论文标题
在小stokes中的细胞流中的惯性颗粒的分散体
Dispersion of inertial particles in cellular flows in the small-Stokes, large-Péclet regime
论文作者
论文摘要
当对流占主导地位和扩散时，我们通过细胞流来调查惯性颗粒的传输，也就是说，对于满足$ \ mathrm {st} \ ll 1 $和$ \ mathrm {pe}} \ gg 1 $的$ \ mathrm {st} \ ll 1 $ \ mathrm {st} \ ll 1 $ \ mathrm {st} \ ll 1 $。从Maxey-Riley模型开始，我们考虑了划分的缩放$ \ mathrm {st} \，\ Mathrm {pe} = o（1）$，并得出近似于完整langevin动力学的有效的brownian动力学。然后，我们应用均质化并匹配的拼图技术来获得有效扩散率$ \ operline {d} $表征长期分散体的显式表达。此表达式量化了$ \叠加{d} $的方式，与$ \ mathrm {pe}^{ - 1/2} $成比例时，当被忽略惯性时，比流体重的粒子增加并减少较轻的颗粒。特别是，当$ \ mathrm {st} \ gg \ mathrm {pe}^{ - 1} $时，我们发现$ \ overline {d} $与$ \ mathrm {st}}^{st}^{1/2}/（1/2}/（\ log} $ \ mathrm {st} \，\ mathrm {pe} $的粒子和指数较小。我们验证了针对粒子动力学数值模拟的渐近预测。
We investigate the transport of inertial particles by cellular flows when advection dominates over inertia and diffusion, that is, for Stokes and Péclet numbers satisfying $\mathrm{St} \ll 1$ and $\mathrm{Pe} \gg 1$. Starting from the Maxey--Riley model, we consider the distinguished scaling $\mathrm{St} \, \mathrm{Pe} = O(1)$ and derive an effective Brownian dynamics approximating the full Langevin dynamics. We then apply homogenisation and matched-asymptotics techniques to obtain an explicit expression for the effective diffusivity $\overline{D}$ characterising long-time dispersion. This expression quantifies how $\overline{D}$, proportional to $\mathrm{Pe}^{-1/2}$ when inertia is neglected, increases for particles heavier than the fluid and decreases for lighter particles. In particular, when $\mathrm{St} \gg \mathrm{Pe}^{-1}$, we find that $\overline{D}$ is proportional to $\mathrm{St}^{1/2}/(\log ( \mathrm{St} \, \mathrm{Pe}))^{1/2}$ for heavy particles and exponentially small in $\mathrm{St} \, \mathrm{Pe}$ for light particles. We verify our asymptotic predictions against numerical simulations of the particle dynamics.
