4,366 research outputs found
On buoyant convection in binary solidification
We consider the problem of nonlinear steady buoyant convection in horizontal mushy layers during the solidification of binary alloys. We investigate both cases of zero vertical volume flux and constant pressure, referred to as impermeable and permeable conditions, respectively, at the upper mush???liquid interface. We analyze the effects of several parameters of the problem on the stationary modes of convection in the form of either hexagonal cells or non-hexagonal cells, such as rolls, rectangles and squares. [More ...]published or submitted for publicationis not peer reviewe
Boundary-induced inhomogeneity of particle layers in the solidification of suspensions
When a suspension freezes, a compacted particle layer builds up at the
solidification front with noticeable implications on the freezing process. In a
directional solidification experiment of monodispersed suspensions in thin
samples, we evidence a link between the thickness of this layer and the sample
depth. We attribute it to an inhomogeneity of particle density induced by the
sample plates. A mechanical model enables us to relate it to the layer
thickness with a dependency on the sample depth and to select the distribution
of particle density that yields the best fit to our data. This distribution
involves an influence length of sample plates of about nine particle diameters.
These results clarify the implications of boundaries on suspension freezing.
They may be useful to model polydispersed suspensions since large particles
could play the role of smooth boundaries with respect to small ones.Comment: 16 pages, 13 figure
Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview
Here, we review the basic concepts and applications of the
phase-field-crystal (PFC) method, which is one of the latest simulation
methodologies in materials science for problems, where atomic- and microscales
are tightly coupled. The PFC method operates on atomic length and diffusive
time scales, and thus constitutes a computationally efficient alternative to
molecular simulation methods. Its intense development in materials science
started fairly recently following the work by Elder et al. [Phys. Rev. Lett. 88
(2002), p. 245701]. Since these initial studies, dynamical density functional
theory and thermodynamic concepts have been linked to the PFC approach to serve
as further theoretical fundaments for the latter. In this review, we summarize
these methodological development steps as well as the most important
applications of the PFC method with a special focus on the interaction of
development steps taken in hard and soft matter physics, respectively. Doing
so, we hope to present today's state of the art in PFC modelling as well as the
potential, which might still arise from this method in physics and materials
science in the nearby future.Comment: 95 pages, 48 figure
Pattern formation in directional solidification under shear flow. I: Linear stability analysis and basic patterns
An asymptotic interface equation for directional solidification near the
absolute stabiliy limit is extended by a nonlocal term describing a shear flow
parallel to the interface. In the long-wave limit considered, the flow acts
destabilizing on a planar interface. Moreover, linear stability analysis
suggests that the morphology diagram is modified by the flow near the onset of
the Mullins-Sekerka instability. Via numerical analysis, the bifurcation
structure of the system is shown to change. Besides the known hexagonal cells,
structures consisting of stripes arise. Due to its symmetry-breaking
properties, the flow term induces a lateral drift of the whole pattern, once
the instability has become active. The drift velocity is measured numerically
and described analytically in the framework of a linear analysis. At large flow
strength, the linear description breaks down, which is accompanied by a
transition to flow-dominated morphologies, described in a companion paper.
Small and intermediate flows lead to increased order in the lattice structure
of the pattern, facilitating the elimination of defects. Locally oscillating
structures appear closer to the instability threshold with flow than without.Comment: 20 pages, Latex, accepted for Physical Review
Renormalization group approach to multiscale modelling in materials science
Dendritic growth, and the formation of material microstructure in general,
necessarily involves a wide range of length scales from the atomic up to sample
dimensions. The phase field approach of Langer, enhanced by optimal asymptotic
methods and adaptive mesh refinement, copes with this range of scales, and
provides an effective way to move phase boundaries. However, it fails to
preserve memory of the underlying crystallographic anisotropy, and thus is
ill-suited for problems involving defects or elasticity. The phase field
crystal (PFC) equation-- a conserving analogue of the Hohenberg-Swift equation
--is a phase field equation with periodic solutions that represent the atomic
density. It can natively model elasticity, the formation of solid phases, and
accurately reproduces the nonequilibrium dynamics of phase transitions in real
materials. However, the PFC models matter at the atomic scale, rendering it
unsuitable for coping with the range of length scales in problems of serious
interest. Here, we show that a computationally-efficient multiscale approach to
the PFC can be developed systematically by using the renormalization group or
equivalent techniques to derive appropriate coarse-grained coupled phase and
amplitude equations, which are suitable for solution by adaptive mesh
refinement algorithms
Mechanism for Spontaneous Growth of Nanopillar Arrays in Ultrathin Films Subject to a Thermal Gradient
Several groups have reported spontaneous formation of periodic pillar-like
arrays in molten polymer nanofilms confined within closely spaced substrates
maintained at different temperatures. These formations have been attributed to
a radiation pressure instability caused by acoustic phonons. In this work, we
demonstrate how variations in the thermocapillary stress along the nanofilm
interface can produce significant periodic protrusions in any viscous film no
matter how small the initial transverse thermal gradient. The linear stability
analysis of the interface evolution equation explores an extreme limit of
B\'{e}nard-Marangoni flow peculiar to films of nanoscale dimensions in which
hydrostatic forces are altogether absent and deformation amplitudes are small
in comparison to the pillar spacing. Finite element simulations of the full
nonlinear equation are also used to examine the array pitch and growth rates
beyond the linear regime. Inspection of the Lyapunov free energy as a function
of time confirms that in contrast to typical cellular instabilities in
macroscopically thick films, pillar-like elongations are energetically
preferred in nanofilms. Provided there occurs no dewetting during film
deformation, it is shown that fluid elongations continue to grow until contact
with the cooler substrate is achieved. Identification of the mechanism
responsible for this phenomenon may facilitate fabrication of extended arrays
for nanoscale optical, photonic and biological applications.Comment: 20 pages, 9 figure
On mathematical modeling, nonlinear properties and stability of secondary flow in a dendrite layer
This paper studies instabilities in the flow of melt within a horizontal dendrite layer with deformed upper boundary and in the presence or absence of rotation during the solidification of a binary alloy. In the presence of rotation, it is assumed that the layer is rotating about a vertical axis at a constant angular velocity. Linear and weakly nonlinear stability analyses provide results about various flow features such as the critical mode of convection, neutral stability curve, preferred flow pattern and the solid fraction distribution within the dendrite layer. The preferred shape of the deformed upper boundary of the layer, which is found to be caused by the temperature variations of the secondary flow, is detected to be the same as that for the stable and preferred horizontal flow pattern within the dendrite layer
Solidification and structure formation in soft-core fluids
This thesis analyses the structure, phase behaviour and dynamics of two dimensional (2D) systems of interacting soft-core particles, focussing in particular on how these can solidify and the properties of the resulting crystalline structures. Classical density functional theory (DFT) and dynamical density functional theory (DDFT) is used in the analysis, and an introduction to these is given. The first systems studied are particles interacting via the generalised exponential model of index n (GEM-n) pair potential, including binary mixtures of different types of GEM-n particles. We confirm that a simple mean-field approximate DFT (the RPA-DFT) provides a good approximation for the structure and thermodynamics. We study how solidification fronts advance into the unstable liquid after a temperature quench. We find that the length scale of the density modulations chosen by the front is not necessarily the length scale corresponding the equilibrium crystal structure. This results in the presence of defects and disorder in the structures formed. We analyse how these evolve over time, after the front has passed. We also find that for the binary mixtures, the defects and disorder persists for much longer and in-fact can remain indefinitely.
In the final part of this thesis we analyse the Barkan-Engel-Lifshitz (BEL) model, which consists of particles interacting via a soft core potential that is more complicated than the GEM-n potential and can include a minimum in the potential and soft repulsion over several competing length scales. The form of the BEL potential gives good control over the shape of the dispersion relation, which allows it to be tuned to the regime where the system forms quasicrystals. In this regime, we study in detail the nature of the liquid state pair correlations and in particular the form of the asymptotic decay as the distance between the particles r tends to infinity. The usual approach used for fluids in three dimensions has to be generalised, in order to be applicable in 2D. It is found that there is a line in the phase diagram at which the asymptotic decay crosses over from being oscillatory with one wavelength to oscillatory with a different wavelength. We expect this to be a general characteristic of systems that form quasicrystals
- …