63 research outputs found
Flow instabilities in complex fluids: Nonlinear rheology and slow relaxations
We here present two simplified models aimed at describing the long-term,
irregular behaviours observed in the rheological response of certain complex
fluids, such as periodic oscillations or chaotic-like variations. Both models
exploit the idea of having a (non-linear) rheological equation, controlling the
temporal evolution of the stress, where one of the participating variables (a
"structural" variable) is subject to a distinct dynamics with a different
relaxation time. The coupling between the two dynamics is a source of
instability.Comment: Proceedings of "Slow Dynamics in Complex Systems 2003" (Sendai,
Japan, Nov. 2003
Instability and spatiotemporal rheochaos in a shear-thickening fluid model
We model a shear-thickening fluid that combines a tendency to form
inhomogeneous, shear-banded flows with a slow relaxational dynamics for fluid
microstructure. The interplay between these factors gives rich dynamics, with
periodic regimes (oscillating bands, travelling bands, and more complex
oscillations) and spatiotemporal rheochaos. These phenomena, arising from
constitutive nonlinearity not inertia, can occur even when the steady-state
flow curve is monotonic. Our model also shows rheochaos in a low-dimensional
truncation where sharply defined shear bands cannot form
Dewetting on porous media with aspiration
We consider a porous solid covered with a water film (or with a drop) in
situations where the liquid is pumped in, either spontaneously (if the porous
medium is hydrophilic) or mechanically (by an external pump). The dynamics of
dewetting is then strongly modified. We analyse a few major examples: a)
horizontal films, which break at a certain critical thickness, b) the "modified
Landau-Levich problem" where a porous plate moves up from a bath and carries a
film: aspiration towards the plate limits the height H reached by the film, c)
certain situation where the hysteresis of contact angles is important.Comment: Revised version: The analysis of the 'modified Landau-Levich problem'
(section 3) has been significantly revised. It is now treated as a singular
perturbation problem (using boundary-layer techniques), leading to a more
accurate physical pictur
Adhesion between a viscoelastic material and a solid surface
In this paper, we present a qualitative analysis of the dissipative processes
during the failure of the interface between a viscoelastic polymer and a solid
surface. We reassess the "viscoelastic trumpet" model [P.-G. de Gennes, C. R.
Acad. Sci. Paris, 307, 1949 (1988)], and show that, for a crosslinked polymer,
the interface toughness G(V) starts from a relatively low value, G_0, due to
local processes near the fracture tip, and rises up to a maximum of order (where and stand for the elastic
modulus of the material, respectively at low and high strain frequencies). This
enhancement of fracture energy is due to far-field viscous dissipation in the
bulk material, and begins for peel-rates V much lower than previously thought.
For a polymer melt, the adhesion energy is predicted to scale as 1/V. In the
second part of this paper, we compare some of our theoretical predictions with
experimental results about the viscoelastic adhesion between a
polydimethylsiloxane polymer melt and a glass surface. In particular, the
expected dependence of the fracture energy versus separation rate is confirmed
by the experimental data, and the observed changes in the concavity of the
crack profile are in good agreement with our simple model.Comment: Revised version to appear in Macromolecule
A minimal model for chaotic shear banding in shear-thickening fluids
We present a minimal model for spatiotemporal oscillation and rheochaos in
shear-thickening complex fluids at zero Reynolds number. In the model, a
tendency towards inhomogeneous flows in the form of shear bands combines with a
slow structural dynamics, modelled by delayed stress relaxation. Using
Fourier-space numerics, we study the nonequilibrium `phase diagram' of the
fluid as a function of a steady mean (spatially averaged) stress, and of the
relaxation time for structural relaxation. We find several distinct regions of
periodic behavior (oscillating bands, travelling bands, and more complex
oscillations) and also regions of spatiotemporal rheochaos. A low-dimensional
truncation of the model retains the important physical features of the full
model (including rheochaos) despite the suppression of sharply defined
interfaces between shear bands. Our model maps onto the FitzHugh-Nagumo model
for neural network dynamics, with an unusual form of long-range coupling.Comment: Revised version (in particular, new section III.E. and Appendix A
"Marginal pinching" in soap films
We discuss the behaviour of a thin soap film facing a frame element: the
pressure in the Plateau border around the frame is lower than the film
pressure, and the film thins out over a certain distance lambda(t), due to the
formation of a well-localized pinched region of thickness h(t) and extension
w(t). We construct a hydrodynamic theory for this thinning process, assuming a
constant surface tension: Marangoni effects are probably important only at late
stages, where instabilitites set in. We find lambda(t) ~ t^{1/4}, and for the
pinch dimensions h(t) ~ t^{-1/2}$ and w(t) ~ t^{-1/4}. These results may play a
useful role for the discussion of later instabilitites leading to a global film
thinning and drainage, as first discussed by K. Mysels under the name
``marginal regeneration''.Comment: 7 pages, 2 figure
Internal Stress in a Model Elasto-Plastic Fluid
Plastic materials can carry memory of past mechanical treatment in the form
of internal stress. We introduce a natural definition of the vorticity of
internal stress in a simple two-dimensional model of elasto-plastic fluids,
which generates the internal stress. We demonstrate how the internal stress is
induced under external loading, and how the presence of the internal stress
modifies the plastic behavior.Comment: 4 pages, 3 figure
Creep motion in a granular pile exhibiting steady surface flow
We investigate experimentally granular piles exhibiting steady surface flow.
Below the surface flow, it has been believed exisitence of a `frozen' bulk
region, but our results show absence of such a frozen bulk. We report here that
even the particles in deep layers in the bulk exhibit very slow flow and that
such motion can be detected at an arbitrary depth. The mean velocity of the
creep motion decays exponentially with depth, and the characteristic decay
length is approximately equal to the particle-size and independent of the flow
rate. It is expected that the creep motion we have seeen is observable in all
sheared granular systems.Comment: 3 pages, 4 figure
Oscillatory settling in wormlike-micelle solutions: bursts and a long time scale
We study the dynamics of a spherical steel ball falling freely through a
solution of entangled wormlike-micelles. If the sphere diameter is larger than
a threshold value, the settling velocity shows repeated short oscillatory
bursts separated by long periods of relative quiescence. We propose a model
incorporating the interplay of settling-induced flow, viscoelastic stress and,
as in M. E. Cates, D. A. Head and A. Ajdari, Phys. Rev. E, 2002, 66, 025202(R)
and A. Aradian and M. E. Cates, Phys. Rev. E, 2006, 73, 041508, a slow
structural variable for which our experiments offer independent evidence.Comment: To appear in Soft Matte
Continuous Avalanche Segregation of Granular Mixtures in Thin Rotating Drums
We study segregation of granular mixtures in the continuous avalanche regime
(for frequencies above ~ 1 rpm) in thin rotating drums using a continuum theory
for surface flows of grains. The theory predicts profiles in agreement with
experiments only when we consider a flux dependent velocity of flowing grains.
We find the segregation of species of different size and surface properties,
with the smallest and roughest grains being found preferentially at the center
of the drum. For a wide difference between the species we find a complete
segregation in agreement with experiments. In addition, we predict a transition
to a smooth segregation regime - with an power-law decay of the concentrations
as a function of radial coordinate - as the size ratio between the grains is
decreased towards one.Comment: 4 pages, 4 figures, http://polymer.bu.edu/~hmaks
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