R. González-Cinca

Phase-field simulations and experiments of faceted growth in liquid crystals

We present numerical simulations directed at the description of smectic-B germs growing into the supercooled nematic phase for two different liquid crystalline substances. The simulations are done by means of a phase-field model appropriate to study strong anisotropy and also faceted interfaces. The most important ingredient is the angle-dependent surface energy, but kinetic effects are also relevant. The simulations reproduce qualitatively a rich variety of morphologies observed in the experiments for different value of undercooling, extending from the faceted equilibrium shape to fully developed dendrites.

Sidebranching induced by external noise in solutal dendritic growth.

We have studied sidebranching induced by fluctuations in dendritic growth. The amplitude of sidebranching induced by internal (equilibrium) concentration fluctuations in the case of solidification with solutal diffusion is computed. This amplitude turns out to be significantly smaller than values reported in previous experiments. The effects of other possible sources of fluctuations (of an external origin) are examined by introducing nonconserved noise in a phase-field model. This reproduces the characteristics of sidebranching found in experiments. Results also show that sidebranching induced by external noise is qualitatively similar to that of internal noise, and it is only distinguished by its amplitude.

Heat diffusion anisotropy in dendritic growth:: phase field simulations and experiments in liquid crystals

An anisotropic heat diffusion coefficient is introduced in order to study some interfacial growth phenomena. This anisotropy has been incorporated in a phase field model which has been studied numerically to reproduce some fundamental solidification situations (needle crystal growth) as well as the dynamics of a nematic–smectic-B interface. As a general result, we find that dendrites grow faster in the lower heat diffusion direction. Simulation results are compared with experiments with remarkable qualitative agreement.

Pattern forming instabilities of the nematic smectic-B interface

Free growth properties of the smectic B liquid crystalline phase into the supercooled nematic have been investigated in quasi-two-dimensional geometry. Different orientation combinations of the two phases have been achieved experimentally and the interfacial patterns have been studied and analysed as a function of undercooling. The angular dependence of the surface tension has been deduced from the shape of the interface in thermal equilibrium. The experimentally determined surface tension anisotropy has been incorporated into computer simulations based on the phase-field model. The simulations have reproduced qualitatively the rich variety of morphologies (extending from the faceted shape to fully developed dendrites) observed in the experiments for a given set of undercoolings in three geometries. Anisotropic heat diffusion on the nematic side, relevant to our experimental system has also been introduced. Both in the experiments and in the simulations we find that the growth is faster in the lower heat diffusion direction.

Liquid jet breakup and subsequent droplet dynamics under normal gravity and in microgravity conditions

We present an experimental study on the characteristics of liquid jets in different configurations. We consider jets injected perpendicular to gravity, jets injected parallel to gravity, and jets injected in a microgravity environment. We study the role played by gravity in the jet breakup length and in the dynamics of the droplets generated after breakup. We analyze droplets obtained in the dripping and jetting regimes, focusing the study on their size, trajectory, oscillation, and rotation. The particularities of the considered injection configurations are analyzed. In normal gravity conditions, in the dripping and jetting regimes, the breakup length increases with the Weber number. The transition between these regimes occurs at Wecr ≈ 3.2. Droplets are notably larger in the dripping regime than in the jetting one. In the latter case, droplet mean size decreases as the liquid flow rate is increased. In microgravity conditions, droplet trajectories form a conical shape due to droplet bouncing after colli...

Numerical study of the shape and integral parameters of a dendrite.

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 been distinguished outside the linear region: a first one in which sidebranching is in a competition process and a second one further down where branches behave as independent of each other. The shape of the dendrite and integral parameters characterizing the whole dendrite (contour length and area of the dendrite) have been computed and related to the characteristic tip radius for both surface tension and kinetic dominated dendrites. Conclusions about the different behaviors observed and comparison with available experiments and theoretical predictions are presented.

THE ROLE OF NOISE IN SIDEBRANCHING DEVELOPMENT

In this paper we study the sidebranching development of solidifying dendrites both experimentally and by numerical integration of a phase-field model with a noise term. Our results support the idea that sidebranching is originated through the selective amplification of natural noise at the tip. The initial stages turn to be of crucial importance in the selection of the final noisy shape. However, our results suggest that after the stochastic initial disturbance, a deterministic mechanism dominates the growth and screening-off process of sidebranching.

Deterministic Behaviour in Sidebranching Development

The development of sidebranching in solidifying dendrites in a regime of finite diffusion length is studied both experimentally and by means of a phase-field model. The growth rate of each sidebranch shows a power-law behaviour from the early stages of its life. From their birth, branches which finally succeed in the competition process of sidebranching development have a greater growth exponent than branches which are stopped.

Low Weber number jet collision regimes in microgravity

The outcome of the collision between two liquid jets depends on the liquid properties, jet velocity, and impact angle. So far studies on liquid jet impingement have been carried out in normal gravity conditions. In microgravity, jets are not accelerated and can show a different behavior than on ground. We perform an experimental analysis of the injection of liquid jets in microgravity, focusing in the jet impingement at different velocities and impact angles at low Weber numbers. Several regimes are obtained, some of which are not observable on ground. Other regimes take place at different parameter ranges than in normal gravity. A map of the observed regimes is proposed in terms of the Weber number and the impact angle.

Deterministic versus noisy behavior in sidebranching

In this paper we study the sidebranching development of solidifying dendrites both experimentally and by numerical integration of a phase-field model with a noise term. Our results support the idea that sidebranching is originated through the selective amplification of natural noise at the tip. The initial stages turn to be of crucial importance in the selection of the final noisy shape. However, our results suggest that after the stochastic initial disturbance, a deterministic mechanism dominates the growth and screening-off process of sidebranching.