Navier边界条件下的边界流动
Boundary streaming with Navier boundary condition
摘要：
在涉及固体边界上的高频声波的微流体应用中，斯托克斯边界层厚度$δ$非常小，以至于在流体-固体界面处可能发生一些不可忽略的滑移。本文评估的影响，通过重温经典问题的稳态声流在一个平坦的边界与Navier边界条件$u|_{y=0} = L_\mathrm{s} \partial_y u|_{y=0}$，其中$u$是速度切线的边界$y=0$，和参数$L_\mathrm{s}$是滑移长度。边界层外的边界提供了有效的滑移速度。作为无量纲参数$L_\mathrm{s}/δ$的函数，获得了边界层外流动速度的一般表达式。特别是行波和驻波表明，边界滑移分别增加和减少流动速度。
英文摘要：
In microfluidic applications involving high-frequency acoustic waves over a solid boundary, the Stokes boundary-layer thickness $δ$ is so small that some non-negligible slip may occur at the fluid-solid interface. This paper assesses the impact of the slip by revisiting the classical problem of steady acoustic streaming over a flat boundary with the Navier boundary condition $u|_{y=0} = L_\mathrm{s} \partial_y u|_{y=0}$, where $u$ is the velocity tangent to the boundary $y=0$, and the parameter $L_\mathrm{s}$ is the slip length. The limit outside the boundary layer provide an effective slip velocity. A general expression is obtained for the streaming velocity outside the boundary layer as a function of the dimensionless parameter $L_\mathrm{s}/δ$. Particularising to travelling and standing waves shows that the boundary slip respectively increases and decreases the streaming velocity.
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