321 research outputs found
Self-ratcheting Stokes drops driven by oblique vibrations
We develop and analyze a minimal hydrodynamic model in the overdamped limit
to understand why a drop climbs a smooth homogeneous incline that is
harmonically vibrated at an angle different from the substrate normal [Brunet,
Eggers and Deegan, Phys. Rev. Lett. 99, 144501 (2007)]. We find that the
vibration component orthogonal to the substrate induces a nonlinear
(anharmonic) response in the drop shape. This results in an asymmetric response
of the drop to the parallel vibration and, in consequence, in the observed net
motion. Beside establishing the basic mechanism, we identify scaling laws valid
in a broad frequency range and a flow reversal at high frequencies.Comment: 4 pages, 7 figure
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
Modelling of surfactant-driven front instabilities in spreading bacterial colonies
The spreading of bacterial colonies at solid-air interfaces is determined by
the physico-chemical properties of the involved interfaces. The production of
surfactant molecules by bacteria is a widespread strategy that allows the
colony to efficiently expand over the substrate. On the one hand, surfactant
molecules lower the surface tension of the colony, effectively increasing the
wettability of the substrate, which facilitates spreading. On the other hand,
gradients in the surface concentration of surfactant molecules result in
Marangoni flows that drive spreading. These flows may cause an instability of
the circular colony shape and the subsequent formation of fingers. In this
work, we study the effect of bacterial surfactant production and substrate
wettability on colony growth and shape within the framework of a hydrodynamic
thin film model. We show that variations in the wettability and surfactant
production are sufficient to reproduce four different types of colony growth,
which have been described in the literature, namely, arrested and continuous
spreading of circular colonies, slightly modulated front lines and the
formation of pronounced fingers
From a thin film model for passive suspensions towards the description of osmotic biofilm spreading
Biofilms are ubiquitous macro-colonies of bacteria that develop at various
interfaces (solid-liquid, solid-gas or liquid-gas). The formation of biofilms
starts with the attachment of individual bacteria to an interface, where they
proliferate and produce a slimy polymeric matrix - two processes that result in
colony growth and spreading. Recent experiments on the growth of biofilms on
agar substrates under air have shown that for certain bacterial strains, the
production of the extracellular matrix and the resulting osmotic influx of
nutrient-rich water from the agar into the biofilm are more crucial for the
spreading behaviour of a biofilm than the motility of individual bacteria. We
present a model which describes the biofilm evolution and the advancing biofilm
edge for this spreading mechanism. The model is based on a gradient dynamics
formulation for thin films of biologically passive liquid mixtures and
suspensions, supplemented by bioactive processes which play a decisive role in
the osmotic spreading of biofilms. It explicitly includes the wetting
properties of the biofilm on the agar substrate via a disjoining pressure and
can therefore give insight into the interplay between passive surface forces
and bioactive growth processes
Collapsed heteroclinic snaking near a heteroclinic chain in dragged meniscus problems
We study a liquid film that is deposited onto a flat plate that is inclined
at a constant angle to the horizontal and is extracted from a liquid bath at a
constant speed. We additionally assume that there is a constant temperature
gradient along the plate that induces a Marangoni shear stress. We analyse
steady-state solutions of a long-wave evolution equation for the film
thickness. Using centre manifold theory, we first obtain an asymptotic
expansion of solutions in the bath region. The presence of the temperature
gradient significantly changes these expansions and leads to the presence of
logarithmic terms that are absent otherwise. Next, we obtain numerical
solutions of the steady-state equation and analyse the behaviour of the
solutions as the plate velocity is changed. We observe that the bifurcation
curve exhibits snaking behaviour when the plate inclination angle is beyond a
certain critical value. Otherwise, the bifurcation curve is monotonic. The
solutions along these curves are characterised by a foot-like structure that is
formed close to the meniscus and is preceded by a thin precursor film further
up the plate. The length of the foot increases along the bifurcation curve.
Finally, we explain that the snaking behaviour of the bifurcation curves is
caused by the existence of an infinite number of heteroclinic orbits close to a
heteroclinic chain that connects in an appropriate three-dimensional phase
space the fixed point corresponding to the precursor film with the fixed point
corresponding to the foot and then with the fixed point corresponding to the
bath.Comment: Final revised version. 18 pages. To be published in Eur. Phys. J.
Time integration and steady-state continuation for 2d lubrication equations
Lubrication equations allow to describe many structurin processes of thin
liquid films. We develop and apply numerical tools suitable for their analysis
employing a dynamical systems approach. In particular, we present a time
integration algorithm based on exponential propagation and an algorithm for
steady-state continuation. In both algorithms a Cayley transform is employed to
overcome numerical problems resulting from scale separation in space and time.
An adaptive time-step allows to study the dynamics close to hetero- or
homoclinic connections. The developed framework is employed on the one hand to
analyse different phases of the dewetting of a liquid film on a horizontal
homogeneous substrate. On the other hand, we consider the depinning of drops
pinned by a wettability defect. Time-stepping and path-following are used in
both cases to analyse steady-state solutions and their bifurcations as well as
dynamic processes on short and long time-scales. Both examples are treated for
two- and three-dimensional physical settings and prove that the developed
algorithms are reliable and efficient for 1d and 2d lubrication equations,
respectively.Comment: 33 pages, 16 figure
Coarsening modes of clusters of aggregating particles
There are two modes by which clusters of aggregating particles can coalesce:
The clusters can merge either (i) by the Ostwald ripening process in which
particles diffuse from one cluster to the other whilst the cluster centres
remain stationary, or (ii) by means of a cluster translation mode, in which the
clusters move towards each other and join. To understand in detail the
interplay between these different modes, we study a model system of hard
particles with an additional attraction between them. The particles diffuse
along narrow channels with smooth or periodically corrugated walls, so that the
system may be treated as one-dimensional. When the attraction between the
particles is strong enough, they aggregate to form clusters. The channel
potential influences whether clusters can move easily or not through the system
and can prevent cluster motion. We use Dynamical Density Functional theory to
study the dynamics of the aggregation process, focusing in particular on the
coalescence of two equal size clusters. As long as the particle hard-core
diameter is non-zero, we find that the coalescence process can be halted by a
sufficiently strong corrugation potential. The period of the potential
determines the size of the final stable clusters. For the case of smooth
channel walls, we demonstrate that there is a cross-over in the dominance of
the two different coarsening modes, that depends on the strength of the
attraction between particles, the cluster sizes and the separation distance
between clusters
Morphology changes in the evolution of liquid two-layer films
We consider two thin layers of immiscible liquids on a heated solid
horizontal substrate. The free liquid-liquid and liquid-gas interfaces of such
a two-layer (or bilayer) liquid film may be unstable due to effective molecular
interactions or the Marangoni effect. Using a long wave approximation we derive
coupled evolution equations for the interafce profiles for a general
non-isothermal situation allowing for slip at the substrate. Linear and
nonlinear analyses are performed for isothermal ultrathin layers below 100 nm
thickness under the influence of destabilizing long-range and stabilizing
short-range interactions. Flat films may be unstable to varicose, zigzag or
mixed modes. During the long-time evolution the nonlinear mode type can change
via switching between two different branches of stable stationary solutions or
via coarsening along a single such branch.Comment: 14 eps figures and 1 tex fil
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