超疏水沟槽气体区的边界条件
Boundary conditions at the gas sectors of superhydrophobic grooves
摘要：
研究了单向超疏水表面上液体流过气体扇区的流体动力学问题。注意力集中在液-气界面处的局部滑移边界条件上，该边界条件等效于气体空腔对液体流动的影响。该系统的特征在于液体和气体之间的大粘度对比$μ/μ_g \gg 1$。我们解释早期的结果，即依赖于流动方向的局部滑移长度，在张量局部滑移边界条件和相关的特征值的局部滑移长度张量的纹理参数，如宽度的凹槽，$δ$，和凹槽的局部深度，$e(y, α)$。后者在$y$方向上变化，垂直于条纹的方向，并且取决于在三相相交的点处的凹槽边缘的斜角$π/2 - α$。我们的理论表明，当凹槽是足够深的本地滑移长度张量的特征值只依赖于$μ/μ_g$，$δ$，和$α$，但不依赖于深度。浅槽的局部滑移长度的特征值依赖于$μ/μ_g$和$e(y, α)$，尽管斜角的贡献是中等的。为了评估我们的理论的有效性，我们提出了一种新的方法来解决两相流体动力学问题，这显着方便和加速计算相比，传统的数值方案。数值结果表明，我们的简单的解析描述得到的深槽和浅槽的极限情况下仍然有效的各种单向纹理。
英文摘要：
The hydrodynamics of liquid flowing past gas sectors of unidirectional superhydrophobic surfaces is revisited. Attention is focussed on the local slip boundary condition at the liquid-gas interface, which is equivalent to the effect of a gas cavity on liquid flow. The system is characterized by a large viscosity contrast between liquid and gas, $μ/μ_g \gg 1$. We interpret earlier results, namely the dependence of the local slip length on the flow direction, in terms of a tensorial local slip boundary condition and relate the eigenvalues of the local slip length tensor to the texture parameters, such as the width of the groove, $δ$, and the local depth of the groove, $e(y, α)$. The latter varies in the direction $y$, orthogonal to the orientation of stripes, and depends on the bevel angle of groove's edges, $π/2 - α$, at the point, where three phases meet. Our theory demonstrates that when grooves are sufficiently deep their eigenvalues of the local slip length tensor depend only on $μ/μ_g$, $δ$, and $α$, but not on the depth. The eigenvalues of the local slip length of shallow grooves depend on $μ/μ_g$ and $e(y, α)$, although the contribution of the bevel angle is moderate. In order to assess the validity of our theory we propose a novel approach to solve the two-phase hydrodynamic problem, which significantly facilitates and accelerates calculations compared to conventional numerical schemes. The numerical results show that our simple analytical description obtained for limiting cases of deep and shallow grooves remains valid for various unidirectional textures.
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