Slip length for longitudinal shear flow over an arbitrary-protrusion-angle bubble mattress: the small-solid-fraction singularity
Slip length for longitudinal shear flow over an arbitrary-protrusion-angle bubble mattress: the small-solid-fraction singularity
复制标题
任意凸角气泡床垫上纵向剪切流的滑移长度：小固体分数奇点
DOI：
--
复制
发表时间：
2017
影响因子：
3.7
通讯作者：
Ory Schnitzer
中科院分区：
文献类型：
--
作者：
Ory Schnitzer
研究了超疏水气泡床层在小固相分数极限下单向流动的有效滑移长度。利用标度变元和理想流类比，我们解释了滑移长度的奇异性为$\Unicode[stix]{x1D716}\right tarrow 0$：相对于周期，对于突出角$0\leqslant\unicode[STIX]{x1D6FC}<；\unicode[STIX]{x03C0}/2$，它的标度为$\log(1/\unicode[stix]{x1D716})$，对于$0和lt，其标度为$\unicode[stix]{x1D716}^{-1/2}$；\unicode[STIX]{x03C0}/2-\unicode[STIX]{x1D6FC}=O(\unicode[STIX]{x1D716}^{1/2})$.我们继续使用匹配渐近展开的方法进行详细的渐近分析，其中在实心段附近有效的“内”解与在周期尺度上有效的“外”解相匹配，其中从实心凹槽突出的气泡似乎接触。分析得到了在每个凸角区域内有效滑移长度的渐近展开式。这些展开式对于中间突出角重叠，这允许我们对任意突出角$0\leqslant\unicode[stix]{x1D6FC}\leqslant\unicode[stix]{x03C0}/2$形成一致有效的近似。由此，我们明确地描述了随着突出角的增加，从对数到代数小固体分数滑移长度奇点的转变。
We study the effective slip length for unidirectional flow over a superhydrophobic mattress of bubbles in the small-solid-fraction limit $\unicode[STIX]{x1D716}\ll 1$ . Using scaling arguments and utilising an ideal-flow analogy we elucidate the singularity of the slip length as $\unicode[STIX]{x1D716}\rightarrow 0$ : relative to the periodicity it scales as $\log (1/\unicode[STIX]{x1D716})$ for protrusion angles $0\leqslant \unicode[STIX]{x1D6FC}<\unicode[STIX]{x03C0}/2$ and as $\unicode[STIX]{x1D716}^{-1/2}$ for $0<\unicode[STIX]{x03C0}/2-\unicode[STIX]{x1D6FC}=O(\unicode[STIX]{x1D716}^{1/2})$ . We continue with a detailed asymptotic analysis using the method of matched asymptotic expansions, where ‘inner’ solutions valid close to the solid segments are matched with ‘outer’ solutions valid on the scale of the periodicity, where the bubbles protruding from the solid grooves appear to touch. The analysis yields asymptotic expansions for the effective slip length in each of the protrusion-angle regimes. These expansions overlap for intermediate protrusion angles, which allows us to form a uniformly valid approximation for arbitrary protrusion angles $0\leqslant \unicode[STIX]{x1D6FC}\leqslant \unicode[STIX]{x03C0}/2$ . We thereby explicitly describe the transition with increasing protrusion angle from a logarithmic to an algebraic small-solid-fraction slip-length singularity.
具有弯曲弯液面的气泡垫上的纵向剪切流：任意突出角和固体分数
影响因子：
1.2
作者：
Luca E
通讯作者：
Luca E
影响因子：
4.6
作者：
D. Crowdy
通讯作者：
D. Crowdy