5,746 research outputs found
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
Liquid transport generated by a flashing field-induced wettability ratchet
We develop and analyze a model for ratchet-driven macroscopic transport of a
continuous phase. The transport relies on a field-induced dewetting-spreading
cycle of a liquid film with a free surface based on a switchable, spatially
asymmetric, periodic interaction of the liquid-gas interface and the substrate.
The concept is exemplified using an evolution equation for a dielectric liquid
film under an inhomogeneous voltage. We analyse the influence of the various
phases of the ratchet cycle on the transport properties. Conditions for maximal
transport and the efficiency of transport under load are discussed.Comment: 10 pages, 5 figure
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
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
Experimental observation of nanoscale radiative heat flow due to surface plasmons in graphene and doped silicon
Owing to its two dimensional electronic structure, graphene exhibits many
unique properties. One of them is a wave vector and temperature dependent
plasmon in the infrared range. Theory predicts that due to these plasmons,
graphene can be used as a universal material to enhance nanoscale radiative
heat exchange for any dielectric substrate. Here we report on radiative heat
transfer experiments between SiC and a SiO2 sphere which have non matching
phonon polariton frequencies, and thus only weakly exchange heat in near field.
We observed that the heat flux contribution of graphene epitaxially grown on
SiC dominates at short distances. The influence of plasmons on radiative heat
transfer is further supported with measurements for doped silicon. These
results highlight graphenes strong potential in photonic nearfield and energy
conversion devices.Comment: 4 pages, 3 figure
Pointwise convergence of vector-valued Fourier series
We prove a vector-valued version of Carleson's theorem: Let Y=[X,H]_t be a
complex interpolation space between a UMD space X and a Hilbert space H. For
p\in(1,\infty) and f\in L^p(T;Y), the partial sums of the Fourier series of f
converge to f pointwise almost everywhere. Apparently, all known examples of
UMD spaces are of this intermediate form Y=[X,H]_t. In particular, we answer
affirmatively a question of Rubio de Francia on the pointwise convergence of
Fourier series of Schatten class valued functions.Comment: 26 page
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
Solidification fronts in supercooled liquids: how rapid fronts can lead to disordered glassy solids
We determine the speed of a crystallisation (or more generally, a
solidification) front as it advances into the uniform liquid phase after the
system has been quenched into the crystalline region of the phase diagram. We
calculate the front speed by assuming a dynamical density functional theory
model for the system and applying a marginal stability criterion. Our results
also apply to phase field crystal (PFC) models of solidification. As the
solidification front advances into the unstable liquid phase, the density
profile behind the advancing front develops density modulations and the
wavelength of these modulations is a dynamically chosen quantity. For shallow
quenches, the selected wavelength is precisely that of the crystalline phase
and so well-ordered crystalline states are formed. However, when the system is
deeply quenched, we find that this wavelength can be quite different from that
of the crystal, so that the solidification front naturally generates disorder
in the system. Significant rearrangement and ageing must subsequently occur for
the system to form the regular well-ordered crystal that corresponds to the
free energy minimum. Additional disorder is introduced whenever a front
develops from random initial conditions. We illustrate these findings with
results obtained from the PFC.Comment: 14 pages, 7 figure
Dynamical density functional theory for the dewetting of evaporating thin films of nanoparticle suspensions exhibiting pattern formation
Recent experiments have shown that the striking structure formation in
dewetting films of evaporating colloidal nanoparticle suspensions occurs in an
ultrathin `postcursor' layer that is left behind by a mesoscopic dewetting
front. Various phase change and transport processes occur in the postcursor
layer, that may lead to nanoparticle deposits in the form of labyrinthine,
network or strongly branched `finger' structures. We develop a versatile
dynamical density functional theory to model this system which captures all
these structures and may be employed to investigate the influence of
evaporation/condensation, nanoparticle transport and solute transport in a
differentiated way. We highlight, in particular, the influence of the subtle
interplay of decomposition in the layer and contact line motion on the observed
particle-induced transverse instability of the dewetting front.Comment: 5 pages, 5 figure
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