PNP模型的正弦粗糙微通道幂律流体电渗流研究

摘要

To investigate the effects of sinusoidal surface roughness on power-law fluids electroosmotic flow (EOF) flow characteristics in microchannels,the Poisson-Nernst-Planck (PNP) mathematical model of power-law fluid EOF in two-dimensional parallel-plate rough microchannels was established.The Poisson equation for electric double layers (EDL) potential,the Nernst-Planck equation for the ion concentration,the Cauchy momentum equation and the constitutive equation for flows of power-law fluid electrolyte solution were solved using the finite element method.After the PNP model of power-law fluid EOF is verified,the effects of sinusoidal surface roughness relative height and frequency on the EDL potential and EOF flow of power-law fluid were investigated.The computer simulation results show that the sinusoidal surface roughness greatly affects the distribution of externally applied electric potential,the EDL potential and velocity vectors of EOF near the roughness surface.The EDL potential at the wave trough area increases with the roughness relative height and frequency,while an opposite trend occurs at the wave crest region.The flow of power-law fluid decreases with the increase of the roughness relative height only,but with the increase of the roughness frequency,it first decreases to the lowest value,where the roughness frequency equals to 2.2 and then increases.Particularly,with the decrease of power-law index,the effects of sinusoidal surface roughness on the fluid increase.%针对正弦表面粗糙元对微通道内幂律流体电渗流(EOF)流动特性的影响,建立了二维平板粗糙微通道内幂律流体EOF的Poisson-Nemst-Planck(PNP)数学模型,采用有限元法耦合求解双电层(EDL)电势的Poisson方程、离子输运的Nemst-Planck方程、幂律流体流动的Cauchy动量方程以及本构方程.在对PNP模型验证之后,研究了正弦粗糙元高度、频率对幂律流体壁面EDL电势分布以及EOF流量的影响.模拟结果表明:正弦粗糙元对近壁面EDL电势、外加电场电势、EOF速度矢量分布有较大影响;粗糙元波谷处EDL电势随着粗糙元相对高度或频率的增加而增大,波峰处反之;幂律流体EOF流量随着粗糙元相对高度的增加而单调减小,随粗糙元频率的增加先减小后增大,且在粗糙元频率为2.2时EOF流量最小;特别地,流体幂律指数越小,其受粗糙元高度或频率的影响越大.