We study the stability of gravitationally unstable transient diffusive boundary layers with variable viscosity in porous media. The previous studies characterize the effect of viscosity variation only in terms of viscosity contrast and generalize their findings. However, conclusions of different studies seem contradictory. Our results demonstrate that stability of diffusive fronts is governed by the boundary layer viscosity and not solely by the viscosity contrast. In other words, the use of viscosity contrast to ascertain the stability of the system cannot be generalized. Nonlinear simulations are conducted based on a finite difference scheme to validate the results of linear stability analysis for which the amplification theory is adopted. We also revisit other available scaling approaches used to characterize the effect of viscosity variation on the onset of convective dissolution and explain why previously made conclusions are not inclusive and sometimes appeared to be contradictory. A critical Rayleigh number is found to predict stability of Rayleigh-Darcy convection in a porous layer with variable viscosity. The results reveal that this critical value can differ highly from the conventional value of 4π². © 2017 American Institute of Chemical Engineers AIChE J, 2017

中文翻译：

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重力作用下多孔介质中可变粘度扩散边界层稳定性的新认识

我们研究了在多孔介质中具有可变粘度的重力不稳定瞬态扩散边界层的稳定性。先前的研究仅根据粘度对比来表征粘度变化的影响，并概括了他们的发现。但是，不同研究的结论似乎是矛盾的。我们的结果表明，扩散前沿的稳定性受边界层粘度的控制，而不仅由粘度对比值决定。换句话说，不能一概而论地使用粘度对比来确定系统的稳定性。基于有限差分方案进行了非线性仿真，以验证采用放大理论的线性稳定性分析的结果。我们还回顾了其他可用的定标方法来表征粘度变化对流溶解开始的影响，并解释了为什么先前得出的结论不具有包容性，有时似乎是矛盾的。发现临界瑞利数可预测具有可变粘度的多孔层中瑞利-达西对流的稳定性。结果表明，该临界值可能与常规值4π有很大差异²。©2017美国化学工程师学会AIChE J，2017