微流道中非線性黏彈電解液擴散滲透流之探究

Diffusioosmotic Flows of Non-linear Viscoelastic Electrolytic Liquids in Microchannels

姚承宏(Cheng-Hung Yao)

指導教授 ： 黃信富

國立臺灣大學/工學院/機械工程學研究所/碩士(2014年)

https://doi.org/10.6342/NTU.2014.10212

摘要

近年來，因為微流道系統和實驗室晶片的蓬勃發展，擴散滲透流的機制和應用越來越受到重視。在這些應用中，工作流體多為複雜的非牛頓黏彈流體。然而，黏彈流體擴散滲透流的相關文獻卻相當稀少。本研究主要目的是探究微流道中非線性黏彈電解液擴散滲透流在不同參數條件下，所具有的流況和流變效應，以提供相關實驗或數值分析可參考的基準解。本研究以能斯特-普朗克(Nernst-Planck)方程式、波瓦松-波茲曼(Poisson-Boltzmann)方程式、范善-譚納(Phan-Thien-Tanner)黏彈模型和動量方程式分析黏彈擴散滲透流。在二維、穩態和潤滑理論等假設下，得到流場速度、第一正向應力差、第二正向應力差、有效黏性和體積流率的半解析數值解以及體積流率方向分佈圖。而這些物理量皆為管寬與德拜長度(Debye length)之比值、壁面電位、離子擴散係數差、威森堡(Weissenberg)數、拉伸黏性上限和網絡與連體介質間的滑移等參數之函數。此外，本論文也提供PTT黏彈模型簡化與否以及描述電位分佈的波瓦松-波茲曼方程式線性化與否的比較。結果顯示，網絡與連體介質間的滑移不為零會產生臨界威森堡數，使參數的變化範圍和影響都有限。而雖然增加其他參數的值也會增加波瓦松-波茲曼方程式線性化與否的差異，但線性與非線性電位解之間的差異以及因為此電位差異所造成流況和流場之差異，主要還是由壁面電位的高低來決定。

關鍵字

微流道 ； 電解液 ； 黏彈流體 ； 擴散滲透流 ； Phan-Thien-Tanner模型 ； 波瓦松-波茲曼方程式

並列摘要

Recently, the fundamental physics and engineering applications of diffusioosmotic flows are widely studied due to rapid development of microfluidic systems and “Lab-on-a-chip” devices. However, the working fluids employed in these applications are mostly non-Newtonian viscoelastic liquids, which are generally less investigated in the past several years. The goal of this thesis is aimed at investigating the flow field and rheological responses of diffusioosmotic flows under different physical parameter settings and at providing the benchmark solutions for future experimental examinations and numerical analyses. The full governing equations included the Nernst-Planck equation, Poisson-Boltzmann equation, Phan-Thien-Tanner (PTT) viscoelastic constitutive model and the Cauchy momentum equation. Based on two-dimensional, steady, and lubricating flow conditions, semi-numerical solutions to the flow velocity, the first normal stress difference, the second normal stress difference, the apparent viscosity, and the volume flow rate are obtained as functions of the ratio of the microchannel width to Debye thickness, the wall zeta potential, the diffusivity difference parameter, the Weissenberg number, the upper limit of elongational viscosity parameter, and the slip parameter between the molecules network and the continuum medium. Moreover, the comparisons between the results respectively obtained from the PTT model and the simplified PTT model as well as the results respectively obtained from the Poisson-Boltzmann equation and the linearized Poisson-Boltzmann equation are also provided. Our parametric studies show that the non-zero slip parameter causes the critical Weissenberg number which limits the available and attainable parametric ranges of all parameters. Finally, differences in as well as variations in the difference of the results respectively obtained from the linear and non-linear Poisson-Boltzmann equations are most dependent on variations in the wall zeta potential despite the fact that variations in the rest of the system parameters may also influence the differences between the linear and non-linear solutions.

並列關鍵字

Viscoelastic liquid ； diffusioosmotic flows ； Phan-Thien-Tanner (PTT) viscoelastic constitutive model ； Poisson-Boltzmann equation ； microchannels ； electrolytes

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