284 research outputs found
Dissipative flows of 2D foams
We analyze the flow of a liquid foam between two plates separated by a gap of
the order of the bubble size (2D foam). We concentrate on the salient features
of the flow that are induced by the presence, in an otherwise monodisperse
foam, of a single large bubble whose size is one order of magnitude larger than
the average size. We describe a model suited for numerical simulations of flows
of 2D foams made up of a large number of bubbles. The numerical results are
successfully compared to analytical predictions based on scaling arguments and
on continuum medium approximations. When the foam is pushed inside the cell at
a controlled rate, two basically different regimes occur: a plug flow is
observed at low flux whereas, above a threshold, the large bubble migrates
faster than the mean flow. The detailed characterization of the relative
velocity of the large bubble is the essential aim of the present paper. The
relative velocity values, predicted both from numerical and from analytical
calculations that are discussed here in great detail, are found to be in fair
agreement with experimental results
Experimental evidence of flow destabilization in a 2D bidisperse foam
Liquid foam flows in a Hele-Shaw cell were investigated. The plug flow
obtained for a monodisperse foam is strongly perturbed in the presence of
bubbles whose size is larger than the average bubble size by an order of
magnitude at least. The large bubbles migrate faster than the mean flow above a
velocity threshold which depends on its size. We evidence experimentally this
new instability and, in case of a single large bubble, we compare the large
bubble velocity with the prediction deduced from scaling arguments. In case of
a bidisperse foam, an attractive interaction between large bubbles induces
segregation and the large bubbles organize themselves in columns oriented along
the flow. These results allow to identify the main ingredients governing 2D
polydisperse foam flows
Embeddings of SL(2,Z) into the Cremona group
Geometric and dynamic properties of embeddings of SL(2,Z) into the Cremona
group are studied. Infinitely many non-conjugate embeddings which preserve the
type (i.e. which send elliptic, parabolic and hyperbolic elements onto elements
of the same type) are provided. The existence of infinitely many non-conjugate
elliptic, parabolic and hyperbolic embeddings is also shown.
In particular, a group G of automorphisms of a smooth surface S obtained by
blowing-up 10 points of the complex projective plane is given. The group G is
isomorphic to SL(2,Z), preserves an elliptic curve and all its elements of
infinite order are hyperbolic.Comment: to appear in Transformation Group
An analytical analysis of vesicle tumbling under a shear flow
Vesicles under a shear flow exhibit a tank-treading motion of their membrane,
while their long axis points with an angle < 45 degrees with respect to the
shear stress if the viscosity contrast between the interior and the exterior is
not large enough. Above a certain viscosity contrast, the vesicle undergoes a
tumbling bifurcation, a bifurcation which is known for red blood cells. We have
recently presented the full numerical analysis of this transition. In this
paper, we introduce an analytical model that has the advantage of being both
simple enough and capturing the essential features found numerically. The model
is based on general considerations and does not resort to the explicit
computation of the full hydrodynamic field inside and outside the vesicle.Comment: 19 pages, 9 figures, to be published in Phys. Rev.
Normal subgroups in the Cremona group (long version)
Let k be an algebraically closed field. We show that the Cremona group of all
birational transformations of the projective plane P^2 over k is not a simple
group. The strategy makes use of hyperbolic geometry, geometric group theory,
and algebraic geometry to produce elements in the Cremona group that generate
non trivial normal subgroups.Comment: With an appendix by Yves de Cornulier. Numerous but minors
corrections were made, regarding proofs, references and terminology. This
long version contains detailled proofs of several technical lemmas about
hyperbolic space
Mechanical probing of liquid foam aging
We present experimental results on the Stokes experiment performed in a 3D
dry liquid foam. The system is used as a rheometric tool : from the force
exerted on a 1cm glass bead, plunged at controlled velocity in the foam in a
quasi static regime, local foam properties are probed around the sphere. With
this original and simple technique, we show the possibility of measuring the
foam shear modulus, the gravity drainage rate and the evolution of the bubble
size during coarsening
Hydrodynamic lift on bound vesicles
Bound vesicles subject to lateral forces such as arising from shear flow are
investigated theoretically by combining a lubrication analysis of the bound
part with a scaling approach to the global motion. A minor inclination of the
bound part leads to significant lift due to the additive effects of lateral and
tank-treading motions. With increasing shear rate, the vesicle unbinds from the
substrate at a critical value. Estimates are in agreement with recent
experimental data.Comment: 9 pages, one figur
Damping of liquid sloshing by foams
When a container is set in motion, the free surface of the liquid starts to
oscillate or slosh. Such effects can be observed when a glass of water is
handled carelessly and the fluid sloshes or even spills over the rims of the
container. However, beer does not slosh as readily as water, which suggests
that foam could be used to damp sloshing. In this work, we study experimentally
the effect on sloshing of a liquid foam placed on top of a liquid bath. We
generate a monodisperse two-dimensional liquid foam in a rectangular container
and track the motion of the foam. The influence of the foam on the sloshing
dynamics is experimentally characterized: only a few layers of bubbles are
sufficient to significantly damp the oscillations. We rationalize our
experimental findings with a model that describes the foam contribution to the
damping coefficient through viscous dissipation on the walls of the container.
Then we extend our study to confined three-dimensional liquid foam and observe
that the behavior of 2D and confined 3D systems are very similar. Thus we
conclude that only the bubbles close to the walls have a significant impact on
the dissipation of energy. The possibility to damp liquid sloshing using foam
is promising in numerous industrial applications such as the transport of
liquefied gas in tankers or for propellants in rocket engines.Comment: 17 pages, accepted in Physics of Fluid
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