Related papers: Dendritic growth at very low undercoolings
We investigate the three-dimensional morphology of the dendrite tip using the phase-field method. We find that, for low undercoolings, this morphology is ostensibly independent of anisotropy strength except for a localized shape distortion…
Dendritic crystal growth in a pure undercooled melt is simulated quantitatively in three dimensions using a phase-field approach. The full non-axisymmetric morphology of the steady-state dendrite tip and $\sigma^*$ are determined as a…
A phase-field model for diffusion-limited crystal growth is formulated that is capable of handling highly anisotropic interfaces. It uses a Willmore regularization that yields corners of finite size. An asymptotic analysis reveals that…
We investigate dendritic sidebranching during crystal growth in an undercooled melt by simulation of a phase-field model which incorporates thermal noise of microscopic origin. As a non-trivial quantitative test of this model, we first show…
We examine scaling in two-dimensional simulations of dendritic growth at low undercooling, as well as in three-dimensional pivalic acid dendrites grown on NASA's USMP-4 Isothermal Dendritic Growth Experiment. We report new results on…
We report detailed shape measurements of the tips of three-dimensional ammonium chloride dendrites grown from supersaturated aqueous solution. For growth at small supersaturation, we compare two different models: parabolic with a…
Even though our theoretical understanding of dendritic solidification is relatively well developed, our current ability to model this process quantitatively remains extremely limited. This is due to the fact that the morphological…
We present a numerical study of sidebranching of a solidifying dendrite by means of a phase--field model. Special attention is paid to the regions far from the tip of the dendrite, where linear theories are no longer valid. Two regions have…
We study the evolution of solidification microstructures using a phase-field model computed on an adaptive, finite element grid. We discuss the details of our algorithm and show that it greatly reduces the computational cost of solving the…
Extending previous work [T. Pusztai, L. R\'atkai, A. Sz\'all\'as, and L. Gr\'an\'asy, Phys. Rev. E {\bf 87}, 032402 (2013)], we have studied the formation of eutectic dendrites in a model ternary system within the framework of the…
Sea ice growth with lamellar microstructure containing brine channels has been extensively investigated. However, the quantitative growth information of sea ice remains lack due to the uncontrolled crystalline orientation in previous…
The displacement of a fluid by another less viscous one in a quasi-two dimensional geometry typically leads to complex fingering patterns. In an isotropic system, dense-branching growth arises, which is characterized by repeated…
Dendrites with developed sidebranches are numerically studied with a coupled map lattice model. The competitive dynamics among sidebranches determines the shape of the envelope. The envelope has a parabolic shape near the tip of the…
We have studied the conformational and scaling behaviors of a flexible dendrimer immersed in athermal or good solvents. A self-consistent field theory combined with a pre-averaged excluded volume potential representing the two-body…
Given recipe of qualitative, kinetic modelling by geometric methods of three-dimensional dendritic crystals. Characteristic features of the perturbations appearing on the surface of a spherical body, leading to different scenarios of the…
In this paper, we have formulated a phase-field model based on the grand-potential functional for the simulation of precipitate growth in the presence of coherency stresses. In particular, we study the development of dendrite-like patterns…
Ice crystals growing in highly supersaturated air at temperatures near -5 C exhibit a distinctive, nonplanar dendritic morphology that has not been previously documented or explained. We examine this structure and identify its most…
We report measurements of the initial growth and subsequent transient response of dendritic crystals of ammonium chloride grown from supersaturated aqueous solution. Starting from a small, nearly spherical seed held in unstable equilibrium,…
We investigate analytically and computationally the dynamics of 2D needle crystal growth from the melt in a narrow channel. Our analytical theory predicts that, in the low supersaturation limit, the growth velocity $V$ decreases in time $t$…
Dendritic growth patterns exhibiting four-fold anisotropy are observed when polyethylene oxide undergoes phase segregation from a solution phase to a solid phase. When this phase transition occurs on a substrate that has patterns of…