Zhou Wenchao, Loney Drew, Fedorov Andrei G, Degertekin F Levent, Rosen David W
The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0405, USA.
The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0405, USA and Parker H. Petit Institute for Bioengineering and Bioscience, Georgia Institute of Technology, Atlanta, Georgia 30332-0405, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Mar;89(3):033311. doi: 10.1103/PhysRevE.89.033311. Epub 2014 Mar 21.
A lattice Boltzmann (LB) formulation, which is consistent with the phase-field model for two-phase incompressible fluid, is proposed to model the interface dynamics of droplet impingement. The interparticle force is derived by comparing the macroscopic transport equations recovered from LB equations with the governing equations of the continuous phase-field model. The inconsistency between the existing LB implementations and the phase-field model in calculating the relaxation time at the phase interface is identified and an approximation is proposed to ensure the consistency with the phase-field model. It is also shown that the commonly used equilibrium velocity boundary for the binary fluid LB scheme does not conserve momentum at the wall boundary and a modified scheme is developed to ensure the momentum conservation at the boundary. In addition, a geometric formulation of the wetting boundary condition is proposed to replace the popular surface energy formulation and results show that the geometric approach enforces the prescribed contact angle better than the surface energy formulation in both static and dynamic wetting. The proposed LB formulation is applied to simulating droplet impingement dynamics in three dimensions and results are compared to those obtained with the continuous phase-field model, the LB simulations reported in the literature, and experimental data from the literature. The results show that the proposed LB simulation approach yields not only a significant speed improvement over the phase-field model in simulating droplet impingement dynamics on a submillimeter length scale, but also better accuracy than both the phase-field model and the previously reported LB techniques when compared to experimental data. Upon validation, the proposed LB modeling methodology is applied to the study of multiple-droplet impingement and interactions in three dimensions, which demonstrates its powerful capability of simulating extremely complex interface phenomena.
提出了一种与两相不可压缩流体的相场模型相一致的格子玻尔兹曼（LB）公式，用于模拟液滴撞击的界面动力学。通过将从LB方程恢复的宏观输运方程与连续相场模型的控制方程进行比较，推导了粒子间作用力。识别出了现有LB方法与相场模型在计算相界面处弛豫时间时的不一致性，并提出了一种近似方法以确保与相场模型的一致性。还表明，二元流体LB方案常用的平衡速度边界在壁边界处不守恒动量，因此开发了一种改进方案以确保边界处的动量守恒。此外，提出了一种润湿边界条件的几何公式来取代流行的表面能公式，结果表明，在静态和动态润湿中，几何方法比表面能公式能更好地强制规定的接触角。将所提出的LB公式应用于三维液滴撞击动力学模拟，并将结果与连续相场模型、文献中报道的LB模拟以及文献中的实验数据进行了比较。结果表明，所提出的LB模拟方法不仅在亚毫米长度尺度上模拟液滴撞击动力学时比相场模型具有显著的速度提升，而且与实验数据相比，比相场模型和先前报道的LB技术具有更高的精度。经过验证后，将所提出的LB建模方法应用于三维多液滴撞击和相互作用的研究，这证明了其模拟极其复杂界面现象的强大能力。
