Flows involving immiscible displacement of one fluid by another in a porous media are known to destabilize and form fluid fingering. When the non-wetting fluid is a highly mobile gas (air) and the wetting fluid is an in-compressible liquid (water) the classical macroscopic theory is unable to describe the fingered flow. In Part I of this study we have introduced a model that interprets the mixture of wetting and non-wetting fluids within the pore space as a single saturating non-uniform pore fluid characterized by a phase field parameter, which is considered to be the saturation degree of the wetting fluid. In the current study we present a linear stability analysis of its solutions which describe both imbibition and drainage. The analysis sheds light on the sensitivity of the flow stability on injection flux, imposed pressure gradient and initial saturation degree. Two-dimensional numerical simulation results are as well presented which verify the stability analysis and reveal the rich structure of the fluid fingering realized by this model. While these results are found to be in qualitative agreement with experimental observations, they also warrant further experimentation to explore the additional features predicted by the model.

已知在多孔介质中涉及一种流体与另一种流体的不混溶置换的流动会破坏稳定性并形成流体指进。当非润湿流体是高度流动的气体（空气）而润湿流体是不可压缩的液体（水）时，经典宏观理论无法描述指状流动。在本研究的第一部分中，我们介绍了一个模型，该模型将孔隙空间内的润湿流体和非润湿流体的混合物解释为单一的饱和非均匀孔隙流体，其特征在于相场参数，该参数被认为是饱和度的润湿液。在目前的研究中，我们对其解决方案进行了线性稳定性分析，描述了吸水和排水。该分析揭示了流动稳定性对注入通量的敏感性，施加的压力梯度和初始饱和度。同时给出了二维数值模拟结果，验证了稳定性分析，揭示了该模型所实现的流体指进结构的丰富结构。虽然发现这些结果与实验观察结果在定性上一致，但它们也需要进一步的实验来探索模型预测的其他特征。