AI 中文总结
研究Hele-Shaw流中粘性指进模式，用水平集方法全非线性数值模拟，测试Beeson-Jones-Woods饱和模型，发现其对单相流有效，对两相流因表面张力等因素存在差异，该模型对类扩散限制聚集模式有效但非通用。
AI 中文摘要
具有界面的Hele-Shaw流会产生复杂图案形成，Saffman-Taylor不稳定性引发粘性指进过程并伴有尖端分裂和分支。最常见的实验是将低粘性流体注入高粘性流体的径向配置。Beeson-Jones和Woods提出了一种简单经验模型来预测侵入指状物的饱和剖面。我们用水平集方法进行全非线性数值模拟，在广泛参数范围内测试该模型有效性。发现该模型在预测单相流粘性指进模式的一些近通用特性时很有效，但对于较大表面张力参数值和两相流，模型与观测结果存在差异。通过研究前进指状物的形态解释了这些差异。总体而言，研究表明Beeson-Jones-Woods饱和模型对类扩散限制聚集模式有效，但在两相流中不通用，因为表面张力和粘度比会显著改变指状物形态和饱和剖面。
英文摘要
Hele-Shaw flows with an interface are known to give rise to complex pattern formation, whereby the Saffman-Taylor instability triggers a viscous fingering process accompanied by tip splitting and branching. The most popular of these experiments involves a radial configuration with a less viscous fluid injected into a more viscous fluid. In an attempt to characterize the resulting complexity in such an experiment, Beeson-Jones and Woods (2019) have proposed a type of simple empirical model that aims to predict the saturation profile of the invading fingers as a function of a radial coordinate. We revisit the proposed saturation model and test its validity over a broad parameter range using fully nonlinear numerical simulations computed with a level set method. We find that the saturation model is very effective at predicting some near-universal properties of the viscous fingering patterns for one-phase flows, where the invading fluid is neglected, with a sufficiently small surface tension parameter. For larger values of this parameter and for two-phase flows, there are discrepancies between the model and our observations. We explain these differences by studying the morphology of the advancing fingers, including pinching at the base and the rate of tip splitting. Overall, our study shows that the Beeson-Jones-Woods saturation model serves as a valid description of DLA-like patterns, but is not universal over two-phase flows, where surface tension and viscosity ratio substantially alter finger morphology and the resulting saturation profile.
Commentsto be published in Physical Review Fluids
