We present the study of viscous fingering in the radial hele shaw cell, using the shear-dependent rheological fluid which transitions from the Newtonian to shear thinning behaviour, at low shear rates. The experimental observations show that the characteristic features of the fingering phenomena in the case of shear-thinning flow (such as side branching, growth of second generation fingers, inhibition of tip splitting), is observed at late times, from an initial Newtonian regime. On account of the asymmetry of the fingering structure, the local shear rate is non-uniform. This leads to different rheological behaviour in different sections of the network locally, revealing contrasting local fingering patterns, specific to the respective fluid rheological state based on the local shear rate. This is also explained using the numerical simulations for such rheological fluid, in the two-phase porous media flow. The fingering features, such as the length, width are quantified as a function of the flowrate. We have also observed detachment of the fingers beyond a certain critical size of the fingering network. Finally, the stability of the fingering is also investigated at ultra low flow rates, which suggests that the duration of stability exists much beyond what is predicted using the linear stability analysis for classical Newtonian flows.

我们使用剪切相关的流变流体在低剪切速率下从牛顿流体转变为剪切稀化行为，对径向 hele shaw 单元中的粘性指法进行了研究。实验观察表明，在剪切稀化流的情况下，指法现象的特征特征（例如侧分支、第二代指状物的生长、尖端分裂的抑制）在晚期观察到，从最初的牛顿状态开始。由于指状结构的不对称性，局部剪切速率是不均匀的。这导致局部网络不同部分的不同流变行为，揭示了对比鲜明的局部指法模式，特定于基于局部剪切速率的相应流体流变状态。这也可以在两相多孔介质流中使用此类流变流体的数值模拟来解释。指法特征，例如长度、宽度，被量化为流速的函数。我们还观察到手指脱离超过指法网络的某个临界尺寸。最后，还在超低流速下研究了指法的稳定性，这表明稳定性的持续时间远远超出使用经典牛顿流动的线性稳定性分析预测的时间。