Pressure-driven transient flows of Newtonian fluids through microtubes with slip boundary
Pressure-driven transient flows of Newtonian fluids through microtubes with slip boundary
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DOI：
10.1016/j.physa.2008.06.043
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发表时间：
2008-10
影响因子：
3.3
通讯作者：
Yonghong Wu;B. Wiwatanapataphee;Maobin Hu
中科院分区：
文献类型：
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作者：
Yonghong Wu;B. Wiwatanapataphee;Maobin Hu
微尺度实验和分子模拟的最新进展证实，流体在固体表面的滑移是在小尺度下发生的，因此传统的流体力学无滑移边界条件不能适用于微米和纳米尺度的管和通道中的流动。另一方面，由于生物化学芯片实验室系统和微机电系统制造技术的出现，迫切需要了解微米尺度下的流体流动。本文研究了不可压缩牛顿流体在具有Navier滑移边界条件的微管中的压力驱动瞬态流动。一个精确的解决方案，推导出，包括一些现有的已知结果作为特殊情况。通过对所得解的分析，发现对于不同的驱动压力场，边界滑移对流动特性的影响是不同的。对于具有恒定压力梯度的压力场，边界滑移不会改变内部材料的变形和应力场;而对于具有波形压力梯度的压力场，边界滑移会改变内部材料的变形，从而改变速度分布和应力场。我们还导出了精确解的渐近表达式，通过该表达式确定了一个参数β_（？）控制波形压力梯度驱动的流动行为，并建立了导致最大瞬态流量的临界滑移参数的显式公式。
Recent advances in microscale experiments and molecular simulations confirm that slip of fluid on solid surface occurs at small scale, and thus the traditional no-slip boundary condition in fluid mechanics cannot be applied to flow in micrometer and nanometer scale tubes and channels. On the other hand, there is an urgent need to understand fluid flow in micrometer scale due to the emergence of biochemical lab-on-the-chip system and micro-electromechanical system fabrication technologies. In this paper, we study the pressure driven transient flow of an incompressible Newtonian fluid in microtubes with a Navier slip boundary condition. An exact solution is derived and is shown to include some existing known results as special cases. Through analysis of the derived solution, it is found that the influences of boundary slip on the flow behaviour are qualitatively different for different types of pressure fields driving the flow. For pressure fields with a constant pressure gradient, the boundary slip does not alter the interior material deformation and stress field; while, for pressure fields with a wave form pressure gradient, the boundary slip causes the change of interior material deformation and consequently the velocity profile and stress field. We also derive asymptotic expressions for the exact solution through which a parameter β̄ is identified to dominate the behaviour of the flow driven by the wave form pressure gradient, and an explicit formulae for the critical slip parameter leading to the maximum transient flow rate is established.