微管道中具有自由面非牛顿流体电渗流动的不稳定性

Microfluidic devices have become important due to their applications in micro-electro-mechanical systems (MEMS) and microbiological sensors. When an electrolyte comes in contact with a microchannel wall in which the fluid flows, it will result in a charge transfer between the electrolyte and the wall, depending on the chemical composition of the microchannel and the electrolyte chemical processes at the surface. The surface charge leads to the formation of an electric double layer (EDL) by influencing the distribution of counter-ions and co-ions in the liquid phase. When an electric field is applied tangentially along the charged surface, it will exert a Coulombic force on the ions within the EDL. The migration of the mobile ions will carry the adjacent and bulk liquid phase by viscosity, resulting in an electroosmotic flow (EOF).Now the EOF is widely used in the fields of biology, chemistry and medicine.Currently studies are mainly concerned with Newtonian fluids. However, microfluidic devices are often open and it is usually used to analyze biofluids, which are often solutions of long chain molecules which impart a non-Newtonian rheological behavior. Thus we have to consider the EOF of non-Newtonian fluid with a free surface. By theoretical analysis and numerical computations, taking the microfluid with a free surface as non-Newtonian thin film, using lubrication approximation, we will derive the evolution equation of the non-Newtonian thin film. Furthermore, the EOF instability of the non-Newtonian fluid will be studied.

微流体在微电子系统（MEMS）和生物传感器领域有很重要的应用。当电解质与微管道管道壁相互接触时，就会引起壁面与电解质之间的电荷交换。表面的电荷通过影响流体中阴离子和阳离子的分布形成了双电层 (EDL)。受外加电场的作用，双电层 (EDL) 中的离子将会受到库伦力的作用而运动。由于流体的粘性，可以移动的（自由）离子将会带动附近流体微团运动，最终形成了电渗流 (EOF)。现在电渗流被广泛地用于生物、化学和制药领域。目前对电渗流动的研究主要局限于牛顿流体，但微流体装置常被用来分析生物流体，这些流体经常是长链分子的非牛顿流体，并且是在开的微管道中进行的，这样就必须考虑自由面非牛顿流体电渗流问题。本项目通过理论分析和数值计算，将具有自由面的微流体当做非牛顿流体薄膜来处理，利用润滑近似导出幂律流体和粘弹性流体薄膜高度满足的时空演化方程，进而研究它的电渗流动的不稳定性问题，揭示其不稳定性机理。

本项目研究了微管道中具有自由面上随体Maxwell流体电渗流动的不稳定性和非牛顿流体电渗流动问题。对于上随体Maxwell流体，得到了描述自由表面运动的Orr-Sommerfeld特征问题方程。运用线性稳定性理论分析了表面长因子(增长速率)对线性黏弹性(上随体Maxwell模型)流体电渗流动的影响。对于具有自由表面幂律流体电渗流动的不稳定性以及高zeta势下具有自由表面非牛顿流体的稳定性问题，因为此类问题具有较强非线性效应，寻找解析解较为困难，此研究内容做了相应的调整。此外，本项目执行期间除了研究电渗流自由面不稳定性外，还研究了线性黏弹性流体(包括广义Maxwell流体和Jeffreys流体)在不同微管道(包括一维平行板、圆形、圆环和二维半圆形)中周期/瞬时电渗流动，得到了无量纲速度和体积流率的解析表达式。另外，本项目还研究了垂向磁场作用下，平行微管道内Jeffreys流体的非定常电渗流动和具有正弦粗糙度的平行微管道间牛顿流体的电磁流动，得到了受磁场强度相关的无量纲参数Ha等影响的速度表达式和受粗糙度影响的平均速度(体积流率)。