988 research outputs found
Motion of nanodroplets near edges and wedges
Nanodroplets residing near wedges or edges of solid substrates exhibit a
disjoining pressure induced dynamics. Our nanoscale hydrodynamic calculations
reveal that non-volatile droplets are attracted or repelled from edges or
wedges depending on details of the corresponding laterally varying disjoining
pressure generated, e.g., by a possible surface coating.Comment: 12 pages, 7 figure
Droplet motion driven by surface freezing or melting: A mesoscopic hydrodynamic approach
A fluid droplet may exhibit self-propelled motion by modifying the wetting
properties of the substrate. We propose a novel model for droplet propagation
upon a terraced landscape of ordered layers formed as a result of surface
freezing driven by the contact angle dependence on the terrace thickness.
Simultaneous melting or freezing of the terrace edge results in a joint
droplet-terrace motion. The model is tested numerically and compared to
experimental observations on long-chain alkane system in the vicinity of the
surface melting point.Comment: 4 pages, 3 figure
Dissipation in Dynamics of a Moving Contact Line
The dynamics of the deformations of a moving contact line is studied assuming
two different dissipation mechanisms. It is shown that the characteristic
relaxation time for a deformation of wavelength of a contact line
moving with velocity is given as . The velocity
dependence of is shown to drastically depend on the dissipation
mechanism: we find for the case when the dynamics is governed
by microscopic jumps of single molecules at the tip (Blake mechanism), and
when viscous hydrodynamic losses inside the moving
liquid wedge dominate (de Gennes mechanism). We thus suggest that the debated
dominant dissipation mechanism can be experimentally determined using
relaxation measurements similar to the Ondarcuhu-Veyssie experiment [T.
Ondarcuhu and M. Veyssie, Nature {\bf 352}, 418 (1991)].Comment: REVTEX 8 pages, 9 PS figure
"Marginal pinching" in soap films
We discuss the behaviour of a thin soap film facing a frame element: the
pressure in the Plateau border around the frame is lower than the film
pressure, and the film thins out over a certain distance lambda(t), due to the
formation of a well-localized pinched region of thickness h(t) and extension
w(t). We construct a hydrodynamic theory for this thinning process, assuming a
constant surface tension: Marangoni effects are probably important only at late
stages, where instabilitites set in. We find lambda(t) ~ t^{1/4}, and for the
pinch dimensions h(t) ~ t^{-1/2}$ and w(t) ~ t^{-1/4}. These results may play a
useful role for the discussion of later instabilitites leading to a global film
thinning and drainage, as first discussed by K. Mysels under the name
``marginal regeneration''.Comment: 7 pages, 2 figure
Dynamical Model for Chemically Driven Running Droplets
We propose coupled evolution equations for the thickness of a liquid film and
the density of an adsorbate layer on a partially wetting solid substrate.
Therein, running droplets are studied assuming a chemical reaction underneath
the droplets that induces a wettability gradient on the substrate and provides
the driving force for droplet motion. Two different regimes for moving droplets
-- reaction-limited and saturated regime -- are described. They correspond to
increasing and decreasing velocities with increasing reaction rates and droplet
sizes, respectively. The existence of the two regimes offers a natural
explanation of prior experimental observations.Comment: 4 pages, 5 figure
Rayleigh and depinning instabilities of forced liquid ridges on heterogeneous substrates
Depinning of two-dimensional liquid ridges and three-dimensional drops on an
inclined substrate is studied within the lubrication approximation. The
structures are pinned to wetting heterogeneities arising from variations of the
strength of the short-range polar contribution to the disjoining pressure. The
case of a periodic array of hydrophobic stripes transverse to the slope is
studied in detail using a combination of direct numerical simulation and
branch-following techniques. Under appropriate conditions the ridges may either
depin and slide downslope as the slope is increased, or first breakup into
drops via a transverse instability, prior to depinning. The different
transition scenarios are examined together with the stability properties of the
different possible states of the system.Comment: Physics synopsis link:
http://physics.aps.org/synopsis-for/10.1103/PhysRevE.83.01630
Capillary-Gravity Waves on Depth-Dependent Currents: Consequences for the Wave Resistance
We study theoretically the capillary-gravity waves created at the water-air
interface by a small two-dimensional perturbation when a depth-dependent
current is initially present in the fluid. Assuming linear wave theory, we
derive a general expression of the wave resistance experienced by the
perturbation as a function of the current profile in the case of an inviscid
fluid. We then analyze and discuss in details the behavior of the wave
resistance in the particular case of a linear current, a valid approximation
for some wind generated currents.Comment: Submitted to EP
Scattering below critical energy for the radial 4D Yang-Mills equation and for the 2D corotational wave map system
We describe the asymptotic behavior as time goes to infinity of solutions of
the 2 dimensional corotational wave map system and of solutions to the 4
dimensional, radially symmetric Yang-Mills equation, in the critical energy
space, with data of energy smaller than or equal to a harmonic map of minimal
energy. An alternative holds: either the data is the harmonic map and the
soltuion is constant in time, or the solution scatters in infinite time
- …