球形粒子之介電泳交越頻率因次分析與預測

Dimensional Analysis and Prediction of Dielectrophoretic Crossover Frequency of Spherical Particles

葉哲愷(Che-Kai Yeh)

指導教授 ： 莊嘉揚

國立臺灣大學/工學院/機械工程學研究所/碩士(2017年)

https://doi.org/10.6342/NTU201700928

摘要

近年來人們對醫學檢驗技術的需求日漸升高，因此生物晶片技術也隨之蓬勃發展。而在生物晶片中，介電泳現象扮演著舉足輕重的角色，只要透過改變外加電場頻率、溶液種類、電極形狀，就可以非接觸方式輕易操控流體中微米粒子的運動，將不同性質、大小的微粒分離，已達各種生物醫學目的。
在介電泳研究中，常見計算交越頻率方法有電偶模型(Dipole model)理論與與馬克斯威應力張量(Maxwell stress tensor, MST)理論輔以有限元素軟體計算等兩大種。在電偶模型理論上，其計算快速但在大粒子尺寸或大溶液導電度下易失準且無法預測交越頻率(Crossover frequency)何時不存在。在馬克斯威應力張量理論上，其計算精準但速度較慢且不易了解重要參數之間影響關係。故本研究利用白金漢理論(Buckingham pi theorem)建立一數學模型，預測不同參數組合下球形粒子之交越頻率與交越頻率不存在的狀況。
本研究流程，先透過白金漢理論進行無因次分析，再以MST模擬輔助建立一介電泳參數資料庫，將其代入無因次參數組合中，找出交越頻率與五個重要參數(溶液導電度、溶液電容率、微粒電容率、微粒尺寸、微粒表面電導)之間關係，進一步建立數學模型以預測不同狀態下之交越頻率落點與交越頻率不存在之狀況，並比較前人實驗、馬克斯威應力張量方法及傳統常用的電偶模型理論求解之結果，最後提出電偶模型失準原因，此外我們也透過本研究建立之數學模型提供一物理見解。

關鍵字

介電泳 ； 電雙層 ； 白金漢理論 ； 微粒子操控

並列摘要

In recent years, the biochip technology is flourishing as the demand for medical laboratory has been increasing. However, the phenomenon of dielectrophoresis (DEP) plays an indispensable role in the biochip for many biological and colloidal science application. We can easily manipulate the motion of micro particle with non-contact by changing the alternating current (AC) electric field frequency, the kinds of medium and electrode shape, to separate different properties and size of particle. Then we can reach a variety of biomedical purposes.
In dielectrophoresis research, the general calculation of the crossover frequency method include the dipole model and numerical simulations based on Maxwell stress tensor (MST). The dipole model is high computation efficiency but cannot predict the crossover frequency for larger particles or large medium conductivity accurately and the situation of no crossover frequency. The MST method is accuracy but time-consuming and may lack predictive understanding of the interplay between key parameters. Here, we present a mathematical model using Buckingham pi theorem and predict the crossover frequency of different parameter sets and the situation of no crossover frequency.
The first research process is dimensional analysis using Buckingham pi theorem. Secondly, we establish a database of electrophoretic parameters using MST simulation and insert them to dimensional parameter set. Third, we can find the relationship between the crossover frequency and five import parameters (medium conductivity, medium permittivity, particle permittivity, particle size and particle surface conductivity) and built mathematical model to predict the crossover frequency of different situations and the situation of no crossover frequency. Finally we compare the results with previous experiment, dipole model and MST. In addition, we explore the reasons for dipole model error and provide physical insights through our mathematic model our research establish.

並列關鍵字

Dielectrophoresis ； electric double layer ； Buckingham pi theorem ； micro particle manipulation

參考文獻

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