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首页> 外文期刊>Applied Mathematical Modelling >Stability analysis of an interface between immiscible liquids in Hele-Shaw flow in the presence of a magnetic field
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Stability analysis of an interface between immiscible liquids in Hele-Shaw flow in the presence of a magnetic field

机译：磁场作用下Hele-Shaw流中不混溶液体之间界面的稳定性分析

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Hydrodynamic instabilities may occur when a viscous fluid is driven by a less viscous one through a porous medium. These penetrations are common in enhanced oil recovery, dendrite formation and aquifer flow. Recent studies have shown that the use of magnetic suspensions allow the external control of the instability. The problem is nonlinear and some further improvements of both theory and experimental observations are still needed and continue being a current source of investigation. In this paper we present a generalized Darcy law formulation in order to examine the growth of finger instabilities as a magnetic field is applied to the interface between the fluids in a Hele-Shaw cell. A new linear stability analysis is performed in the presence of magnetic effects and provides a stability criterion in terms of the non-dimensional physical parameters of the examined flow and the wavenumber of the finger disturbances. The interfacial tension inhibits small wavelength instabilities. The magnetic field contributes to the interface stability for moderate wavelength as it is applied parallel to the liquid-interface. In particular, we find an explicit expression, as a function of the susceptibility, for a critical angle between the interface and the magnetic field direction, in which its effect on the interface is neutral. We have developed a new asymptotic solution for the flow problem in a weak nonlinear regime. The first correction captures the second order nonlinear effects of the magnetic field, which tends to align the fingers with the field orientation and have a destabilizing effect. The analysis predicts that the non-linear effects at second order can counterbalance the first order stabilizing effect of a parallel magnetic field which results in a loss of effectiveness for controlling the investigated finger instabilities. The relevant physical parameters for controlling these finger instabilities are clearly identified by our non-dimensional analysis. (C) 2019 Elsevier Inc. All rights reserved.
机译：当粘性较低的流体通过多孔介质驱动粘性流体时，可能会发生流体动力学不稳定性。这些渗透在提高采收率，枝晶形成和含水层流动方面很常见。最近的研究表明，磁性悬架的使用可以对不稳定性进行外部控制。这个问题是非线性的，理论上和实验上的观察都需要进一步的改进，并且仍然是当前的研究来源。在本文中，我们提出了一个广义的达西定律公式，以检查在磁场作用于Hele-Shaw细胞中的流体之间的界面时，手指不稳定性的增长。在存在磁效应的情况下进行了新的线性稳定性分析，该线性稳定性分析提供了关于检查流的无量纲物理参数和手指干扰波数的稳定性标准。界面张力抑制了小的波长不稳定性。当磁场平行于液体界面施加时，磁场有助于中等波长的界面稳定性。尤其是，我们根据磁化率找到了界面和磁场方向之间的临界角的显式表达式，该角度对界面的影响是中性的。我们已经为弱非线性状态下的流动问题开发了一种新的渐近解。第一次校正捕获磁场的二阶非线性效应，该效应倾向于使手指与磁场方向对齐并产生不稳定作用。分析预测，二阶非线性效应可以抵消平行磁场的一阶稳定效应，这会导致失去控制所研究手指不稳定性的有效性。通过我们的无量纲分析，可以清楚地识别出控制手指不稳定的相关物理参数。 （C）2019 Elsevier Inc.保留所有权利。

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