Chui Jane Y Y, de Anna Pietro, Juanes Ruben
Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Oct;92(4):041003. doi: 10.1103/PhysRevE.92.041003. Epub 2015 Oct 28.
We study experimentally the miscible radial displacement of a more viscous fluid by a less viscous one in a horizontal Hele-Shaw cell. For the range of tested injection rates and viscosity ratios we observe two regimes for the evolution of the fluid-fluid interface. At early times the interface length increases linearly with time, which is typical of the Saffman-Taylor instability for this radial configuration. However, as time increases, the interface growth slows down and scales as ∼t(1/2), as one expects in a stable displacement, indicating that the overall flow instability has shut down. Surprisingly, the crossover time between these two regimes decreases with increasing injection rate. We propose a theoretical model that is consistent with our experimental results, explains the origin of this second regime, and predicts the scaling of the crossover time with injection rate and the mobility ratio. The key determinant of the observed scalings is the competition between advection and diffusion time scales at the displacement front, suggesting that our analysis can be applied to other interfacial-evolution problems such as the Rayleigh-Bénard-Darcy instability.
我们通过实验研究了在水平Hele-Shaw盒中低粘度流体对高粘度流体的可混溶径向驱替。对于所测试的注入速率和粘度比范围，我们观察到流体-流体界面演化存在两种状态。在早期，界面长度随时间线性增加，这是这种径向构型的Saffman-Taylor不稳定性的典型特征。然而，随着时间增加，界面增长减缓并按~t(1/2) 缩放，正如在稳定驱替中所预期的那样，这表明整体流动不稳定性已停止。令人惊讶的是，这两种状态之间的转变时间随着注入速率的增加而减小。我们提出了一个理论模型，该模型与我们的实验结果一致，解释了第二种状态的起源，并预测了转变时间与注入速率和迁移率的缩放关系。观察到的缩放关系的关键决定因素是驱替前沿处平流和扩散时间尺度之间的竞争，这表明我们可以将分析应用于其他界面演化问题，如Rayleigh-Bénard-Darcy不稳定性。
