4,992 research outputs found
Determination of Inter-Phase Line Tension in Langmuir Films
A Langmuir film is a molecularly thin film on the surface of a fluid; we
study the evolution of a Langmuir film with two co-existing fluid phases driven
by an inter-phase line tension and damped by the viscous drag of the underlying
subfluid. Experimentally, we study an 8CB Langmuir film via digitally-imaged
Brewster Angle Microscopy (BAM) in a four-roll mill setup which applies a
transient strain and images the response. When a compact domain is stretched by
the imposed strain, it first assumes a bola shape with two tear-drop shaped
reservoirs connected by a thin tether which then slowly relaxes to a circular
domain which minimizes the interfacial energy of the system. We process the
digital images of the experiment to extract the domain shapes. We then use one
of these shapes as an initial condition for the numerical solution of a
boundary-integral model of the underlying hydrodynamics and compare the
subsequent images of the experiment to the numerical simulation. The numerical
evolutions first verify that our hydrodynamical model can reproduce the
observed dynamics. They also allow us to deduce the magnitude of the line
tension in the system, often to within 1%. We find line tensions in the range
of 200-600 pN; we hypothesize that this variation is due to differences in the
layer depths of the 8CB fluid phases.Comment: See (http://www.math.hmc.edu/~ajb/bola/) for related movie
Period fissioning and other instabilities of stressed elastic membranes
We study the shapes of elastic membranes under the simultaneous exertion of
tensile and compressive forces when the translational symmetry along the
tension direction is broken. We predict a multitude of novel morphological
phases in various regimes of a 2-dimensional parameter space
that defines the relevant mechanical and geometrical conditions. Theses
parameters are, respectively, the ratio between compression and tension, and
the wavelength contrast along the tension direction. In particular, our theory
associates the repetitive increase of pattern periodicity, recently observed on
wrinkled membranes floating on liquid and subject to capillary forces, to the
morphology in the regime () where tension is dominant
and the wavelength contrast is large.Comment: 4 pages, 4 figures. submitted to Phys. Rev. Let
The -limit of the two-dimensional Ohta-Kawasaki energy. I. Droplet density
This is the first in a series of two papers in which we derive a
-expansion for a two-dimensional non-local Ginzburg-Landau energy with
Coulomb repulsion, also known as the Ohta-Kawasaki model in connection with
diblock copolymer systems. In that model, two phases appear, which interact via
a nonlocal Coulomb type energy. We focus on the regime where one of the phases
has very small volume fraction, thus creating small "droplets" of the minority
phase in a "sea" of the majority phase. In this paper we show that an
appropriate setting for -convergence in the considered parameter regime
is via weak convergence of the suitably normalized charge density in the sense
of measures. We prove that, after a suitable rescaling, the Ohta-Kawasaki
energy functional -converges to a quadratic energy functional of the
limit charge density generated by the screened Coulomb kernel. A consequence of
our results is that minimizers (or almost minimizers) of the energy have
droplets which are almost all asymptotically round, have the same radius and
are uniformly distributed in the domain. The proof relies mainly on the
analysis of the sharp interface version of the energy, with the connection to
the original diffuse interface model obtained via matching upper and lower
bounds for the energy. We thus also obtain a characterization of the limit
charge density for the energy minimizers in the diffuse interface model
- …