842 research outputs found
Fluctuation assisted spreading of a fluid filled elastic blister
In this theoretical and numerical study, we show how spatially extended
fluctuations can influence and dominate the dynamics of a fluid filled elastic
blister as is deforms onto a pre-wetted solid substrate. To describe the
blister dynamics, we develop a stochastic elastohydrodynamic framework that
couples the viscous flow, the elastic bending of the interface and the noise
from the environment. We deploy a scaling analysis to find the
elastohydrodynamic spreading law a direct analogue
to the capillary spreading of drops, while the inclusion of noise in our model
highlights that the dynamics speed-up significantly
as local changes in curvature enhance the peeling of the elastic interface from
the substrate. Moreover, our analysis identifies a distinct criterion for the
transition between the deterministic and stochastic spreading regime, which is
further illustrated by numerical simulations
Supporting Information: Short and long time drop dynamics on lubricated substrates
Supporting Information: Short and long time drop dynamics on lubricated
substrate
Droplet settling on solids coated with a soft layer
Gravitational settling of a droplet in air onto a soft substrate is a
ubiquitous event relevant to many natural processes and engineering
applications. We study this phenomenon by developing a three-phase lubrication
model of droplet settling onto a solid substrate coated by a thin soft layer
represented by a viscous film, an elastic compressible layer and an elastic
sheet supported by a viscous film. By combining scaling analysis, analytical
methods, and numerical simulations we elucidate how the resulting droplet
dynamics is affected by the nature of the soft layer. We show that these soft
layers can significantly affect the droplet shape during gravitational
settling. When there is a linear response of the deformations of the soft
layer, the air layer takes longer to drain as compared to the case of a droplet
settling onto a rigid substrate. Our results provide new insight into the
coupled interactions between droplets and solids coated by a thin film of a
soft material.Comment: 26 pages, 13 figures, 1 tabl
Screening of the quantum dot F\"orster coupling at small distances
We study the near-field energy transfer rates between two finite size quantum
dot disks, generalizing the result of F\"orster coupling between two point
dipoles. In particular, we derive analytical results for the envelope of the
electronic wavefunction for model potentials at the boundaries of quantum dot
disks and demonstrate how the F\"orster interaction is screened as the size of
the dots becomes comparable to the dot-dot separation.Comment: 5 pages, 2 figure
Universal Self-Similar Attractor in the Bending-Driven Leveling of Thin Viscous Films
We study theoretically and numerically the bending-driven leveling of thin
viscous films within the lubrication approximation. We derive the Green's
function of the linearized thin-film equation and further show that it
represents a universal self-similar attractor at long times. As such, the
rescaled perturbation of the film profile converges in time towards the
rescaled Green's function, for any summable initial perturbation profile. In
addition, for stepped axisymmetric initial conditions, we demonstrate the
existence of another, short-term and one-dimensional-like self-similar regime.
Besides, we characterize the convergence time towards the long-term universal
attractor in terms of the relevant physical and geometrical parameters, and
provide the local hydrodynamic fields and global elastic energy in the
universal regime as functions of time. Finally, we extend our analysis to the
non-linear thin-film equation through numerical simulations
Directional spreading of a viscous droplet on a conical fibre
If a droplet is placed on a substrate with a conical shape it spontaneously
starts to spread in the direction of a growing fibre radius. We describe this
capillary spreading dynamics by developing a lubrication approximation on a
cone and by the perturbation method of matched asymptotic expansions. Our
results show that the droplet appears to adopt a quasi-static shape and the
predictions of the droplet shape and spreading velocity from the two
mathematical models are in excellent agreement for a wide range of slip
lengths, cone angles and equilibrium contact angles. At the contact line
regions, a large pressure gradient is generated by the mismatch between the
equilibrium contact angle and the apparent contact angle that maintains the
viscous flow. It is the conical shape of the substrate that breaks the
front/rear droplet symmetry in terms of the apparent contact angle, which is
larger at the thicker part of the cone than that at its thinner part.
Consequently, the droplet is predicted to move from the cone tip to its base,
consistent with experimental observations
Universality in dynamic wetting dominated by contact line friction
We report experiments on the rapid contact line motion present in the early
stages of capillary driven spreading of drops on dry solid substrates. The
spreading data fails to follow a conventional viscous or inertial scaling. By
integrating experiments and simulations, we quantify a contact line friction
(), which is seen to limit the speed of the rapid dynamic wetting. A
scaling based on this contact line friction is shown to yield a universal curve
for the evolution of the contact line radius as a function of time, for a range
of fluid viscosities, drop sizes and surface wettabilities
Static wetting of a barrel-shaped droplet on a soft-layer-coated fiber
A droplet can deform a soft substrate due to capillary forces when they are
in contact. We study the static deformation of a soft solid layer coated on a
rigid cylindrical fiber when an axisymmetric barrel-shaped droplet is embracing
it. We find that the elastic deformation increases with decreasing rigid fiber
radius. Significant disparities of deformation between the solid-liquid side
and the solid-gas side are found when their solid surface tensions are
different. When the coated layer is soft enough and the rigid fiber radius is
less than the thickness of the coated layer, pronounced displacement
oscillations are observed. Such slow decay of deformation with distances from
the contact line position suggests a possible long-range interaction between
droplets on a soft-layer-coated fiber.Comment: 8 pages, 6 figure
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