153 research outputs found
Regimes of wrinkling in an indented floating elastic sheet
A thin, elastic sheet floating on the surface of a liquid bath wrinkles when
poked at its centre. We study the onset of wrinkling as well as the evolution
of the pattern as indentation progresses far beyond the wrinkling threshold. We
use tension field theory to describe the macroscopic properties of the deformed
film and show that the system passes through a host of different regimes, even
while the deflections and strains remain small. We show that the effect of the
finite size of the sheet ultimately plays a key role in determining the
location of the wrinkle pattern, and obtain scaling relations that characterize
the number of wrinkles at threshold and its variation as the indentation
progresses. Some of our predictions are confirmed by recent experiments of Ripp
\emph{et al.} [arxiv: 1804.02421].Comment: 22 pages, 11 figures, revised versio
The 'Cheerios effect'
Objects that float at the interface between a liquid and a gas interact
because of interfacial deformation and the effect of gravity. We highlight the
crucial role of buoyancy in this interaction, which, for small particles,
prevails over the capillary suction that is often assumed to be the dominant
effect. We emphasize this point using a simple classroom demonstration, and
then derive the physical conditions leading to mutual attraction or repulsion.
We also quantify the force of interaction in some particular instances and
present a simple dynamical model of this interaction. The results obtained from
this model are then validated by comparison to experimental results for the
mutual attraction of two identical spherical particles. We conclude by looking
at some of the applications of the effect that can be found in the natural and
manmade worlds.Comment: 10 pages, 12 figures. (Typos in eqs 7 and 8 corrected
Regimes of wrinkling in pressurized elastic shells
We consider the point-indentation of a pressurized elastic shell. It has
previously been shown that such a shell is subject to a wrinkling instability
as the indentation depth is quasi-statically increased. Here we present
detailed analysis of this wrinkling instability using a combination of
analytical techniques and finite element simulations. In particular, we study
how the number of wrinkles observed at the onset of instability grows with
increasing pressurization. We also study how, for fixed pressurization, the
number of wrinkles changes both spatially and with increasing indentation depth
beyond onset. This `Far from threshold' analysis exploits the largeness of the
wrinkle wavenumber that is observed at high pressurization and leads to
quantitative differences with the standard `Near threshold' stability analysis.Comment: 21 pages, 8 figs. Minor typos correcte
Indentation metrology of clamped, ultra-thin elastic sheets
We study the indentation of ultrathin elastic sheets clamped to the edge of a
circular hole. This classical setup has received considerable attention lately,
being used by various experimental groups as a probe to measure the surface
properties and stretching modulus of thin solid films. Despite the apparent
simplicity of this method, the geometric nonlinearity inherent in the
mechanical response of thin solid objects renders the analysis of the resulting
data a nontrivial task. Importantly, the essence of this difficulty is in the
geometric coupling between in-plane stress and out-of-plane deformations, and
hence is present in the behaviour of Hookean solids even when the slope of the
deformed membrane remains small. Here we take a systematic approach to address
this problem, using the membrane limit of the F\"{o}ppl-von-K\'{a}rm\'{a}n
equations. This approach highlights some of the dangers in the use of
approximate formulae in the metrology of solid films, which can introduce large
errors; we suggest how such errors may be avoided in performing experiments and
analyzing the resulting data
Gravity currents in a porous medium at an inclined plane
We consider the release from a point source of relatively heavy fluid into a
porous saturated medium above an impermeable slope. We consider the case where
the volume of the resulting gravity current increases with time like
and show that for , at short times the current spreads
axisymmetrically, with radius , while at long times it
spreads predominantly downslope. In particular, for long times the downslope
position of the current scales like while the current extends a distance
across the slope. For , this situation is reversed
with spreading occurring predominantly downslope for short times. The governing
equations admit similarity solutions whose scaling behaviour we determine, with
the full similarity form being evaluated by numerical computations of the
governing partial differential equation. We find that the results of these
analyses are in good quantitative agreement with a series of laboratory
experiments. Finally, we briefly discuss the implications of our work for the
sequestration of carbon dioxide in aquifers with a sloping, impermeable cap.Comment: 10 pages, 6 figures - revised versio
Dynamic buckling of an inextensible elastic ring: Linear and nonlinear analyses
Slender elastic objects such as a column tend to buckle under loads. While
static buckling is well understood as a bifurcation problem, the evolution of
shapes during dynamic buckling is much harder to study. Elastic rings under
normal pressure have emerged as a theoretical and experimental paradigm for the
study of dynamic buckling with controlled loads. Experimentally, an elastic
ring is placed within a soap film. When the film outside the ring is removed,
surface tension pulls the ring inward, mimicking an external pressurization.
Here we present a theoretical analysis of this process by performing a
post-bifurcation analysis of an elastic ring under pressure. This analysis
allows us to understand how inertia, material properties, and loading affect
the observed shape. In particular, we combine direct numerical solutions with a
post-bifurcation asymptotic analysis to show that inertia drives the system
towards higher modes that cannot be selected in static buckling. Our
theoretical results explain experimental observations that cannot be captured
by a standard linear stability analysis.Comment: 18 pages, 10 figure
Equilibrium Conditions for the Floating of Multiple Interfacial Objects
We study the effect of interactions between objects floating at fluid
interfaces, for the case in which the objects are primarily supported by
surface tension. We give conditions on the density and size of these objects
for equilibrium to be possible and show that two objects that float when
well-separated may sink as the separation between the objects is decreased.
Finally, we examine the equilbrium of a raft of strips floating at an
interface, and find that rafts of sufficiently low density may have infinite
spatial extent, but that above a critical raft density, all rafts sink if they
are sufficiently large. We compare our numerical and asymptotic results with
some simple table-top experiments, and find good quantitative agreement.Comment: 10 pages, 7 figure
Passive control of viscous flow via elastic snap-through
We demonstrate the passive control of viscous flow in a channel by using an
elastic arch embedded in the flow. Depending on the fluid flux, the arch may
`snap' between two states --- constricting and unconstricting --- that differ
in hydraulic conductivity by up to an order of magnitude. We use a combination
of experiments at a macroscopic scale and theory to study the constricting and
unconstricting states, and determine the critical flux required to transition
between them. We show that such a device may be precisely tuned for use in a
range of applications, and in particular has potential as a passive
microfluidic fuse to prevent excessive fluxes in rigid-walled channels.Comment: Main text 5 pages, Supplementary Information 14 page
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