AI 中文总结
该研究发现，当稀聚合物溶液流动中聚合物局域在基流速剖面最大值附近或通道流中心线附近时，会显著增强中心模式弹性不稳定性，其机制与聚合物浓度梯度产生的弹性反馈力相关。
AI 中文摘要
中心模式弹性不稳定性在稀聚合物溶液的直线流动中普遍存在，即使在无惯性的情况下也能产生动态状态。本研究表明，当基流具有非均匀的聚合物空间分布时，这种不稳定性会显著增强。具体而言，我们考虑了一个载有聚合物的流股被纯溶剂流股夹在中间的流动场景。在这类流动中，聚合物应力不仅取决于构象张量（此处由Oldroyd-B方程确定），还与满足标量输运方程的聚合物浓度场成比例变化。我们研究了斯托克斯极限，并首先聚焦于周期性柯尔莫哥洛夫流的简单场景。线性稳定性分析显示，当基流中的聚合物局域在基流速剖面的最大值附近时，中心模式不稳定性会被强烈促进；而将聚合物集中在最大剪切附近则会抑制该不稳定性。随着聚合物负载量增加，非均匀系统的中性稳定性曲线会呈现双瓣形式，这会导致临界魏森贝格数（弹性弛豫时间与典型应变率的乘积）突然下降。能量分析将这种失稳归因于聚合物浓度梯度产生的弹性反馈力。最后，我们证明了这些发现与通道流的相关性，其中将聚合物局域在中心线附近会强烈促进中心模式不稳定性。
英文摘要
The centre-mode elastic instability, prevalent in rectilinear flows of dilute polymer solutions, allows dynamic states to emerge even in the absence of inertia. Here, we show that this instability can be significantly enhanced when the base flow has a nonuniform spatial-distribution of polymers. In such a flow, the polymeric stress not only depends on the conformation tensor (determined here by the Oldroyd-B equation) but also varies proportionally with the polymer concentration field, which satisfies a scalar transport equation. Focusing on the inertialess Stokes limit, we first consider the simple setting of periodic Kolmogorov flow. A linear stability analysis shows that a nonuniform polymer concentration either promotes or suppresses the centre-mode instability, depending on whether the polymers are localised near or away from the maximum of the base-velocity profile. We then focus on a base flow with a distinct polymer-laden stream overlying the base-velocity maximum, and sandwiched between polymer-free streams. We find that the critical Weissenberg number (product of the elastic relaxation time and the typical strain-rate) at the onset of instability undergoes a sudden decrease as the total polymer loading is increased. An energy analysis attributes this destabilisation to elastic feedback forces that arise from concentration gradients near the interfaces between the polymer-laden and polymer-free streams. The insights from Kolmogorov flow are shown to carry over to channel flow, where localising polymers about the centreline strongly promotes the centre-mode instability.
Comments23 pages, 15 figures
