We numerically investigate the deformation of a train of power-law droplets in a highly viscous suspending medium in nonlinear microfluidic geometry. We examine how viscous stresses conspire against surface tension in two-dimensional incompressible liquid–liquid flow in a corrugated microchannel using the finite volume technique with the volume of fluid method. To instill the influences of shear thinning, Newtonian, and shear-thickening fluids, the range of power-law indices $\left(n\right)$ is varied from $0.7-1.3$. We validate our numerical model with the available literature data in good agreement. Interestingly, the corrugated cavities are found to have an elongating effect on the non-Newtonian droplets, whereas literature delineates a compressive effect of the nonlinear geometry on bubbles. Specific orbital trajectories are found in the (droplet length A, spacing B) space with dispersed and synchronized orbitals at low and high capillary number for all power-law droplets, respectively. Furthermore, the hysteresis in the droplet shape is found to increase with the capillary number. Consequently, the hysteretic area $A_p$ revealed that the slope increases with $\left(n\right)$. An interesting finding is elucidated where the hysteresis loops are found to rotate from low capillary to high capillary number for all power-law droplets. A new finding is reported where the evolution of the droplet perimeter revealed the development of secondary peaks as the capillary number increases. The power-law droplets are found to pack themselves up in the corrugated section in two distinct regimes: smaller droplets obey the linear deformation regime. In contrast, large droplets lie in the flow-induced deformation regime. The instantaneous cap velocities produce a nonmonotonic behavior for the front velocity as the capillary number increases for all power-law droplets. We develop functional relationships between flow parameters of segmented flows at the pore scale for every non-Newtonian droplet. Given the implications of this setup with industrial and biomedical applications, the illustrations shown herein could be beneficial in tackling problems at the pore scale with nonlinear fluids.

我们数值研究了非线性微流体几何中高粘性悬浮介质中一列幂律液滴的变形。我们使用有限体积技术和流体体积法研究了粘性应力如何与波纹微通道中二维不可压缩液-液流动中的表面张力共同作用。为了灌输剪切稀化、牛顿流体和剪切增稠流体的影响，幂律指数的范围$\left(n\right)$不同于$0.7-1.3$. 我们用现有的文献数据验证了我们的数值模型，结果非常吻合。有趣的是，发现波纹腔对非牛顿液滴具有拉长效应，而文献描述了非线性几何结构对气泡的压缩效应。在（液滴长度A，间距B ）空间中发现特定的轨道轨迹，所有幂律液滴的低毛细管数和高毛细管数分别具有分散和同步的轨道。此外，发现液滴形状的滞后现象随着毛细管数的增加而增加。因此，滞后区$A_p$显示斜率随着$\left(n\right)$. 阐明了一个有趣的发现，发现所有幂律液滴的滞后回线从低毛细管数旋转到高毛细管数。报告了一项新发现，其中液滴周长的演变揭示了随着毛细管数量的增加，二次峰的发展。发现幂律液滴以两种不同的方式在波纹部分中自行堆积：较小的液滴服从线性变形方式。相反，大液滴位于流动引起的变形区域。随着所有幂律液滴的毛细管数增加，瞬时帽速度产生前沿速度的非单调行为。我们为每个非牛顿液滴在孔隙尺度上建立了分段流动的流动参数之间的函数关系。