23,615 research outputs found
Coffee-stain growth dynamics on dry and wet surfaces
The drying of a drop containing particles often results in the accumulation
of the particles at the contact line. In this work, we investigate the drying
of an aqueous colloidal drop surrounded by a hydrogel that is also evaporating.
We combine theoretical and experimental studies to understand how the
surrounding vapor concentration affects the particle deposit during the
constant radius evaporation mode. In addition to the common case of evaporation
on an otherwise dry surface, we show that in a configuration where liquid is
evaporating from a flat surface around the drop, the singularity of the
evaporative flux at the contact line is suppressed and the drop evaporation is
homogeneous. For both conditions, we derive the velocity field and we establish
the temporal evolution of the number of particles accumulated at the contact
line. We predict the growth dynamics of the stain and the drying timescales.
Thus, dry and wet conditions are compared with experimental results and we
highlight that only the dynamics is modified by the evaporation conditions, not
the final accumulation at the contact line
The Lefschetz-Lunts formula for deformation quantization modules
We adapt to the case of deformation quantization modules a formula of V.
Lunts who calculates the trace of a kernel acting on Hochschild homology.Comment: 19 pages; Mathematische Zeitschrift 201
Homogeneous deposition of particles by absorption on hydrogels
When a drop containing colloidal particles evaporates on a surface, a
circular stain made of these particles is often observed due to an internal
flow toward the contact line. To hinder this effect, several approaches have
been proposed such as flow modification by addition of surfactants or control
of the interactions between the particles. All of these strategies involve the
liquid phase while maintaining the drying process. However, substitution of
evaporation by absorption into the substrate of the solvent has been
investigated less. Here, we show that a droplet containing colloidal particles
deposited on swelling hydrogels can lead to a nearly uniform coating. We report
experiments and theory to explore the relation between the gel swelling,
uniformity of deposition and the adsorption dynamics of the particles at the
substrate. Our findings suggest that draining the solvent by absorption
provides a robust route to homogeneous coatings
Self-crumpling elastomers: bending induced by the drying stimulus of a nanoparticle suspension
We report an experimental study of the drying-induced peeling of a bilayer,
consisting of an elastomeric disk coated with a suspension of nanoparticles. We
show that although capillary forces associated with the scale of the droplet
can not compete with the adhesion of the elastomer on a surface, nevertheless
large tensile stresses develop in the coating, which results in a moment
bending the bilayer. We attribute this stress to the nano-menisci in the pores
of the colloidal material and we propose a model that describes successfully
the early stage curvature of the bilayer. Thus, we show that the peeling can be
conveniently controlled by the particle size and the coating thickness.Comment: 6 pages, 5 figures, 1 table, accepted in EP
Bounded normal generation is not equivalent to topological bounded normal generation
We show that some derived full groups provide examples of non
simple Polish groups with the topological bounded normal generation property.
In particular, it follows that there are Polish groups with the topological
bounded normal generation property but not the bounded normal generation
property.Comment: 11 page
Mean-field limit for the stochastic Vicsek model
We consider the continuous version of the Vicsek model with noise, proposed
as a model for collective behavior of individuals with a fixed speed. We
rigorously derive the kinetic mean-field partial differential equation
satisfied when the number N of particles tends to infinity, quantifying the
convergence of the law of one particle to the solution of the PDE. For this we
adapt a classical coupling argument to the present case in which both the
particle system and the PDE are defined on a surface rather than on the whole
space. As part of the study we give existence and uniqueness results for both
the particle system and the PDE
A note on the derivation of rigid-plastic models
This note is devoted to a rigorous derivation of rigid-plasticity as the
limit of elasto-plasticity when the elasticity tends to infinity
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