2,554 research outputs found
Decomposition driven interface evolution for layers of binary mixtures: {II}. Influence of convective transport on linear stability
We study the linear stability with respect to lateral perturbations of free
surface films of polymer mixtures on solid substrates. The study focuses on the
stability properties of the stratified and homogeneous steady film states
studied in Part I [U. Thiele, S. Madruga and L. Frastia, Phys. Fluids 19,
122106 (2007)]. To this aim, the linearized bulk equations and boundary
equations are solved using continuation techniques for several different cases
of energetic bias at the surfaces, corresponding to linear and quadratic
solutal Marangoni effects.
For purely diffusive transport, an increase in film thickness either
exponentially decreases the lateral instability or entirely stabilizes the
film. Including convective transport leads to a further destabilization as
compared to the purely diffusive case. In some cases the inclusion of
convective transport and the related widening of the range of available film
configurations (it is then able to change its surface profile) change the
stability behavior qualitatively.
We furthermore present results regarding the dependence of the instability on
several other parameters, namely, the Reynolds number, the Surface tension
number and the ratio of the typical velocities of convective and diffusive
transport.Comment: Published in Physics of Fluic
Thin film evolution equations from (evaporating) dewetting liquid layers to epitaxial growth
In the present contribution we review basic mathematical results for three
physical systems involving self-organising solid or liquid films at solid
surfaces. The films may undergo a structuring process by dewetting,
evaporation/condensation or epitaxial growth, respectively. We highlight
similarities and differences of the three systems based on the observation that
in certain limits all of them may be described using models of similar form,
i.e., time evolution equations for the film thickness profile. Those equations
represent gradient dynamics characterized by mobility functions and an
underlying energy functional.
Two basic steps of mathematical analysis are used to compare the different
system. First, we discuss the linear stability of homogeneous steady states,
i.e., flat films; and second the systematics of non-trivial steady states,
i.e., drop/hole states for dewetting films and quantum dot states in epitaxial
growth, respectively. Our aim is to illustrate that the underlying solution
structure might be very complex as in the case of epitaxial growth but can be
better understood when comparing to the much simpler results for the dewetting
liquid film. We furthermore show that the numerical continuation techniques
employed can shed some light on this structure in a more convenient way than
time-stepping methods.
Finally we discuss that the usage of the employed general formulation does
not only relate seemingly not related physical systems mathematically, but does
as well allow to discuss model extensions in a more unified way
Effect of the orientational relaxation on the collective motion of patterns formed by self-propelled particles
We investigate the collective behavior of self-propelled particles (SPPs)
undergoing competitive processes of pattern formation and rotational relaxation
of their self-propulsion velocities. In full accordance with previous work, we
observe transitions between different steady states of the SPPs caused by the
intricate interplay among the involved effects of pattern formation,
orientational order, and coupling between the SPP density and orientation
fields. Based on rigorous analytical and numerical calculations, we prove that
the rate of the orientational relaxation of the SPP velocity field is the main
factor determining the steady states of the SPP system. Further, we determine
the boundaries between domains in the parameter plane that delineate
qualitatively different resting and moving states. In addition, we analytically
calculate the collective velocity of the SPPs and show that it
perfectly agrees with our numerical results. We quantitatively demonstrate that
does not vanish upon approaching the transition boundary between the
moving pattern and homogeneous steady states.Comment: 3 Figure
Modelling the evaporation of thin films of colloidal suspensions using Dynamical Density Functional Theory
Recent experiments have shown that various structures may be formed during
the evaporative dewetting of thin films of colloidal suspensions. Nano-particle
deposits of strongly branched `flower-like', labyrinthine and network
structures are observed. They are caused by the different transport processes
and the rich phase behaviour of the system. We develop a model for the system,
based on a dynamical density functional theory, which reproduces these
structures. The model is employed to determine the influences of the solvent
evaporation and of the diffusion of the colloidal particles and of the liquid
over the surface. Finally, we investigate the conditions needed for
`liquid-particle' phase separation to occur and discuss its effect on the
self-organised nano-structures
Solidification in soft-core fluids: disordered solids from fast solidification fronts
Using dynamical density functional theory we calculate the speed of
solidification fronts advancing into a quenched two-dimensional model fluid of
soft-core particles. We find that solidification fronts can advance via two
different mechanisms, depending on the depth of the quench. For shallow
quenches, the front propagation is via a nonlinear mechanism. For deep
quenches, front propagation is governed by a linear mechanism and in this
regime we are able to determine the front speed via a marginal stability
analysis. We find that the density modulations generated behind the advancing
front have a characteristic scale that differs from the wavelength of the
density modulation in thermodynamic equilibrium, i.e., the spacing between the
crystal planes in an equilibrium crystal. This leads to the subsequent
development of disorder in the solids that are formed. For the one-component
fluid, the particles are able to rearrange to form a well-ordered crystal, with
few defects. However, solidification fronts in a binary mixture exhibiting
crystalline phases with square and hexagonal ordering generate solids that are
unable to rearrange after the passage of the solidification front and a
significant amount of disorder remains in the system.Comment: 18 pages, 14 fig
Depinning of three-dimensional drops from wettability defects
Substrate defects crucially influence the onset of sliding drop motion under
lateral driving. A finite force is necessary to overcome the pinning influence
even of microscale heterogeneities. The depinning dynamics of three-dimensional
drops is studied for hydrophilic and hydrophobic wettability defects using a
long-wave evolution equation for the film thickness profile. It is found that
the nature of the depinning transition explains the experimentally observed
stick-slip motion.Comment: 6 pages, 9 figures, submitted to ep
Dewetting of thin films on heterogeneous substrates: Pinning vs. coarsening
We study a model for a thin liquid film dewetting from a periodic
heterogeneous substrate (template). The amplitude and periodicity of a striped
template heterogeneity necessary to obtain a stable periodic stripe pattern,
i.e. pinning, are computed. This requires a stabilization of the longitudinal
and transversal modes driving the typical coarsening dynamics during dewetting
of a thin film on a homogeneous substrate. If the heterogeneity has a larger
spatial period than the critical dewetting mode, weak heterogeneities are
sufficient for pinning. A large region of coexistence between coarsening
dynamics and pinning is found.Comment: 4 pages, 4 figure
The relation of steady evaporating drops fed by an influx and freely evaporating drops
We discuss a thin film evolution equation for a wetting evaporating liquid on
a smooth solid substrate. The model is valid for slowly evaporating small
sessile droplets when thermal effects are insignificant, while wettability and
capillarity play a major role. The model is first employed to study steady
evaporating drops that are fed locally through the substrate. An asymptotic
analysis focuses on the precursor film and the transition region towards the
bulk drop and a numerical continuation of steady drops determines their fully
non-linear profiles.
Following this, we study the time evolution of freely evaporating drops
without influx for several initial drop shapes. As a result we find that drops
initially spread if their initial contact angle is larger than the apparent
contact angle of large steady evaporating drops with influx. Otherwise they
recede right from the beginning
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Dynamic unbinding transitions and deposition patterns in dragged meniscus problems
This paper was presented at the 4th Micro and Nano Flows Conference (MNF2014), which was held at University College, London, UK. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute, ASME Press, LCN London Centre for Nanotechnology, UCL University College London, UCL Engineering, the International NanoScience Community, www.nanopaprika.eu.We sketch main results of our recent work on the transfer of a thin liquid film onto a flat plate
that is extracted from a bath of pure non-volatile liquid. Employing a long-wave hydrodynamic model, that
incorporates wettability via a Derjaguin (disjoining) pressure, we analyse steady-state meniscus profiles as the
plate velocity is changed. We identify four qualitatively different dynamic transitions between microscopic
and macroscopic coatings that are out-of-equilibrium equivalents of equilibrium unbinding transitions. The
conclusion briefly discusses how the gradient dynamics formulation of the problem allows one to systematically
extend the employed one-component model into thermodynamically consistent two-component models as used
to describe, e.g., the formation of line patterns during the Langmuir-Blodgett transfer of a surfactant layer
Bifurcation analysis of the behavior of partially wetting liquids on a rotating cylinder
We discuss the behavior of partially wetting liquids on a rotating cylinder
using a model that takes into account the effects of gravity, viscosity,
rotation, surface tension and wettability. Such a system can be considered as a
prototype for many other systems where the interplay of spatial heterogeneity
and a lateral driving force in the proximity of a first- or second-order phase
transition results in intricate behavior. So does a partially wetting drop on a
rotating cylinder undergo a depinning transition as the rotation speed is
increased, whereas for ideally wetting liquids the behavior \bfuwe{only changes
quantitatively. We analyze the bifurcations that occur when the rotation speed
is increased for several values of the equilibrium contact angle of the
partially wetting liquids. This allows us to discuss how the entire bifurcation
structure and the flow behavior it encodes changes with changing wettability.
We employ various numerical continuation techniques that allow us to track
stable/unstable steady and time-periodic film and drop thickness profiles. We
support our findings by time-dependent numerical simulations and asymptotic
analyses of steady and time-periodic profiles for large rotation numbers
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