Bending of elastic fibres in viscous flows: the influence of confinement ‡
Bending of elastic fibres in viscous flows: the influence of confinement ‡
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粘性流中弹性纤维的弯曲：限制的影响 ‡
DOI：
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发表时间：
2013
影响因子：
3.7
通讯作者：
H. Stone
中科院分区：
文献类型：
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作者：
J. Wexler;Philippe H. Trinh;H. Berthet;N. Quennouz;O. du Roure;H. Huppert;A. Lindner;H. Stone
摘要本文提出了一个数学模型和相应的一系列微流体实验，研究了粘性流体在三维通道中通过弹性纤维的流动。所述纤维的轴线垂直于流动方向，其基部夹紧在所述通道的一侧壁上；通道的侧壁靠近纤维，限制了流动。实验表明，在低流量下，高度受限纤维的挠度与流量之间存在线性关系，这启发了在这种情况下对问题的渐近处理。三维问题被简化为二维模型，包括通过屏障的Hele-Shaw流，屏障处的边界条件允许柔性和三维泄漏的影响。该分析深入了解了弯曲和泄漏的竞争效应，并推导出了一个解析解，该解析解对应于部分阻塞二维通道的狭缝所对应的一级压力场。我们的模型预测结果与实验结果一致，可以测量纤维的弹性和通道中的流速。
Abstract We present a mathematical model and corresponding series of microfluidic experiments examining the flow of a viscous fluid past an elastic fibre in a three-dimensional channel. The fibre’s axis lies perpendicular to the direction of flow and its base is clamped to one wall of the channel; the sidewalls of the channel are close to the fibre, confining the flow. Experiments show that there is a linear relationship between deflection and flow rate for highly confined fibres at low flow rates, which inspires an asymptotic treatment of the problem in this regime. The three-dimensional problem is reduced to a two-dimensional model, consisting of Hele-Shaw flow past a barrier, with boundary conditions at the barrier that allow for the effects of flexibility and three-dimensional leakage. The analysis yields insight into the competing effects of flexion and leakage, and an analytical solution is derived for the leading-order pressure field corresponding to a slit that partially blocks a two-dimensional channel. The predictions of our model show favourable agreement with experimental results, allowing measurement of the fibre’s elasticity and the flow rate in the channel.
影响因子：
3.4
作者：
Yuan-Nan Young;Matthew Downs;Christopher R. Jacobs
通讯作者：
Yuan-Nan Young;Matthew Downs;Christopher R. Jacobs