Classical viscous fingering patterns in flow displacement can be modulated by incorporating polymers into either of the two fluids. The polymeric solutions are viscoelastic fluids exhibiting both shear-thinning as well as elastic behavior. The present numerical study examines the dynamics of viscous fingering in miscible flow displacement with either displacing or displaced fluid being treated as polymeric fluid. The nonlinear rheology of the polymeric fluid is described using the White–Metzner model. The role of fluid rheology in the transient evolution of concentration field and fingering patterns defined using quantities such as mixing length, relative contact area, finger width, and the number of fingers, is investigated by performing numerical simulations. The correlation between fingering structure and rheological properties is established. The study shows that incorporation of polymer into the fluid alters the viscous fingering attributed to the three main factors: viscosity modification, shear-thinning behavior, and fluid elasticity. Primarily, incorporating polymers into the displaced (displacing) fluid leads to suppressed (enhanced) fingering patterns, attributed to modification of the viscosity contrast between two fluids, the governing parameter for viscous fingering. Interestingly, when the viscosity contrast at a gap-averaged shear-rate is held fixed, the shear-thinning behavior promotes the longitudinal growth of fingers irrespective of the fluid to which polymers are added. Moreover, the fluid elasticity ends to inhibit the growth of fingers leading to a more efficient flow displacement regardless of the flow arrangement. Thus, the study suggests that in addition to the viscosity at the gap-averaged shear-rate, the nature of the entire flow curve representing nonlinear rheology plays an important role in fingering dynamics. The mechanism for the destabilization due to shear-thinning behavior is explained by analyzing the vorticity structures, local shear-rate, and local viscosity distribution in the flow domain. The normal stress distribution is analyzed to comprehend the stabilization attributed to the fluid elasticity. Overall, the interplay between the viscosity contrast and the complete rheological description of the fluid governs the fingering dynamics.

可以通过将聚合物掺入两种流体中的任何一种来调节流动置换中的经典粘性指法模式。聚合物溶液是表现出剪切稀化以及弹性行为的粘弹性流体。目前的数值研究检查了混相流驱替中粘性指进的动力学，其中驱替或驱替流体被视为聚合物流体。使用 White-Metzner 模型描述了聚合物流体的非线性流变学。通过进行数值模拟，研究了流体流变学在浓度场的瞬态演变中的作用，以及使用混合长度、相对接触面积、手指宽度和手指数量等量定义的手指模式。建立了指型结构和流变特性之间的相关性。研究表明，将聚合物掺入流体会改变粘性指进，这归因于三个主要因素：粘度改性、剪切稀化行为和流体弹性。首先，将聚合物掺入置换（置换）流体会导致抑制（增强）指进模式，这归因于两种流体之间的粘度对比的修改，即粘性指进的控制参数。有趣的是，当间隙平均剪切速率下的粘度对比保持固定时，剪切变稀行为会促进手指的纵向生长，而与添加聚合物的流体无关。此外，流体弹性结束以抑制指状物的生长，从而导致更有效的流动置换，而与流动布置无关。因此，该研究表明，除了间隙平均剪切速率下的粘度外，代表非线性流变学的整个流动曲线的性质在指进动力学中也起着重要作用。通过分析流动域中的涡量结构、局部剪切速率和局部粘度分布，解释了由于剪切稀化行为导致的失稳机制。分析法向应力分布以理解归因于流体弹性的稳定性。总体而言，粘度对比和流体的完整流变描述之间的相互作用决定了指进动力学。通过分析流动域中的涡量结构、局部剪切速率和局部粘度分布，解释了由于剪切稀化行为导致的失稳机制。分析法向应力分布以理解归因于流体弹性的稳定性。总体而言，粘度对比和流体的完整流变描述之间的相互作用决定了指进动力学。通过分析流动域中的涡量结构、局部剪切速率和局部粘度分布，解释了由于剪切稀化行为导致的失稳机制。分析法向应力分布以理解归因于流体弹性的稳定性。总体而言，粘度对比和流体的完整流变描述之间的相互作用决定了指进动力学。