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ABSTRACT: The development of side-branching in solidifying dendrites in a regime of large values of the Peclet number is studied by means of a phase-field model. We have compared our numerical results with experiments of the preceding paper and we obtain good qualitative agreement. The growth rate of each side branch shows a power-law behavior from the early stages of its life. From their birth, branches which finally succeed in the competition process of side-branching development have a greater growth exponent than branches which are stopped. Coarsening of branches is entirely defined by their geometrical position relative to their dominant neighbors. The winner branches escape from the diffusive field of the main dendrite and become independent dendrites.
Physical Review E 06/2005; 71(5 Pt 1):051601. · 2.26 Impact Factor
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ABSTRACT: The dynamics of growth of dendrites' side branches is investigated experimentally during the crystallization of solutions of ammonium bromide in a quasi-two-dimensional cell. Two regimes are observed. At small values of the Peclet number a self-affine fractal forms. In this regime it is known that the mean lateral front grows as t(0.5). Here the length of each individual branch is shown to grow (before being screened off) with a power-law behavior t (alpha(n)). The value of the exponent alpha(n) (0.5< or = alpha(n) < or =1) is determined from the start by the strength of the initial disturbance. Coarsening then takes place, when the branches of small alpha(n) are screened off by their neighbors. The corresponding decay of the growth of a weak branch is exponential and defined by its geometrical position relative to its dominant neighbors. These results show that the branch structure results from a deterministic growth of initially random disturbances. At large values of the Peclet number, the faster of the side branches escape and become independent dendrites. The global structure then covers a finite fraction of the two-dimensional space. The crossover between the two regimes and the spacing of these independent branches are characterized.
Physical Review E 03/2005; 71(3 Pt 1):031602. · 2.26 Impact Factor
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ABSTRACT: 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.
Physical Review E 12/2004; 70(5 Pt 1):051612. · 2.26 Impact Factor
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ABSTRACT: 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.
Physical Review E 06/2001; 63(5 Pt 1):051602. · 2.26 Impact Factor
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ABSTRACT: 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.
Physica D: Nonlinear Phenomena.
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ABSTRACT: We perform a characterization of a recently reported minibubbles (bubbles with a diameter of the order of 10−3 m) generator in microgravity related conditions. Generation of bubbles is based on the generation of a slug flow in a capillary T-junction, whose operation is robust to changes in the gravity level. We address questions regarding the performance under different working regimes. In particular, we focus on the regimes found within a large range of gas and liquid injection flow rates. The injection performance is characterized by measuring bubble generation frequency. We propose curves obtained empirically for the behaviour of generation frequency and crossover between regimes.
Colloids and Surfaces A: Physicochemical and Engineering Aspects.
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ABSTRACT: 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.
Journal of Crystal Growth.
