Longitudinal thermocapillary slip about a dilute periodic mattress of protruding bubbles
Longitudinal thermocapillary slip about a dilute periodic mattress of protruding bubbles
复制标题
围绕突出气泡的稀周期性床垫的纵向热毛细管滑移
DOI：
--
复制
发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Toby L. Kirk
中科院分区：
文献类型：
--
作者：
E. Yariv;Toby L. Kirk
超疏水表面的一种常见实现包括捕获在周期性槽状固体衬底中的圆柱形气泡的周期性阵列。我们考虑了液体运动的热毛细动画的宏观温度梯度，这是纵向施加在这种气泡床垫。假设界面张力随温度呈线性变化，斜率为$\sigma _T$，我们寻求液体在远离床垫很远的地方获得的有效速度滑移。我们将重点放在稀释极限上，其中槽宽$2c$与阵列周期$2l$相比较小。在施加梯度方向上所需的速度滑移，由对单个气泡的局部分析确定，由近似$$\begin{align*}& \pi \frac{G\sigma_T c^2}{\mu l} I(\alpha), \end{align*}$$提供，其中$G$是施加梯度幅度，$\mu $是液体粘度，$I(\alpha )$是突出角$\alpha $的非单调函数，由正交函数提供。 $$\begin{align*}& I(\alpha) = \frac{2}{\sin\alpha} \int_0^\infty\frac{\sinh s\alpha}{ \cosh s(\pi-\alpha) \sinh s \pi} \, \textrm{d} s. \end{align*}$$
A common realization of superhydrophobic surfaces comprises of a periodic array of cylindrical bubbles which are trapped in a periodically grooved solid substrate. We consider the thermocapillary animation of liquid motion by a macroscopic temperature gradient which is longitudinally applied over such a bubble mattress. Assuming a linear variation of the interfacial tension with the temperature, at slope $\sigma _T$, we seek the effective velocity slip attained by the liquid at large distances away from the mattress. We focus upon the dilute limit, where the groove width $2c$ is small compared with the array period $2l$. The requisite velocity slip in the applied-gradient direction, determined by a local analysis about a single bubble, is provided by the approximation $$\begin{align*}& \pi \frac{G\sigma_T c^2}{\mu l} I(\alpha), \end{align*}$$wherein $G$ is the applied-gradient magnitude, $\mu $ is the liquid viscosity and $I(\alpha )$, a non-monotonic function of the protrusion angle $\alpha $, is provided by the quadrature, $$\begin{align*}& I(\alpha) = \frac{2}{\sin\alpha} \int_0^\infty\frac{\sinh s\alpha}{ \cosh s(\pi-\alpha) \sinh s \pi} \, \textrm{d} s. \end{align*}$$
影响因子：
4.6
作者：
D. Crowdy
通讯作者：
D. Crowdy