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首页> 外文期刊>The European physical journal, B. Condensed matter physics >Diffusive growth of a single droplet with three different boundary conditions
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Diffusive growth of a single droplet with three different boundary conditions

机译：具有三个不同边界条件的单个液滴的扩散生长

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摘要

We study a single, motionless three-dimensional droplet growing by adsorption of diffusing monomers on a 2D substrate. The diffusing monomers are adsorbed at the aggregate perimeter of the droplet with different boundary conditions. Models with both an adsorption boundary condition and a radiation boundary condition, as well as a phenomenological model, are considered and solved in a quasistatic approximation. The latter two models allow particle detachment. In the short time limit, the droplet radius grows as a power of the time with exponents of 1/4, 1/2 and 3/4 for the models with adsorption, radiation and phenomenological boundary conditions, respectively. In the long time limit a universal growth rate as [t/ln(t)]~(1/3) is observed for the radius of the droplet for all models independent of the boundary conditions. This asymptotic behaviour was obtained by Krapivsky [15] where a similarity variable approach was used to treat the growth of a droplet with an adsorption boundary condition based on a quasistatic approximation. Another boundary condition with a constant flux of monomers at the aggregate perimeter is also examined. The results exhibit a power law growth rate with an exponent of 1/3 for all times.
机译：我们研究了通过扩散单体在2D基板上的吸附而生长的单个，静止的三维液滴。扩散单体在不同边界条件下吸附在液滴的总周长上。同时考虑和解决了具有吸附边界条件和辐射边界条件的模型以及现象学模型。后两个模型允许粒子分离。在短时限内，对于具有吸附，辐射和现象学边界条件的模型，液滴半径随时间的增长而增长，其指数分别为1 / 4、1 / 2和3/4。在较长的时间范围内，对于所有模型，在不受边界条件影响的情况下，对于液滴的半径，观察到的通用增长率为[t / ln（t）]〜（1/3）。这种渐近行为是由Krapivsky [15]获得的，其中使用基于准静态近似的具有吸附边界条件的相似变量方法来处理液滴的生长。还检查了在聚集体周界具有恒定单体通量的另一种边界条件。结果显示幂律增长率始终为1/3的指数。

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