37 research outputs found
Comment on: `Pipe Network Model for Scaling of Dynamic Interfaces in Porous Media'
We argue that a proposed exponent identity [Phys. Rev. Lett 85, 1238 (2000)]
for interface roughening in spontaneous imbibition is wrong. It rests on the
assumption that the fluctuations are controlled by a single time scale, but
liquid conservation imposes two distinct time scales.Comment: 1 page, to appear in Phys. Rev. Let
Multiscale modelling of microstructure formation in polymerc asting
A data bank approach to multi-scale modelling of polymer solidification under flow and holding conditions is presented with applications to injection molding. The latent heat of solidification, which acts as an input parameter for large scale simulations, is determined as a function of different process dependent parameters such as the flow speed, supersaturation and geometric properties including the seed density of emerging spherulitic microstructures. Supersaturation and flow velocities are obtained from the larger scale simulation code as input values as function of which the released latent heat can be obtained from the pre-computed data bank thereby offering a possibility to circumvent the spatial and temporal coarse-graining problem associated with large scale simulations
Interface dynamics and kinetic roughening in fractals
We consider the dynamics and kinetic roughening of single-valued interfaces in two-dimensional fractal media. Assuming that the local height difference distribution function of the fronts obeys Levý statistics with a well-defined power-law decay exponent, we derive analytic expressions for the local scaling exponents. We also show that the kinetic roughening of the interfaces displays anomalous scaling and multiscaling in the relevant correlation functions. For invasion percolation models, the exponents can be obtained from the fractal geometry of percolation clusters. Our predictions are in excellent agreement with numerical simulations.Peer reviewe
Interface Equations for Capillary Rise in Random Environment
We consider the influence of quenched noise upon interface dynamics in 2D and
3D capillary rise with rough walls by using phase-field approach, where the
local conservation of mass in the bulk is explicitly included. In the 2D case
the disorder is assumed to be in the effective mobility coefficient, while in
the 3D case we explicitly consider the influence of locally fluctuating
geometry along a solid wall using a generalized curvilinear coordinate
transformation. To obtain the equations of motion for meniscus and contact
lines, we develop a systematic projection formalism which allows inclusion of
disorder. Using this formalism, we derive linearized equations of motion for
the meniscus and contact line variables, which become local in the Fourier
space representation. These dispersion relations contain effective noise that
is linearly proportional to the velocity. The deterministic parts of our
dispersion relations agree with results obtained from other similar studies in
the proper limits. However, the forms of the noise terms derived here are
quantitatively different from the other studies
Interface pinning in spontaneous imbibition
Evaporation and gravity induced pinning in spontaneous imbibition are examined within a phase field formalism. Evaporation is introduced via a nonconserving term and gravity through a convective term that constrains the influx of liquid. Their effects are described by dimensionless coupling constants ε and g, respectively. From liquid conservation, the early time behavior of the average interface position follows H(t)∼t1/2 until a crossover time t*(g,ε). After that the pinning height Hp(g,ε) is approached exponentially in time, in accordance with mean field theory. The statistical roughness of the interface is described by an exponent χ≃1.25 at all stages of the rise, but the dynamic length scale controlling roughness crosses over from ξ×∼H1/2 to a time independent pinning length scale ξp(ε,g).Peer reviewe
Phase-field crystal modelling of crystal nucleation, heteroepitaxy and patterning
We apply a simple dynamical density functional theory, the
phase-field-crystal (PFC) model, to describe homogeneous and heterogeneous
crystal nucleation in 2d monodisperse colloidal systems and crystal nucleation
in highly compressed Fe liquid. External periodic potentials are used to
approximate inert crystalline substrates in addressing heterogeneous
nucleation. In agreement with experiments in 2d colloids, the PFC model
predicts that in 2d supersaturated liquids, crystalline freezing starts with
homogeneous crystal nucleation without the occurrence of the hexatic phase. At
extreme supersaturations crystal nucleation happens after the appearance of an
amorphous precursor phase both in 2d and 3d. We demonstrate that contrary to
expectations based on the classical nucleation theory, corners are not
necessarily favourable places for crystal nucleation. Finally, we show that
adding external potential terms to the free energy, the PFC theory can be used
to model colloid patterning experiments.Comment: 21 pages, 16 figure
Correlation functions and queuing phenomena in growth processes with drift
We suggest a novel stochastic discrete growth model which describes the
drifted Edward-Wilkinson (EW) equation . From the stochastic model, the
anomalous behavior of the drifted EW equation with a defect is analyzed. To
physically understand the anomalous behavior the height-height correlation
functions and are
also investigated, where the defect is located at . The height-height
correlation functions follow the power law and with around a perfect defect at which no
growth process is allowed. is the same as the anomalous
roughness exponent . For the weak defect at which the growth
process is partially allowed, the normal EW behavior is recovered. We also
suggest a new type queuing process based on the asymmetry of
the correlation function around the perfect defect
Dynamics and Kinetic Roughening of Interfaces in Two-Dimensional Forced Wetting
We consider the dynamics and kinetic roughening of wetting fronts in the case
of forced wetting driven by a constant mass flux into a 2D disordered medium.
We employ a coarse-grained phase field model with local conservation of
density, which has been developed earlier for spontaneous imbibition driven by
a capillary forces. The forced flow creates interfaces that propagate at a
constant average velocity. We first derive a linearized equation of motion for
the interface fluctuations using projection methods. From this we extract a
time-independent crossover length , which separates two regimes of
dissipative behavior and governs the kinetic roughening of the interfaces by
giving an upper cutoff for the extent of the fluctuations. By numerically
integrating the phase field model, we find that the interfaces are superrough
with a roughness exponent of , a growth exponent of
, and as a function of the
velocity. These results are in good agreement with recent experiments on
Hele-Shaw cells. We also make a direct numerical comparison between the
solutions of the full phase field model and the corresponding linearized
interface equation. Good agreement is found in spatial correlations, while the
temporal correlations in the two models are somewhat different.Comment: 9 pages, 4 figures, submitted to Eur.Phys.J.
Linear theory of unstable growth on rough surfaces
Unstable homoepitaxy on rough substrates is treated within a linear continuum
theory. The time dependence of the surface width is governed by three
length scales: The characteristic scale of the substrate roughness, the
terrace size and the Ehrlich-Schwoebel length . If (weak step edge barriers) and ,
then displays a minimum at a coverage , where the initial surface width is reduced by a factor
. The r\^{o}le of deposition and diffusion noise is analyzed. The
results are applied to recent experiments on the growth of InAs buffer layers
[M.F. Gyure {\em et al.}, Phys. Rev. Lett. {\bf 81}, 4931 (1998)]. The overall
features of the observed roughness evolution are captured by the linear theory,
but the detailed time dependence shows distinct deviations which suggest a
significant influence of nonlinearities