Onset and growth of viscous fingering in miscible annular ring

Joung-Sook Hong, L. Palodhi, Manoranjan Mishra, Min Chan Kim
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Abstract

We investigate the onset and growth of viscous fingering (VF) of miscible annulus in a radial Hele-Shaw cell. Systematic numerical study on a finite annulus domain is performed by employing finite element method solver in COMSOL Multiphysics software. We justify that concentration field analysis is not a good choice for dynamic study in radial flows. Instead, velocity magnitude is a better tool to understand the dynamics. Therefore, we propose velocity field analysis to better differentiate the stable and unstable states and present a new stability criterion using the velocity field method. Most interestingly, using the velocity field analysis and the new stability criterion, we show a restabilization of the VF at a critical time when the system becomes diffusion dominant and able to provide both the onset time, τon (time at which instability develops), and the time at which the interface returns to the stable state, τd. Furthermore, the study successfully suggests the critical values for several dimensionless parameters, the Péclet number (Pe), log-viscosity ratio (R), and volumetric ratio (ra) and time (τ), to induce instability. When Pe is higher than 103, the evolution of VF instability is no longer enhanced by Pe, and Rc converges to a certain value. In particular, for the transiently unstable system of low Pe, the restabilization of VF instability is identified even though R is higher than Rc. The unstable system (τ>τon) returns to the stable state as injection time increases further. Moreover, we obtained a critical value of the volumetric ratio (rc,a).
可混溶环形圈中粘性指状结构的形成与发展
我们研究了径向 Hele-Shaw 单元中混溶环的粘性指状(VF)的发生和增长。通过使用 COMSOL Multiphysics 软件中的有限元法求解器,对有限环形域进行了系统的数值研究。我们证明,浓度场分析不是径向流动态研究的最佳选择。相反,速度大小是了解动态的更好工具。因此,我们建议采用速度场分析来更好地区分稳定和不稳定状态,并利用速度场方法提出了一种新的稳定准则。最有趣的是,利用速度场分析和新的稳定性标准,我们显示了 VF 在临界时间的重新稳定,此时系统变得以扩散为主,并能提供起始时间 τon(不稳定状态出现的时间)和界面恢复到稳定状态的时间 τd。此外,研究还成功地提出了几个无量纲参数的临界值,即佩克莱特数(Pe)、对数粘度比(R)、体积比(ra)和时间(τ),以诱发不稳定性。当 Pe 大于 103 时,VF 不稳定性的演变不再受 Pe 的影响,Rc 收敛到一定值。特别是对于低 Pe 的瞬态不稳定系统,即使 R 大于 Rc,也能发现 VF 不稳定的再稳定。随着注入时间的进一步增加,不稳定系统(τ>τon)会恢复到稳定状态。此外,我们还获得了体积比 (rc,a) 的临界值。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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