Induced side-branching in smooth and faceted dendrites: theory and phase-field simulations

Abstract

The present work is devoted to the phenomenon of induced side branching stemming from the disruption of free dendrite growth. We postulate that the secondary branching instability can be triggered by the departure of the morphology of the dendrite from its steady state shape. Thence, the instability results from the thermodynamic trade-off between non monotonic variations of interface temperature, surface energy, kinetic anisotropy and interface velocity within the Gibbs–Thomson equation. For the purposes of illustration, the toy model of capillary anisotropy modulation is prospected both analytically and numerically by means of phase-field simulations. It is evidenced that side branching can befall both smooth and faceted dendrites, at a normal angle from the front tip which is specific to the nature of the capillary anisotropy shift applied. This article is part of the theme issue ‘Transport phenomena in complex systems (part 2)’.

The phase field method—From fundamentals to practical applications in crystal growth

“…We choose a classical one that is easy to implement. It can be noticed that some advanced studies in literature [17,11,39] employed an anisotropy function which enables to check the position of the first branch and side branching of snow in a quantitative manner. Parameters (see section 3.2) are chosen to respect the thermodynamic consistency of the system.…”

Deep Learning Model to Predict Ice Crystal Growth

“…The effect of anisotropy was investigated in a study by Gilles Demange et al. [ 44 ] The magnitude of anisotropy influences side branch curves, causing them to be faceted or smoothed out. In cases where the change in anisotropy is discontinuous, initially, when the smoothness is minimal and the anisotropy shifts to a larger value, the change is not immediately visible.…”

Transport phenomena in complex systems (part 2)

“…Transport phenomena during phase transitions leading to various patterns and microstructure formation are studied in works [33][34][35][36]. These studies are continued in the papers [37][38][39][40], where multiscale modelling of such phenomena based on the phase-field, phase-field crystal, molecular dynamics and cellular automata methods has been carried out. The effects of external processes such as magnetic fields and hydrodynamic flows on transport peculiarities have been analysed in [19,[41][42][43].…”