Buoyancy-driven motion of a two-dimensional bubble or drop through a viscous liquid in the presence of a vertical electric field
Buoyancy-driven motion of a two-dimensional bubble or drop through a viscous liquid in the presence of a vertical electric field
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DOI：
10.1007/s00162-009-0158-x
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发表时间：
2009-10
影响因子：
3.4
通讯作者：
Stefan Mählmann;D. Papageorgiou
中科院分区：
文献类型：
--
作者：
Stefan Mählmann;D. Papageorgiou
计算研究了电场对二维气泡在静止液体中上升时浮力驱动运动的影响。通过跟踪矩形封闭腔垂直间隙中产生的静电场作用下的气液界面，对气泡的动力学进行了数值模拟。假定系统的两相是介电常数不变但不同的理想介质，在没有外加电荷的情况下，流体体区或界面上不存在自由电荷。电应力在气泡界面得到支持，但在整体上不存在，我们计算的目标之一是量化这些麦克斯韦应力对整体气泡动力学的影响。求解自由边界问题的数值算法依赖于Level-Set技术和Navier-Stokes方程的有限体积离散。尖晶界面用有限厚度过渡区近似，材料性质在过渡区上平滑变化，表面张力和电场效应用连续表面力方法考虑。采用多重网格法求解描述压力场的泊松方程和控制电场的拉普拉斯方程。计算结果表明，粘度、表面张力和电场对气泡运动动力学的综合影响是雷诺数、引力键数、电键数、密度比和粘度比的函数。通过大量的计算证实，电场的存在可以对动力学产生重要的影响。我们给出的结果表明，与相应的不带电系统相比，带电系统中气泡的上升速度有显著的提高。此外，对于带电系统，气泡形状变形和振荡较小，气泡通过越来越大的振荡破裂的倾向降低。
The effect of an electric field on the buoyancy-driven motion of a two-dimensional gas bubble rising through a quiescent liquid is studied computationally. The dynamics of the bubble is simulated numerically by tracking the gas–liquid interface when an electrostatic field is generated in the vertical gap of the rectangular enclosure. The two phases of the system are assumed to be perfect dielectrics with constant but different permittivities, and in the absence of impressed charges, there is no free charge in the fluid bulk regions or at the interface. Electric stresses are supported at the bubble interface but absent in the bulk and one of the objectives of our computations is to quantify the effect of these Maxwell stresses on the overall bubble dynamics. The numerical algorithm to solve the free-boundary problem relies on the level-set technique coupled with a finite-volume discretization of the Navier–Stokes equations. The sharp interface is numerically approximated by a finite-thickness transition zone over which the material properties vary smoothly, and surface tension and electric field effects are accounted for by employing a continuous surface force approach. A multi-grid solver is applied to the Poisson equation describing the pressure field and the Laplace equation governing the electric field potential. Computational results are presented that address the combined effects of viscosity, surface tension, and electric fields on the dynamics of the bubble motion as a function of the Reynolds number, gravitational Bond number, electric Bond number, density ratio, and viscosity ratio. It is established through extensive computations that the presence of the electric field can have an important effect on the dynamics. We present results that show a substantial increase in the bubble’s rise velocity in the electrified system as compared with the corresponding non-electrified one. In addition, for the electrified system, the bubble shape deformations and oscillations are smaller, and there is a reduction in the propensity of the bubble to break up through increasingly larger oscillations.