscillatory shear may thus constitute the first experimental
realization of an inactive-active phase transition which is not in the
universality class of conventional directed percolation.Comment: 4 pages, 2 figures, final versio
Navier-Stokes equations on the flat cylinder with vorticity production on the boundary
We study the two-dimensional Navier-Stokes system on a flat cylinder with the
usual Dirichlet boundary conditions for the velocity field u. We formulate the
problem as an infinite system of ODE's for the natural Fourier components of
the vorticity, and the boundary conditions are taken into account by adding a
vorticity production at the boundary. We prove equivalence to the original
Navier-Stokes system and show that the decay of the Fourier modes is
exponential for any positive time in the periodic direction, but it is only
power-like in the other direction.Comment: 25 page
Capillary rise of a liquid between two vertical plates making a small angle.
The penetration of a wetting liquid in the narrow gap between two vertical plates making a small angle is analyzed in the framework of the lubrication approximation. At the beginning of the process, the liquid rises independently at different distances from the line of intersection of the plates except in a small region around this line where the effect of the gravity is negligible. The maximum height of the liquid initially increases as the cubic root of time and is attained at a point that reaches the line of intersection only after a certain time. At later times, the motion of the liquid is confined to a thin layer around the line of intersection whose height increases as the cubic root of time and whose thickness decreases as the inverse of the cubic root of time. The evolution of the liquid surface is computed numerically and compared with the results of a simple experiment
Excitation of inertial modes in a closed grid turbulence experiment under rotation
We report an experimental study of the decay of grid-generated turbulence in
a confined geometry submitted to a global rotation. Turbulence is generated by
rapidly towing a grid in a parallelepipedic water tank. The velocity fields of
a large number of independent decays are measured in a vertical plane parallel
to the rotation axis using a corotating Particle Image Velocimetry system. We
first show that, when a "simple" grid is used, a significant amount of the
kinetic energy (typically 50%) is stored in a reproducible flow composed of
resonant inertial modes. The spatial structure of those inertial modes,
extracted by band-pass filtering, is found compatible with the numerical
results of Maas [Fluid Dyn. Res. 33, 373 (2003)]. The possible coupling between
these modes and turbulence suggests that turbulence cannot be considered as
freely decaying in this configuration. Finally, we demonstrate that these
inertial modes may be significantly reduced (down to 15% of the total energy)
by adding a set of inner tanks attached to the grid. This suggests that it is
possible to produce an effectively freely decaying rotating turbulence in a
confined geometry
Channel Flow of a Tensorial Shear-Thinning Maxwell Model: Lattice Boltzmann Simulations
We introduce a nonlinear generalized tensorial Maxwell-type constitutive
equation to describe shear-thinning glass-forming fluids, motivated by a recent
microscopic approach to the nonlinear rheology of colloidal suspensions. The
model captures a nonvanishing dynamical yield stress at the glass transition
and incorporates normal-stress differences. A modified lattice-Boltzmann (LB)
simulation scheme is presented that includes non-Newtonian contributions to the
stress tensor and deals with flow-induced pressure differences. We test this
scheme in pressure-driven 2D Poiseuille flow of the nonlinear generalized
Maxwell fluid. In the steady state, comparison with an analytical solution
shows good agreement. The transient dynamics after startup and cessation of the
pressure gradient are studied; the simulation reproduces a finite stopping time
for the cessation flow of the yield-stress fluid in agreement with previous
analytical estimates
Locating the source of projectile fluid droplets
The ill-posed projectile problem of finding the source height from spattered
droplets of viscous fluid is a longstanding obstacle to accident reconstruction
and crime scene analysis. It is widely known how to infer the impact angle of
droplets on a surface from the elongation of their impact profiles. However,
the lack of velocity information makes finding the height of the origin from
the impact position and angle of individual drops not possible. From aggregate
statistics of the spatter and basic equations of projectile motion, we
introduce a reciprocal correlation plot that is effective when the polar launch
angle is concentrated in a narrow range. The vertical coordinate depends on the
orientation of the spattered surface, and equals the tangent of the impact
angle for a level surface. When the horizontal plot coordinate is twice the
reciprocal of the impact distance, we can infer the source height as the slope
of the data points in the reciprocal correlation plot. If the distribution of
launch angles is not narrow, failure of the method is evident in the lack of
linear correlation. We perform a number of experimental trials, as well as
numerical calculations and show that the height estimate is insensitive to
aerodynamic drag. Besides its possible relevance for crime investigation,
reciprocal-plot analysis of spatter may find application to volcanism and other
topics and is most immediately applicable for undergraduate science and
engineering students in the context of crime-scene analysis.Comment: To appear in the American Journal of Physics (ms 23338). Improved
readability and organization in this versio
Transport in a highly asymmetric binary fluid mixture
We present molecular dynamics calculations of the thermal conductivity and
viscosities of a model colloidal suspension with colloidal particles roughly
one order of magnitude larger than the suspending liquid molecules. The results
are compared with estimates based on the Enskog transport theory and effective
medium theories (EMT) for thermal and viscous transport. We find, in
particular, that EMT remains well applicable for predicting both the shear
viscosity and thermal conductivity of such suspensions when the colloidal
particles have a ``typical'' mass, i.e. much larger than the liquid molecules.
Very light colloidal particles on the other hand yield higher thermal
conductivities, in disagreement with EMT. We also discuss the consequences of
these results to some proposed mechanisms for thermal conduction in
nanocolloidal suspensions.Comment: 13 pages, 6 figures, to appear in Physical Review E (2007
Sign-symmetry of temperature structure functions
New scalar structure functions with different sign-symmetry properties are
defined. These structure functions possess different scaling exponents even
when their order is the same. Their scaling properties are investigated for
second and third orders, using data from high-Reynolds-number atmospheric
boundary layer. It is only when structure functions with disparate
sign-symmetry properties are compared can the extended self-similarity detect
two different scaling ranges that may exist, as in the example of convective
turbulence.Comment: 18 pages, 5 figures, accepted for publication in Physical Review
Destabilizing Taylor-Couette flow with suction
We consider the effect of radial fluid injection and suction on
Taylor-Couette flow. Injection at the outer cylinder and suction at the inner
cylinder generally results in a linearly unstable steady spiralling flow, even
for cylindrical shears that are linearly stable in the absence of a radial
flux. We study nonlinear aspects of the unstable motions with the energy
stability method. Our results, though specialized, may have implications for
drag reduction by suction, accretion in astrophysical disks, and perhaps even
in the flow in the earth's polar vortex.Comment: 34 pages, 9 figure
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