Unfavorable fluid-fluid displacement, where a low-viscosity fluid displaces a higher-viscosity fluid in permeable media, is commonly encountered in various subsurface processes. Understanding the formation and evolution of the resulting interfacial instability can have practical benefits for engineering applications. Using gradient capillary tubes as surrogate models of permeable media, we numerically investigate interfacial dynamics during gas-driven drainage. Our focus is on understanding the impact of tube geometry on interface stability. In a gradient tube, since the interface shape changes during the drainage process, we measure interfacial stability using the difference between the contact-line velocity U_cl and the meniscus tip velocity U_tip. We define instability as a rapid reduction in the contact line velocity U_cl compared to the tip velocity U_tip. Beyond the onset of this instability, gas penetrates into the liquid, forming a finger, and entraining a liquid film on the tube wall. The observed stability transition can be rationalized to a large extent by adaptation of an existing theory for cylindrical tubes in terms of a critical capillary number Ca_crit. For an expanding tube, simulations suggest that a stability transition from an initially unstable meniscus to a final stable one, with U_cl catching up with U_tip, can occur if the local capillary number is initially slightly larger than Ca_crit and then drops below Ca_crit. The insights gained from this study can be beneficial in estimating the mode and efficiency of subsurface fluid displacement.

中文翻译：

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梯度毛细管气驱排水界面动力学的几何效应


不利的流体-流体驱替，即低粘度流体置换可渗透介质中的高粘度流体，在各种地下过程中经常遇到。了解由此产生的界面不稳定性的形成和演变可以为工程应用带来实际好处。使用梯度毛细管作为渗透介质的替代模型，我们对气体驱动排水过程中的界面动力学进行数值研究。我们的重点是了解管几何形状对界面稳定性的影响。在梯度管中，由于界面形状在排水过程中发生变化，因此我们使用接触线速度U _cl和弯月面尖端速度U _Tip之间的差异来测量界面稳定性。我们将不稳定性定义为与尖端速度U _Tip相比，接触线速度U _cl的快速减小。除了这种不稳定性的发生之外，气体渗透到液体中，形成指状物，并在管壁上夹带液膜。通过根据临界毛细管数 Ca _crit来适应圆柱形管的现有理论，可以在很大程度上合理化观察到的稳定性转变。对于膨胀管，模拟表明，如果局部毛细管数最初略大于 Ca _Crit然后降至 Ca 以下，则可能会发生从最初不稳定的弯月面到最终稳定弯月面的稳定性过渡，其中U _cl赶上U _Tip 。_暴击。从这项研究中获得的见解有助于估计地下流体驱替的模式和效率。