论文标题
球体中球体的惯性迁移
Inertial migration of a sphere in plane Couette flow
论文作者
论文摘要
我们研究了壁挂式平面couette中无扭矩浮力球的惯性迁移，该球体在宽阔的雷诺数字（$ re_c $）上，在小粒子雷诺数号，（$ re_p \ ll1 $）和约束比（$λ\ ll1 $ ll1 $）中。在这里，$ re_c = v_ \ text {wall} h/ν$其中$ h $表示通道墙之间的分离，$ v_ \ text {wall} $表示移动墙的速度，$ν$是牛顿式悬浮油的运动粘度； $λ= a/h $，$ a $是球形半径，$ re_p =λ^2 re_c $。发现频道中心线是关键$ re_c \，（\大约148）$下方唯一的（稳定）\，平衡，与早期的小$ re_c $分析的预测一致。关键$ re_c $上的超临界干草叉分叉产生了一对稳定的偏心平衡，相对于中心线对称地位于中心线，而原始的中心线平衡同时变得不稳定。新的均衡会随着$ re_c $的增加而迁移墙。与基于最新计算的推论相反，上述分叉发生在任意小$ re_p $提供的$λ$的情况下，足够小。在二维场景中发生了类似的分叉，也就是说，对于在平面couette流中自由悬浮的圆柱体，关键的$ re_c $约为$ 110 $。
We study the inertial migration of a torque-free neutrally buoyant sphere in wall-bounded plane Couette flow over a wide range of channel Reynolds numbers, $Re_c$, in the limit of small particle Reynolds number\,($Re_p\ll1$) and confinement ratio\,($λ\ll1$). Here, $Re_c = V_\text{wall}H/ν$ where $H$ denotes the separation between the channel walls, $V_\text{wall}$ denotes the speed of the moving wall, and $ν$ is the kinematic viscosity of the Newtonian suspending fluid; $λ= a/H$, $a$ being the sphere radius, with $Re_p=λ^2 Re_c$. The channel centerline is found to be the only (stable)\,equilibrium below a critical $Re_c\,(\approx 148)$, consistent with the predictions of earlier small-$Re_c$ analyses. A supercritical pitchfork bifurcation at the critical $Re_c$ creates a pair of stable off-center equilibria, symmetrically located with respect to the centerline, with the original centerline equilibrium simultaneously becoming unstable. The new equilibria migrate wallward with increasing $Re_c$. In contrast to the inference based on recent computations, the aforementioned bifurcation occurs for arbitrarily small $Re_p$ provided $λ$ is sufficiently small. An analogous bifurcation occurs in the two-dimensional scenario, that is, for a circular cylinder suspended freely in plane Couette flow, with the critical $Re_c$ being approximately $110$.
