微扩张管道内幂律流体非定常电渗流动

Electroosmotically-driven flow of power-law fluid in a micro-diffuser

研究了电渗驱动下幂律流体在有限长微扩张管道内非稳态流动特性.基于Ostwald-de Wael幂律模型,采用高精度紧致差分离散二维Poisson-Nernst-Planck方程及修正的Cauchy动量方程,数值模拟了初始及稳态时刻微扩张管道内幂律流体电渗流流场分布情况,研究了管道截面改变对幂律流体无量纲剪切应变率及无量纲表观黏度的影响,以及无量纲表观黏度对拟塑性流体与胀流型流体流速分布的影响.数值模拟结果显示,当扩张角和无量纲电动宽度一定时,电场驱动下的幂律流体在近壁区域速度响应都很快;初始时刻,近壁处表观黏度的变化受到剪切应变率变化的影响,从而影响了三种幂律流体速度峰值的分布,出现拟塑性流体流速在扩张段上游及扩张段近壁处速度峰值均为幂律流体中最大、而在扩张段下游三种幂律流体速度峰值相近的现象;稳态时刻,幂律流体速度剖面呈现塞型分布,且满足连续性条件下,幂律流体流速随扩张管半径增大而减小,牛顿流体流动规律与宏观尺度下流动规律相同;初始时刻,在相同电动宽度、不同壁面电势作用下,幂律流体在扩张管近壁处剪切应变率分布的差异导致表观黏度分布的差异,并最终导致拟塑性流体与胀流型流体流速分布的差异.

The unsteady electroosmotic flow characters of power-law fluids in a finite micro-diffuser are studied in this paper.Based on the Ostwald-de Wael model which is used to describe power-law fluids（the shear thinning, thickening and Newtonian fluids）, high accuracy compact difference schemes are used to solve the two-dimensional Poisson-NernstPlanck equations and the modified Cauchy momentum equations. Electroosmotic flow distributions of power-law fluids at initial instant and steady state are numerically simulated in this paper. It is presented that while the radius of the diffuser is increasing, the dimensionless apparent viscosity influenced by shear strain conduces to the different velocity profiles of power-law fluids. In the micro-diffuser, the shear strains of pseudo plastic and dilatant fluids are decreasing with the radius increasing and the apparent viscosity of pseudo plastic fluid is increasing with the shear strain decreasing,but the apparent viscosity of dilatant fluid is decreasing with the shear strain decreasing. The apparent viscosity of power-law fluids can estimate the flow performance, and the fluid with high viscosity flows more slowly than the one with low viscosity. The numerical results show that a fast speed response of power-law fluid is found near the wall at the beginning and the average dimensionless velocity of power-law fluids is decreasing with the radius increasing when fixing the diffuser angle and dimensionless electrokinetic diameter at the same dimensionless zeta potentials. At the initial instant, the different velocity distributions of power-law fluids from upstream to downstream near the wall in diffuser are essentially due to the change of dimensionless shear strain. Because the dimensionless shear strains of pseudo plastic and dilatant fluids are in a larger value zone in upstream, the dimensionless apparent viscosity of dilatant fluid is larger than that of the pseudo plastic fluid, and the velocity peak of pseudo plastic fluid is larger than that of the dilatant fluid. In downstream, the apparent viscosity of pseudo plastic fluid is larger than that of the dilatant fluid so that their velocity peaks are similar. At the steady state, the velocity profiles of power-law fluids are plug-like and the velocity is decreasing with increasing radius when the continuity conditions are satisfied, and the flow regularity of Newtonian is just like that on a macroscopic scale. The velocity profile of pseudo plastic fluid is larger than that of dilatant fluid in upstream and their velocity profiles in downstream are not much different. The power-law fluid flow distribution at initial instant is similar to that at the steady state. From the flow regularities respectively at initial instant and the steady state it follows that the flow rate of pseudo plastic fluid is larger than that of Newtonian fluid and the dilatant fluid flow rate is smaller than Newtonian fluid rate. At the initial instant, under the same electrokinetic diameter and different zeta potentials, the difference in shear strain among power-law fluids in the micro-diffuser near the wall leads to the difference in the apparent viscosity, and eventually leads to the velocity distribution difference between pseudo plastic and dilatant fluids.