Inertial enhancement of the polymer diffusive instability
Inertial enhancement of the polymer diffusive instability
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DOI：
10.1017/jfm.2024.21
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发表时间：
2023-08
影响因子：
3.7
通讯作者：
M. Couchman;M. Beneitez;Jacob Page;R. Kerswell
中科院分区：
文献类型：
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作者：
M. Couchman;M. Beneitez;Jacob Page;R. Kerswell
[摘要]Beneitez et al.[物理学报]；Rev. Fluids, vol. 8, 2023, L101901)利用Peterlin有限可扩展非线性弹性本质模型（FENE-P），在存在聚合物应力扩散的情况下，在无惯性直线粘弹性剪切流中发现了一种新的线性“聚合物扩散不稳定性”（PDI）。在这里，考虑到FENE-P和更简单的Oldroyd-B本构关系，我们研究了在不同的Weissenberg数${W}$、聚合物应力扩散率$\varepsilon$、溶剂与总粘度比$\beta$和雷诺数${Re}$下，惯量对平面Couette和平面Poiseuille流动的PDI的影响。随着${Re}$的增大，参数空间中不稳定性的流行率和相关的增长率都显著增加。例如，当$Re$随$\beta$固定而增加时，不稳定性在$W$和$\varepsilon$的值逐渐低于无惯性极限时出现，当所有其他参数固定时，相关增长率随$Re$线性增加。对于有限的$Re$，还证明了Schmidt数$Sc=1/(\varepsilon Re)$在不同的$Re$和$\varepsilon$上的中性稳定性曲线的崩溃。观察到的PDI随惯性的增强，以及应力扩散在时间步进算法中总是存在的事实，要么隐式地作为方案的一部分，要么显式地作为稳定器，这意味着不稳定性可能在使用流行的Oldroyd-B和FENE-P本构模型的计算工作中起作用。现在的根本问题是，PDI究竟是物理上的、可在实验中观察到的，还是必须被抑制的本构模型的产物。
Abstract Beneitez et al. (Phys. Rev. Fluids, vol. 8, 2023, L101901) have recently discovered a new linear ‘polymer diffusive instability’ (PDI) in inertialess rectilinear viscoelastic shear flow using the finitely extensible nonlinear elastic constitutive model of Peterlin (FENE-P) when polymer stress diffusion is present. Here, we examine the impact of inertia on the PDI for both plane Couette and plane Poiseuille flows under varying Weissenberg number ${W}$, polymer stress diffusivity $\varepsilon$, solvent-to-total viscosity ratio $\beta$ and Reynolds number ${Re}$, considering the FENE-P and simpler Oldroyd-B constitutive relations. Both the prevalence of the instability in parameter space and the associated growth rates are found to significantly increase with ${Re}$. For instance, as $Re$ increases with $\beta$ fixed, the instability emerges at progressively lower values of $W$ and $\varepsilon$ than in the inertialess limit, and the associated growth rates increase linearly with $Re$ when all other parameters are fixed. For finite $Re$, it is also demonstrated that the Schmidt number $Sc=1/(\varepsilon Re)$ collapses curves of neutral stability obtained across various $Re$ and $\varepsilon$. The observed strengthening of PDI with inertia and the fact that stress diffusion is always present in time-stepping algorithms, either implicitly as part of the scheme or explicitly as a stabilizer, implies that the instability is likely operative in computational work using the popular Oldroyd-B and FENE-P constitutive models. The fundamental question now is whether PDI is physical and observable in experiments, or is instead an artifact of the constitutive models that must be suppressed.