论文标题
粘弹性平面poiseuille流的中心模式不稳定
The center-mode instability of viscoelastic plane Poiseuille flow
论文作者
论文摘要
模态稳定性分析表明，OldRoyd-B流体的平面Poiseuille流对“中心模式”不稳定，相位速度接近最大基础流速度，$ u_ {max {max} $。理事无量纲组为雷诺数$ re re =ρu_{max} h/η$，弹性编号$ e =λη/（h^2ρ）$，以及溶剂与溶液粘度$η_s/η$的比率；在这里，$λ$是聚合物放松时间，$ h $是通道的半径，而$ρ$是流体密度。对于实验相关的值（例如，$ e \ sim 0.1 $和$β\ sim 0.9 $），预测的关键雷诺数，$ re_c $，对于中心模式的不稳定约为$ 200 $，相关的特征模式分布在整个频道中。在$ e（1-β）\ ll 1 $的渐近极限中，$ e $固定，对应于强弹性稀释聚合物溶液，$ re_c \ propto（e（1-β））^{ - \ frac {3} （E（1-β））^{ - \ frac {1} {2}} $。此极限中的不稳定本本元素限制在通道中心线附近的薄层中。以上特征在很大程度上类似于粘弹管流中的中心模式不稳定性（Garg等人，Phys。Phys。Rev.Lett。，121，024502（2018）），并提出了一种通用的线性机制，是通道中湍流和充满弱稀释的稀释聚合物溶液中湍流和管道流中湍流的发作。
A modal stability analysis shows that plane Poiseuille flow of an Oldroyd-B fluid becomes unstable to a `center mode' with phase speed close to the maximum base-flow velocity, $U_{max}$. The governing dimensionless groups are the Reynolds number $Re = ρU_{max} H/η$, the elasticity number $E = λη/(H^2ρ)$, and the ratio of solvent to solution viscosity $η_s/η$; here, $λ$ is the polymer relaxation time, $H$ is the channel half-width, and $ρ$ is the fluid density. For experimentally relevant values (e.g., $E \sim 0.1$ and $β\sim 0.9$), the predicted critical Reynolds number, $Re_c$, for the center-mode instability is around $200$, with the associated eigenmodes being spread out across the channel. In the asymptotic limit of $E(1 -β) \ll 1$, with $E$ fixed, corresponding to strongly elastic dilute polymer solutions, $Re_c \propto (E(1-β))^{-\frac{3}{2}}$ and the critical wavenumber $k_c \propto (E(1-β))^{-\frac{1}{2}}$. The unstable eigenmode in this limit is confined in a thin layer near the channel centerline. The above features are largely analogous to the center-mode instability in viscoelastic pipe flow (Garg et al., Phys. Rev. Lett., 121, 024502 (2018)), and suggest a universal linear mechanism underlying the onset of turbulence in both channel and pipe flows of suffciently elastic dilute polymer solutions.
