3,403 research outputs found
Thermal rupture of a free liquid sheet
We consider a free liquid sheet, taking into account the dependence of
surface tension on temperature, or concentration of some pollutant. The sheet
dynamics are described within a long-wavelength description. In the presence of
viscosity, local thinning of the sheet is driven by a strong temperature
gradient across the pinch region, resembling a shock. As a result, for long
times the sheet thins exponentially, leading to breakup. We describe the quasi
one-dimensional thickness, velocity, and temperature profiles in the pinch
region in terms of similarity solutions, which posses a universal structure.
Our analytical description agrees quantitatively with numerical simulations
Coalescence of Liquid Drops
When two drops of radius touch, surface tension drives an initially
singular motion which joins them into a bigger drop with smaller surface area.
This motion is always viscously dominated at early times. We focus on the
early-time behavior of the radius \rmn of the small bridge between the two
drops. The flow is driven by a highly curved meniscus of length 2\pi \rmn and
width \Delta\ll\rmn around the bridge, from which we conclude that the
leading-order problem is asymptotically equivalent to its two-dimensional
counterpart. An exact two-dimensional solution for the case of inviscid
surroundings [Hopper, J. Fluid Mech. , 349 (1990)] shows that
\Delta \propto \rmn^3 and \rmn \sim (t\gamma/\pi\eta)\ln [t\gamma/(\eta
R)]; and thus the same is true in three dimensions. The case of coalescence
with an external viscous fluid is also studied in detail both analytically and
numerically. A significantly different structure is found in which the outer
fluid forms a toroidal bubble of radius \Delta \propto \rmn^{3/2} at the
meniscus and \rmn \sim (t\gamma/4\pi\eta) \ln [t\gamma/(\eta R)]. This basic
difference is due to the presence of the outer fluid viscosity, however small.
With lengths scaled by a full description of the asymptotic flow for
\rmn(t)\ll1 involves matching of lengthscales of order \rmn^2, \rmn^{3/2},
\rmn\rmn^{7/4}$.Comment: 36 pages, including 9 figure
New bryophyte taxon records for tropical countries 2
Norris & T. Kop. Sabah, Mt. Kinabalu, Mary Strong Clemens. 10741, 15.11.1915 (L) as „Campylopus metzlerioides Broth. nom. nud.“ The species was known before (mostly as Atractylocarpus comosus Dix.) from Sumatra, Celebes, New Guinea, Bhutan and Nepal [JPF]
Self-similar breakup of polymeric threads as described by the Oldroyd-B model
When a drop of fluid containing long, flexible polymers breaks up, it forms
threads of almost constant thickness, whose size decreases exponentially in
time. Using an Oldroyd-B fluid as a model, we show that the thread profile,
rescaled by the thread thickness, converges to a similarity solution. Using the
correspondence between viscoelastic fluids and non-linear elasticity, we derive
similarity equations for the full three-dimensional axisymmetric flow field in
the limit that the viscosity of the solvent fluid can be neglected. A
conservation law balancing pressure and elastic energy permits to calculate the
thread thickness exactly. The explicit form of the velocity and stress fields
can be deduced from a solution of the similarity equations. Results are
validated by detailed comparison with numerical simulations
Cusp-shaped Elastic Creases and Furrows
The surfaces of growing biological tissues, swelling gels, and compressed
rubbers do not remain smooth, but frequently exhibit highly localized inward
folds. We reveal the morphology of this surface folding in a novel experimental
setup, which permits to deform the surface of a soft gel in a controlled
fashion. The interface first forms a sharp furrow, whose tip size decreases
rapidly with deformation. Above a critical deformation, the furrow bifurcates
to an inward folded crease of vanishing tip size. We show experimentally and
numerically that both creases and furrows exhibit a universal cusp-shape, whose
width scales like at a distance from the tip. We provide a
similarity theory that captures the singular profiles before and after the
self-folding bifurcation, and derive the length of the fold from large
deformation elasticity.Comment: 5 pages, 4 figure
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