134 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
A Scaling Theory of the Competition between Interdiffusion and Cross-Linking at Polymer Interfaces
We study theoretically situations where competition arises between an
interdiffusion process and a cross-linking chemical reaction at interfaces
between pieces of the same polymer material. An example of such a situation is
observable in the formation of latex films, where, in the presence of a
cross-linking additive, colloidal polymer particles initially in suspension
come at contact as the solvent evaporates, and, optimally, coalesce into a
continuous coating. We considered the low cross-link density situation in a
previous paper (A. Aradian, E. Raphael, P.-G. de Gennes, Macromolecules 33,
9444 (2000)), and presented a simple control parameter that determines the
final state of the interface. In the present article, with the help of simple
scaling arguments, we extend our description to higher cross-link densities. We
provide predictions for the strength of the interface in different favorable
and unfavorable regimes, and discuss how it can be optimized.Comment: 19 pages, 5 figures. To appear in Macromolecule
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
Surface flows of granular materials: A short introduction to some recent models
We present a short review of recent theoretical descriptions of flows
occuring at the surface of granular piles, and focus mainly on two models: the
phenomenological ``BCRE'' model and the hydrodynamic model, based on
Saint-Venant equations. Both models distinguish a ``static phase'' and a
``rolling'' phase inside the granular packing and write coupled equations for
the evolutions of the height of each of these phases, which prove similar in
both approaches. The BCRE description provides a very intuitive picture of the
flow, whereas the Saint-Venant hydrodynamic description establishes a general
and rigorous framework for granular flow studies.Comment: 10 pages, 3 figures, published in a special issue of C. R. Physique
(Paris) on granular matte
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
Granular Flows in a Rotating Drum: the Scaling Law between Velocity and Thickness of the Flow
The flow of dry granular material in a half-filled rotating drum is studied.
The thickness of the flowing zone is measured for several rotation speeds, drum
sizes and beads sizes (size ratio between drum and beads ranging from 47 to
7400). Varying the rotation speed, a scaling law linking mean velocity vs
thickness of the flow, , is deduced for each couple (beads, drum).
The obtained exponent is not always equal to 1, value previously reported
in a drum, but varies with the geometry of the system. For small size ratios,
exponents higher than 1 are obtained due to a saturation of the flowing zone
thickness. The exponent of the power law decreases with the size ratio, leading
to exponents lower than 1 for high size ratios. These exponents imply that the
velocity gradient of a dry granular flow in a rotating drum is not constant.
More fundamentally, these results show that the flow of a granular material in
a rotating drum is very sensible to the geometry, and that the deduction of the
``rheology'' of a granular medium flowing in such a geometry is not obvious
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
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