Coalescence speed of two equal-sized nanobubbles
Coalescence speed of two equal-sized nanobubbles
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DOI：
10.1063/5.0030406
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发表时间：
2020-12
影响因子：
4.6
通讯作者：
E. Bird;Jun Zhou;Zhi Liang
中科院分区：
文献类型：
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作者：
E. Bird;Jun Zhou;Zhi Liang
在这项工作中，我们使用分子动力学（MD）模拟结合连续理论分析，研究两个相同大小的纳米气泡（NB）的合并动力学。我们首先从轴对称Navier-Stokes方程推导出两个聚结NB之间毛细桥半径演化的控制方程。为了验证从控制方程的预测，我们进行MD模拟的两个NB在Lennard-Jones流体系统中的合并，并直接测量桥半径，rb，作为时间的函数，t。通过改变气泡直径，我们将NB Ohnesorge数从0.46改变到0.33。在所有的情况下，我们发现理论预测高估了扩张速度的毛细桥在早期的NB聚结。然而，一旦我们考虑到曲率依赖的表面张力，并限制在毛细管桥的最小主半径的原子在模型液体中的大小，理论预测符合MD数据非常好，在早期和后期的聚结过程。从理论模型中，我们发现，无论是液体粘性力或液体惯性力占主导地位，在后来的时间合并的模型NBs。在这种情况下，MD模拟结果显示rb（t）<$0.76 ± 0.04，标度指数明显高于粘性和惯性主导区域标度律rb（t）<$0.5。完全合并的NB与原始NB的直径比约为2，这不同于毫泡和微泡合并时的23。
In this work, we use molecular dynamics (MD) simulations coupled with continuum-based theoretical analysis to study the coalescence dynamics of two equal-sized nanobubbles (NBs). We first derive a governing equation for the evolution of the capillary bridge radius between two coalescing NBs from the axisymmetric Navier–Stokes equation. To verify the prediction from the governing equation, we carry out MD simulations of the coalescence of two NBs in a Lennard-Jones fluid system and directly measure the bridge radius, rb, as a function of time, t. By varying the bubble diameter, we change the NB Ohnesorge number from 0.46 to 0.33. In all cases, we find the theoretical prediction overestimates the expansion speed of the capillary bridge at early time of NB coalescence. However, once we take into account the curvature-dependent surface tension and restrict the minimum principal radius at the capillary bridge to the size of the atom in the model liquid, the theoretical prediction agrees with the MD data very well in both early time and later time of the coalescence process. From the theoretical model, we find neither liquid viscous force nor liquid inertial force dominates at later time of coalescence of the model NBs. In this case, the MD simulation results show rb(t) ∝ t0.76 ± 0.04 with the scaling exponent considerably higher than that in the scaling law rb(t) ∝ t0.5 for the viscous and inertial dominated regimes. The diameter ratio of fully merged NB to that of the original NB is about 2, which is different from 23 for the coalescence of millibubbles and microbubbles.