38 research outputs found
Coarsening rates for the dynamics of slipping droplets
We derive reduced finite dimensional ODE models starting from one dimensional
lubrication equations describing coarsening dynamics of droplets in nanometric
polymer film interacting on a hydrophobically coated solid substrate in the
presence of large slippage at the liquid/solid interface. In the limiting case
of infinite slip length corresponding in applications to free films a
collision/absorption model then arises and is solved explicitly. The exact
coarsening law is derived for it analytically and confirmed numerically.
Existence of a threshold for the decay of initial distributions of droplet
distances at infinity at which the coarsening rates switch from algebraic to
exponential ones is shown
Thin film models for active gels
In this study we present a free-boundary problem for an active liquid crystal
based on the Beris-Edwards theory that uses a tensorial order parameter and
includes active contributions to the stress tensor to analyse the rich defect
structure observed in applications such as the Adenosinetriphosphate (ATP)
driven motion of a thin film of an actin filament network. The small aspect
ratio of the film geometry allows for an asymptotic approximation of the
free-boundary problem in the limit of weak elasticity of the network and strong
active terms. The new thin film model captures the defect dynamcs in the bulk
as well as wall defects and thus presents a significant extension of previous
models based on the Lesli-Erickson-Parodi theory. Analytic expression are
derived that reveal the interplay of anchoring conditions, film thickness and
active terms and their control of transitions of flow structure.Comment: 33 pages, 3 figure
Surface Energies Arising in Microscopic Modeling of Martensitic Transformations
In this paper we construct and analyze a two-well Hamiltonian on a 2D atomic
lattice. The two wells of the Hamiltonian are prescribed by two rank-one
connected martensitic twins, respectively. By constraining the deformed
configurations to special 1D atomic chains with position-dependent elongation
vectors for the vertical direction, we show that the structure of ground states
under appropriate boundary conditions is close to the macroscopically expected
twinned configurations with additional boundary layers localized near the
twinning interfaces. In addition, we proceed to a continuum limit, show
asymptotic piecewise rigidity of minimizing sequences and rigorously derive the
corresponding limiting form of the surface energy
Weak solutions to lubrication equations in the presence of strong slippage
The existence of global weak solutions is proved for one-dimensional
lubrication models that describe the dewetting process of nanoscopic thin
polymer films on hydrophobyzed substrates and take account of large slippage at
the polymer-substrate interface. The convergence of these solutions as either
the Reynolds number or the capillarity goes to zero, as well as their limiting
behaviour as the slip length goes to zero or infinity are investigated
Weak solutions to lubrication systems describing the evolution of bilayer thin films
The existence of global nonnegative weak solutions is proved for coupled
one-dimensional lubrication systems that describe the evolution of nanoscopic
bilayer thin polymer films that take account of Navier-slip or no-slip
conditions at both liquid-liquid and liquid-solid interfaces. In addition, in
the presence of attractive van der Waals and repulsive Born intermolecular
interactions existence of positive smooth solutions is shown
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
Coarsening dynamics of slipping droplets
This paper studies the late phase dewetting process of nanoscopic thin polymer films on hydrophobized substrates using some recently derived lubrication models that take account of large slippage at the polymer-substrate interface. The late phase of this process is characterized by the slow-time coarsening dynamics of arrays of droplets that remain after rupture and the initial dewetting phases. For this situation a reduced system of ordinary differential equations is derived from the lubrication model for large slippage using asymptotic analysis. This extends known results for the no-slip case. On the basis of the reduced model, the role of the slippage as a control parameter for droplet migration is analysed and several new qualitative effects for the coarsening process are identified
Asymptotics for the spectrum of a thin film equation in a singular limit
In this paper the linear stability properties of the steady states of a
no-slip lubrication equation are studied. The steady states are configurations
of droplets and arise during the late-phase dewetting process under the
influence of both destabilizing van der Waals and stabilizing Born
intermolecular forces, which in turn give rise to the minimum thickness \eps
of the remaining film connecting the droplets. The goal of this paper is to
give an asymptotic description of the eigenvalues and eigenfunctions of the
problem, linearized about the one-droplet solutions, as \eps\to 0.
For this purpose, corresponding asymptotic eigenvalue problems with piecewise constant coefficients are constructed, such that their
eigenvalue asymptotics can be determined analytically.
A comparison with numerically computed eigenvalues and eigenfunctions
shows good agreement with the asymptotic results and the
existence of a spectrum gap to a single exponentially small eigenvalue for sufficiently small \eps
Thin film models for an active gel
In this study we present a free-boundary problem for an active liquid crystal based on the Beris-Edwards theory that uses a tensorial order parameter and includes active contributions to the stress tensor to analyse the rich defect structure observed in applications such as the Adenosinetriphosphate (ATP) driven motion of a thin film of an actin filament network. The small aspect ratio of the film geometry allows for an asymptotic approximation of the free-boundary problem in the limit of weak elasticity of the network and strong active terms. The new thin film model captures the defect dynamics in the bulk as well as wall defects and thus presents a significant extension of previous models based on the Leslie-Erickson-Parodi theory. Analytic expressions are derived that reveal the interplay of anchoring conditions, film thickness and active terms and their control of transitions of flow structure