335 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
Lateral migration of a 2D vesicle in unbounded Poiseuille flow
The migration of a suspended vesicle in an unbounded Poiseuille flow is
investigated numerically in the low Reynolds number limit. We consider the
situation without viscosity contrast between the interior of the vesicle and
the exterior. Using the boundary integral method we solve the corresponding
hydrodynamic flow equations and track explicitly the vesicle dynamics in two
dimensions. We find that the interplay between the nonlinear character of the
Poiseuille flow and the vesicle deformation causes a cross-streamline migration
of vesicles towards the center of the Poiseuille flow. This is in a marked
contrast with a result [L.G. Leal, Ann. Rev. Fluid Mech. 12,
435(1980)]according to which the droplet moves away from the center (provided
there is no viscosity contrast between the internal and the external fluids).
The migration velocity is found to increase with the local capillary number
(defined by the time scale of the vesicle relaxation towards its equilibrium
shape times the local shear rate), but reaches a plateau above a certain value
of the capillary number. This plateau value increases with the curvature of the
parabolic flow profile. We present scaling laws for the migration velocity.Comment: 11 pages with 4 figure
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
Structure-dependent mobility of a dry aqueous foam flowing along two parallel channels
The velocity of a two-dimensional aqueous foam has been measured as it flows
through two parallel channels, at a constant overall volumetric flow rate. The
flux distribution between the two channels is studied as a function of the
ratio of their widths. A peculiar dependence of the velocity ratio on the width
ratio is observed when the foam structure in the narrower channel is either
single staircase or bamboo. In particular, discontinuities in the velocity
ratios are observed at the transitions between double and single staircase and
between single staircase and bamboo. A theoretical model accounting for the
viscous dissipation at the solid wall and the capillary pressure across a film
pinned at the channel outlet predicts the observed non-monotonic evolution of
the velocity ratio as a function of the width ratio. It also predicts
quantitatively the intermittent temporal evolution of the velocity in the
narrower channel when it is so narrow that film pinning at its outlet
repeatedly brings the flow to a near stop
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
Growth laws and self-similar growth regimes of coarsening two-dimensional foams: Transition from dry to wet limits
We study the topology and geometry of two dimensional coarsening foams with
arbitrary liquid fraction. To interpolate between the dry limit described by
von Neumann's law, and the wet limit described by Marqusee equation, the
relevant bubble characteristics are the Plateau border radius and a new
variable, the effective number of sides. We propose an equation for the
individual bubble growth rate as the weighted sum of the growth through
bubble-bubble interfaces and through bubble-Plateau borders interfaces. The
resulting prediction is successfully tested, without adjustable parameter,
using extensive bidimensional Potts model simulations. Simulations also show
that a selfsimilar growth regime is observed at any liquid fraction and
determine how the average size growth exponent, side number distribution and
relative size distribution interpolate between the extreme limits. Applications
include concentrated emulsions, grains in polycrystals and other domains with
coarsening driven by curvature
Influence of shear flow on vesicles near a wall: a numerical study
We describe the dynamics of three-dimensional fluid vesicles in steady shear
flow in the vicinity of a wall. This is analyzed numerically at low Reynolds
numbers using a boundary element method. The area-incompressible vesicle
exhibits bending elasticity. Forces due to adhesion or gravity oppose the
hydrodynamic lift force driving the vesicle away from a wall. We investigate
three cases. First, a neutrally buoyant vesicle is placed in the vicinity of a
wall which acts only as a geometrical constraint. We find that the lift
velocity is linearly proportional to shear rate and decreases with increasing
distance between the vesicle and the wall. Second, with a vesicle filled with a
denser fluid, we find a stationary hovering state. We present an estimate of
the viscous lift force which seems to agree with recent experiments of Lorz et
al. [Europhys. Lett., vol. 51, 468 (2000)]. Third, if the wall exerts an
additional adhesive force, we investigate the dynamical unbinding transition
which occurs at an adhesion strength linearly proportional to the shear rate.Comment: 17 pages (incl. 10 figures), RevTeX (figures in PostScript
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
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