Change in drag, apparent slip and optimum air layer thickness for laminar flow over an idealised superhydrophobic surface
Change in drag, apparent slip and optimum air layer thickness for laminar flow over an idealised superhydrophobic surface
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DOI：
10.1017/jfm.2013.284
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发表时间：
2013-07-01
影响因子：
3.7
通讯作者：
Newton, M. I.
中科院分区：
文献类型：
--
作者：
Busse, A.;Sandham, N. D.;Newton, M. I.
分析结果推导出的表观滑移长度，阻力的变化和最佳的空气层厚度的层流通道和管流在一个理想化的超疏水表面，即一个气体层的恒定厚度保留在墙上。对于一个简单的Couette流的气体层总是有减阻效果，和表观滑移长度是积极的，假设有一个有利的液体和气体之间的粘度对比。在压力驱动的管道和通道流动中，阻塞限制了由气体层的润滑作用引起的阻力减小;因此可以导出最佳气体层厚度。阻力变化值和表观滑移长度受气相流动假设的强烈影响。与气体层中质量流率为零的替代假设相比，气体层中剪切速率恒定或气体层和液体层中压力梯度相等的标准假设给出的减阻值和表观滑移长度值要高得多。类似地，在零质量流率假设下，必须超过最小粘度对比度4以实现阻力减小，而在常规假设下，对于大于1的粘度对比度，阻力可以减小。因此，传统的润滑理论公式导致高估的最佳滑移长度和减阻时，适用于超疏水表面，气体被困。
Analytic results are derived for the apparent slip length, the change in drag and the optimum air layer thickness of laminar channel and pipe flow over an idealised superhydrophobic surface, i.e. a gas layer of constant thickness retained on a wall. For a simple Couette flow the gas layer always has a drag reducing effect, and the apparent slip length is positive, assuming that there is a favourable viscosity contrast between liquid and gas. In pressure-driven pipe and channel flow blockage limits the drag reduction caused by the lubricating effects of the gas layer; thus an optimum gas layer thickness can be derived. The values for the change in drag and the apparent slip length are strongly affected by the assumptions made for the flow in the gas phase. The standard assumptions of a constant shear rate in the gas layer or an equal pressure gradient in the gas layer and liquid layer give considerably higher values for the drag reduction and the apparent slip length than an alternative assumption of a vanishing mass flow rate in the gas layer. Similarly, a minimum viscosity contrast of four must be exceeded to achieve drag reduction under the zero mass flow rate assumption whereas the drag can be reduced for a viscosity contrast greater than unity under the conventional assumptions. Thus, traditional formulae from lubrication theory lead to an overestimation of the optimum slip length and drag reduction when applied to superhydrophobic surfaces, where the gas is trapped.