Esmaeeli Asghar
School of Mechanical, Aerospace, and Materials Engineering, Southern Illinois University, Carbondale, Illinois 62901, USA.
Phys Rev E. 2022 Jul;106(1-2):015110. doi: 10.1103/PhysRevE.106.015110.
Computer simulations are performed to study some of the less explored aspects of the transient electrohydrodynamics of a liquid drop in uniform DC electric fields. The governing equations of the problem are solved using a parallelized front tracking/finite difference method in the framework of Taylor-Melcher's leaky dielectric theory. For density- and viscosity-matched fluid systems, the evolution of the flow field at a high Ohnesorge-squared number Oh^{2}=μ^{2}/γρa is studied. It is shown that the instantaneous flow pattern is the result of superposition of deformation- and hydrodynamic shear-driven vortices, and that depending on the placement of the fluid systems on the deformation-circulation map, there exists two different paths for the development of the velocity field toward steady state. Examination of the steady-state flow patterns shows that the location of the maximum velocity can shift from the (classically known) drop surface to inside the drop along the poles. The effect of Oh^{2} on the dynamic response of the drop and the kinetic energy of the fluid is studied. For high Oh^{2} number flows, the dynamic response is monotonic while the kinetic energy evolves in a nonmonotonic way, achieving a distinct peak before settling to steady state. However, for low Oh^{2} number flows, both the dynamic response and kinetic energy are oscillatory. Inspection of the results show a two-way coupling between the deformation rate and the fluid flow. The effect of the density ratio ρ[over ̃]=ρ_{i}/ρ_{o} (drop to ambient) on the dynamic response and fluid flow strength shows that for high Oh^{2} number flows both parameters remain essentially intact at steady state, while their evolution modes transition from a monotonic response to an oscillatory one at high density ratio. However, for low Oh^{2} number flows, with an increase in ρ[over ̃], the oscillation frequency of both parameters remain intact, while their oscillation amplitudes increase.
进行计算机模拟以研究均匀直流电场中液滴瞬态电流体动力学的一些较少探索的方面。在泰勒 - 梅尔彻漏电介质理论的框架内，使用并行化的前沿追踪/有限差分方法求解该问题的控制方程。对于密度和粘度匹配的流体系统，研究了高奥内佐格平方数(Oh^{2}=μ^{2}/γρa)下的流场演变。结果表明，瞬时流型是变形驱动和流体动力剪切驱动涡旋叠加的结果，并且根据流体系统在变形 - 环流图上的位置，速度场向稳态发展存在两条不同的路径。对稳态流型的研究表明，最大速度的位置可以从（经典已知的）液滴表面沿极点向液滴内部移动。研究了(Oh^{2})对液滴动态响应和流体动能的影响。对于高(Oh^{2})数流动，动态响应是单调的，而动能以非单调方式演变，在达到稳态之前达到一个明显的峰值。然而，对于低(Oh^{2})数流动，动态响应和动能都是振荡的。结果检查显示变形率和流体流动之间存在双向耦合。密度比(\widetilde{\rho}=\rho_{i}/\rho_{o})（液滴与环境）对动态响应和流体流动强度的影响表明，对于高(Oh^{2})数流动，在稳态下这两个参数基本保持不变，而它们的演变模式在高密度比下从单调响应转变为振荡响应。然而，对于低(Oh^{2})数流动，随着(\widetilde{\rho})的增加，这两个参数的振荡频率保持不变，而它们的振荡幅度增加。
