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Seminars are held on Wednesdays
at 4:00 pm
Room 3361, Engr. II Bldg.
Prof. Alex Levine
University of California, Los Angeles
"Sailing the Surfactant Sea: Hydrodynamics in Flat and Curved Membranes"
Abstract:
We calculate the dynamics of particles embedded in viscous or
viscoelastic membranes. Specializing to viscous membranes or
liquid--liquid interfaces, we examine the mobility of particles embedded
therein as well as the hydrodynamic interactions between them. These
results extend the work of Saffmann and Delbrück to consider the
mobilities of both rigid and deformable extended objects (e.g.
semiflexible polymers) in membranes. We also explore the role of
interfacial geometry by examining the mobilities of point particles and
rigid rods on a spherical liquid--liquid interface. Finally, we compare
our theoretical calculations to interfacial microrheological
measurements [E. Weeks et al.] on flat liquid interfaces and
measurements of the mobilities of colloidal particles and particle
aggregates on the surface of a water droplet in oil [A.D. Dinsmore et al.].
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Prof. C.H.K. Williamson
Cornell University
"New Phenomena in Vortex-Induced Vibrations"
Abstract:
In this presentation, we summarize phenomena concerning vortex-induced
vibration (VIV), that have been discovered over the last few years (see
for example, Williamson & Govardhan, /Annual Review of Fluid Mechanics/,
2004). We pay special attention to the vortex dynamics and energy
transfer that give rise to modes of vibration. We present new vortex
wake modes from several different flow-structure configurations (for
example, involving 2 degrees of freedom, tethered bodies, pivoted
bodies, or freely-falling bodies) often in the framework of the
Williamson-Roshko (1988) map of vortex modes compiled from forced
(controlled) vibration studies. New modes include the formation of
vortex triplets, co-rotating vortices and vortex rings. We have
discovered a generic phenomenon in VIV whereby an elastically-mounted
body can continue to resonate even as the normalised flow velocities
becomes infinitely large, i.e. as the vibration frequency, f >> natural
frequency, f_N , which is radically different from classical resonance,
where f ~ f_N . This is only possible if the mass of the structure falls
just below a special critical value! Correspondingly, we find that
freely rising bodies (spheres and cylinders, for example) will only
vibrate as they rise, if their relative density falls below a critical
value, closely related to that found in our VIV studies. This contrasts
with the general belief, in the case of spheres, that they vibrate for
all rising conditions. We shall throw light on the large unexplained
scatter found in the classical Griffin plot (a plot of the peak
vibration amplitudes versus mass-damping) over the last 30 years. There
exists a distinct trend of increasing peak amplitude as Reynolds number
increases. If we go on to renormalise the axes of the plot to take
account of Reynolds numbers, then we find a beautiful collapse of peak
amplitude data in a "modified" Griffin plot. Finally, we shall present
some preliminary ultra high-resolution forced vibration experiments,
which are able to predict catastrophic jumps and several other
characteristics of free vibration response.
We gratefully acknowledge the support of the ONR, monitored by Tom Swean
(Contract No. N00014-04-1-0031).
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Special CIRF Seminar:
Friday, April 13
1:30 pm
Room 3361 Engr II Bldg.
Marie Farge - ENS Paris, France
Kai Schneider - Universite de Provence, Marseille, France
"Multisolution Modeling and Simulation of Turbulence"
Turbulence is characterized by its nonlinear and multiscale behaviour,
self-organization into coherent structures and generic randomness. The
number of active spatial and temporal scales involved increases with the
Reynolds number, therefore it soon becomes prohibitive for direct
numerical simulation. However, observations show that for a given flow
realization these scales are not homogeneously distributed, neither in
space nor in time, which corresponds to the flow intermittency. To be
able to benefit from this property, a suitable representation of the
flow should reflect the lacunarity of the fine scale activity, in both
space and time.
A prominent tool for multiscale decompositions are wavelets. A wavelet
is a well localized oscillating smooth function, i.e. a wave packet,
which is dilated and translated. The thus obtained wavelet family allows
to decompose a flow field into orthogonal scale-space contributions. The
flow intermittency is reflected in the sparsity of the wavelet
representation, i.e. only few coefficients, the strongest ones, are
necessary to represent the dynamically active part of the flow. We will
illustrate this by considering different 2D
and 3D turbulent flows, either computed by direct numerical simulation
(DNS) or measured by particle image velocimetry (PIV).
To compute the evolution of turbulent flows we have proposed the
Coherent Vortex Simulation (CVS), which is based on the wavelet filtered
Navier-Stokes equations. At each time step the turbulent fluctuations
are split into two orthogonal parts: the first corresponding to the
coherent vortices which are kept, and the second to an incoherent
background flow corresponding to turbulent dissipation which is
discarded. We will present several simulations of 2D and 3D turbulent
flows and show that CVS preserves their nonlinear dynamics.
Related publications can be downloaded from the following web page:
wavelets.ens.fr
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Arun Ramachandran
UC Santa Barbara
"Shear-Induced Migration Phenomena in Concentrated Suspensions"
Abstract:
When a concentrated suspension of non-colloidal particles is subjected
to a shear flow, particle migration is observed from regions of high
shear stress to low, high concentration to low and high streamline
curvature to low. This is the phenomenon of shear-induced migration.
Such migration processes are particularly important in the casting of
composite materials and in the transport of suspensions of biological
cells. Shear-induced migration successfully explains the resuspension
and transport of particles in viscous slurries. Particle migration may
also be exploited to effect separation between particles and suspending
fluid. During my PhD at Notre Dame, I have studied the phenomenon of
shear-induced particle migration and its effect on the flow behavior of
concentrated suspensions both experimentally and theoretically. Some of
these interesting effects are described below and will be presented
during the talk.
A fascinating rheological feature of suspensions is that they exhibit an
anisotropic microstructure which manifests itself as a non-Newtonian
rheology. In particular, particle interactions give rise to both a
particle pressure analogous to the osmotic pressure of colloidal
suspensions, and significant normal stress differences. A short
demonstration will be used to elucidate the non-Newtonian nature of
suspensions. These normal stresses have been shown to quantitatively
describe the shear-induced migration of particles across streamlines.
What is less appreciated, however, is that they also lead to non-zero
secondary currents that can have a profound influence on particle
distributions within the cross-section in 'unidirectional' flow through
a conduit. The implications of secondary currents driven by the second
normal stress differences will be discussed during the presentation. In
particular, these convective flows are expected to reverse the direction
of buoyancy-induced convection in resuspension flows, to sweep particles
out of notches and corners, and to lead to instabilities in such simple
geometries as plane-Poiseuille flow.
Shear-induced migration lends complex dynamics to the flow
of a suspension through an empty conduit. For example, when a
suspension is pumped through an empty rectangular slot of large aspect
ratio, the interface between the suspension, the displacing fluid, and
air, the displaced fluid, is observed to become unstable due to viscous
fingering. This is a rather surprising result considering that the
displacement of a low viscosity medium (air) by a highly viscous medium
(suspension) is actually a favorable mobility combination as regards
stability. The cause of this instability is the well known meniscus
accumulation phenomenon, which is a result of shear-induced migration.
This instability will be demonstrated during the presentation.
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L. Mahadevan
Harvard University
"Extreme Elastrohydrodynamics: of Flags, Flying Carpets, Flytraps"
Abstract:
The borderlands between elasticity and hydrodynamics lead naturally to a
number of moving boundary problems in elastohydrodynamics. I will
discuss some phenomena in this rich area involving extreme geometries:
the flutter of a slender flag in a breeze (and analogies to fish
swimming), the lift on a soft fluid-lubricated solid sliding/rolling
near a wall (with implications for joint lubrication), and the dynamics
of fluid-filled tissues (relevant to a variety of problems involving
soft hydraulics). Back to top
Aditya Khair
UC Santa Barbara
"Particle Motion in Colloidal Dispersions: Applications to Microrheology and Nonequilibruim Depletion Interactions"
Abstract:
Over the past decade, microrheology has burst onto the scene as a
technique to interrogate and manipulate complex fluids and biological
materials at the microscopic scale. In this talk, we investigate a
paradigmatic model for microrheology: an externally driven Brownian
"probe" particle traveling through an otherwise quiescent colloidal
dispersion. From the probe's motion one can infer a "microviscosity" of
the dispersion via application of Stokes drag law. Depending on the
amplitude and time-dependence of the probe's movement, the linear or
nonlinear (micro-)rheological response of the dispersion may be
inferred: from steady, arbitrary-amplitude motion we compute a nonlinear
microviscosity, while small-amplitude oscillatory motion yields a
frequency-dependent (complex) microviscosity. These two microviscosities
are shown, after appropriate scaling, to be in good agreement with their
(macro)-rheological counterparts.
Secondly, on a related theme, we consider two probes translating in-line
with equal velocities through a colloidal dispersion, as a model for
depletion interactions out of equilibrium. The probes disturb the
tranquility of the dispersion; in retaliation, the dispersion exerts an
entropic (depletion) force on each probe, which depends on the velocity
of the probes and their separation. When moving "slowly" we recover the
well-known equilibrium depletion attraction between the probes. For
"rapid" motion, there is a large accumulation of particles in a thin
boundary layer on the upstream side of the leading probe, whereas the
trailing probe moves in a tunnel, or wake, of particle-free solvent
created by the leading probe. Consequently, the entropic force on the
trailing probe vanishes, while the force on the leading probe approaches
a limiting value, equal to that for a single translating probe.
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Lutz Lesshafft
UC Santa Barbara
"Global Modes and Sound Radiation in Self-Excited Hot Jets"
Abstract:
As a jet is sufficiently heated with respect to the ambient air, it may
display self-excited oscillations that give rise to a highly regular
street of ring vortices. This self-excited behavior is described in
theoretical terms as a nonlinear global mode. Theoretical criteria
developed in the context of model equations accurately predict the onset
as well as the naturally selected frequency of these oscillations, as
observed in direct numerical simulations. The acoustic far field
generated by a vortex street in a hot jet is directly resolved in the
DNS: it displays the directivity of a compact dipole. An analysis of the
Lighthill equation identifies entropy fluctuations in the jet as the
dominant acoustic source mechanism. The observability of superdirective
sound radiation in low Mach number jets will be discussed. Back to top
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Page Revised May 30, 2007 - webmaster
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