872 research outputs found
The Liquid Blister Test
We consider a thin elastic sheet adhering to a stiff substrate by means of
the surface tension of a thin liquid layer. Debonding is initiated by imposing
a vertical displacement at the centre of the sheet and leads to the formation
of a delaminated region, or `blister'. This experiment reveals that the
perimeter of the blister takes one of three different forms depending on the
vertical displacement imposed. As this displacement is increased, we observe
first circular, then undulating and finally triangular blisters. We obtain
theoretical predictions for the observed features of each of these three
families of blisters. The theory is built upon the F\"{o}ppl-von K\'{a}rm\'{a}n
equations for thin elastic plates and accounts for the surface energy of the
liquid. We find good quantitative agreement between our theoretical predictions
and experimental results, demonstrating that all three families are governed by
different balances between elastic and capillary forces. Our results may bear
on micrometric tapered devices and other systems where elastic and adhesive
forces are in competition.Comment: 23 pages, 11 figs approx published versio
SLA Establishment with Guaranteed QoS in the Interdomain Network: A Stock Model
The new model that we present in this paper is introduced in the context of
guaranteed QoS and resources management in the inter-domain routing framework.
This model, called the stock model, is based on a reverse cascade approach and
is applied in a distributed context. So transit providers have to learn the
right capacities to buy and to stock and, therefore learning theory is applied
through an iterative process. We show that transit providers manage to learn
how to strategically choose their capacities on each route in order to maximize
their benefits, despite the very incomplete information. Finally, we provide
and analyse some simulation results given by the application of the model in a
simple case where the model quickly converges to a stable state.Comment: 19 pages, 19 figures, IJCNC,
http://airccse.org/journal/cnc/0711cnc13.pd
Buckling of swelling gels
The patterns arising from the differential swelling of gels are investigated
experimentally and theoretically as a model for the differential growth of
living tissues. Two geometries are considered: a thin strip of soft gel clamped
to a stiff gel, and a thin corona of soft gel clamped to a disk of stiff gel.
When the structure is immersed in water, the soft gel swells and bends out of
plane leading to a wavy periodic pattern which wavelength is measured. The
linear stability of the flat state is studied in the framework of linear
elasticity using the equations for thin plates. The flat state is shown to
become unstable to oscillations above a critical swelling rate and the computed
wavelengths are in quantitative agreement with the experiment
Evaporation of a thin film: diffusion of the vapour and Marangoni instabilities
The stability of an evaporating thin liquid film on a solid substrate is
investigated within lubrication theory. The heat flux due to evaporation
induces thermal gradients; the generated Marangoni stresses are accounted for.
Assuming the gas phase at rest, the dynamics of the vapour reduces to
diffusion. The boundary condition at the interface couples transfer from the
liquid to its vapour and diffusion flux. A non-local lubrication equation is
obtained; this non-local nature comes from the Laplace equation associated with
quasi-static diffusion. The linear stability of a flat film is studied in this
general framework. The subsequent analysis is restricted to moderately thick
films for which it is shown that evaporation is diffusion limited and that the
gas phase is saturated in vapour in the vicinity of the interface. The
stability depends only on two control parameters, the capillary and Marangoni
numbers. The Marangoni effect is destabilising whereas capillarity and
evaporation are stabilising processes. The results of the linear stability
analysis are compared with the experiments of Poulard et al (2003) performed in
a different geometry. In order to study the resulting patterns, the amplitude
equation is obtained through a systematic multiple-scale expansion. The
evaporation rate is needed and is computed perturbatively by solving the
Laplace problem for the diffusion of vapour. The bifurcation from the flat
state is found to be a supercritical transition. Moreover, it appears that the
non-local nature of the diffusion problem unusually affects the amplitude
equation
Wrinkling of pressurized elastic shells
We study the formation of localized structures formed by the point loading of an internally pressurized elastic shell. While unpressurized shells (such as a ping pong ball) buckle into polygonal structures, we show that pressurized shells are subject to a wrinkling instability. We present scaling laws for the critical indentation at which wrinkling occurs and the number of wrinkles formed in terms of the internal pressurization and material properties of the shell. These results are validated by numerical simulations. We show that the evolution of the wrinkle length with increasing indentation can be understood for highly pressurized shells from membrane theory. These results suggest that the position and number of wrinkles may be used in combination to give simple methods for the estimation of the mechanical properties of highly pressurized shells
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