论文标题
浮力隔离会抑制多孔层的水平位移中的粘性指法
Buoyancy segregation suppresses viscous fingering in horizontal displacements in a porous layer
论文作者
论文摘要
我们考虑了环境流体的轴对称位移，即在水平多孔层中较低密度和较低粘度的第二个输入流体。如果两种流体通过浮力垂直隔离，则流动与输入流体在上边界附近优先流动变得自相似。我们表明，对于任何粘度比，这种轴对称自相似流与角依赖性扰动稳定。由于流体的浮力隔离，萨夫曼 - 泰勒的不稳定性被抑制。隔离电流的径向范围与粘度比成反比。入侵的水平延伸消除了与粘度对比相关的流体之间的压力梯度的不连续性。因此，即使是任意小的密度差异，也关闭了粘性指法。通过在界面形状和压力梯度的耦合问题的数值整合以及补充渐近分析中确认稳定性，从而预测每种模式的衰减速率。结果扩展到各向异性和垂直异质层。该界面可能具有陡峭的冲击区域，但是当流体被浮力隔离时，流动始终是稳定的，如均匀的层中。
We consider the axisymmetric displacement of an ambient fluid by a second input fluid of lower density and lower viscosity in a horizontal porous layer. If the two fluids have been vertically segregated by buoyancy, the flow becomes self-similar with the input fluid preferentially flowing near the upper boundary. We show that this axisymmetric self-similar flow is stable to angular-dependent perturbations for any viscosity ratio. The Saffman-Taylor instability is suppressed due to the buoyancy segregation of the fluids. The radial extent of the segregated current is inversely proportional to the viscosity ratio. This horizontal extension of the intrusion eliminates the discontinuity in the pressure gradient between the fluids associated with the viscosity contrast. Hence, at late times viscous fingering is shut down even for arbitrarily small density differences. The stability is confirmed through numerical integration of a coupled problem for the interface shape and the pressure gradient, and through complementary asymptotic analysis, which predicts the decay rate for each mode. The results are extended to anisotropic and vertically heterogeneous layers. The interface may have steep shock-like regions but the flow is always stable when the fluids have been segregated by buoyancy, as in a uniform layer.
