牆效應對球狀粒子黏性阻力矩的影響

球狀微小粒子在液體中轉動時所承受的黏性阻力矩是一項基本的力學課題，並在微奈米科技及其應用上(如細胞的介電性檢測、微奈米粒子的定向及定位)扮演重要的角色。傳統流體力學文獻中已有黏性阻力矩在無窮域及固體邊界修正的理論公式，但尚缺實驗驗證。廣義介電泳為透過施加電場以非接觸性方式來操控粒子的工具，包含傳統介電泳、旅波式介電泳及電旋轉；本文以廣義介電泳為基礎工具且光鉗為輔，發展一非接觸性的實驗方法來研究在微流道之中的Sephadex微粒在靠近固體壁面的黏性阻力矩。本實驗以簡易的微機電製程製作實驗裝置，以傳統介電泳和光鉗對粒子作空間定位，以電旋轉來驅策粒子轉動，利用介電泳力矩與黏性阻力矩平衡來量測後者，其中介電泳力矩透過由數值求解所得的電場計算而得；另量測粒子轉速，以求取牆效應的修正因子。經與流體力學理論公式比較，本文實驗所獲修正因子與理論值比較相差在10%；另與前人(黃佳慶)實驗結果(較理論值高0.5-38%)比較，本文結果是較一致性且較集中的。在實驗裝置方面，前人所用者為一具四道電極組的電旋轉槽，而本文所用者為一具八道電極的電旋轉槽，其中四道電極一組與前人者同，新增的另一組四電極可以不同電頻率對粒子施加傳統介電泳力，以達到更佳的粒子位置操控。

關鍵字

黏性阻力矩；牆效應；介電泳；電旋轉；雙頻率操作；光鉗

並列摘要

Viscous resistive torque on a small spherical particle in fluid is fundamental in mechanics, and plays a crucial role in micro and nano technology and their application (characterization of dielectric properties of cells, positioning and orientation of micro and nano particles, for example). Analytical expressions for viscous torque on a spherical particle in an infinite fluid domain and in the vicinity of a solid boundary (or boundaries) are available in the fluid mechanics literatures, but were not fully explored experimentally. Generalized dielectrophoresis is a non-contact method for particle manipulation via applying an appropriate electric field; it includes conventional dielectrophoresis, travelling wave dielectrophoresis and electrorotation. The experimental method of the present study is based on generalized dielectrophoresis together with an optical tweezer. The device was fabricated via standard MEMS techniques, using conventional dielectrophoresis and optical tweezer for particle positioning, and electrorotation for turning the particle. The viscous torque on the particle was measured by balancing it with the dielectrophoretic torque, which was calculated using the electric field of the device obtained numerically. The rotating speed of the particle was also measured and employed for estimating the wall correction factor of the viscous torque. Comparing with those predicted theoretically based on fluid mechanics, the error of data is found within 10%. In comparing with the previous experiment (Ref. [44], 0.5-38% greater than the theoretical prediction), the present data are more consistent and concentrated. The previous experiment was performed using a four-electrode electrorotation chamber, while the present experiment employed an eight-electrode chamber, with a set of four electrodes the same as in the previous experiment. An additional set of four electrodes was employed for exerting additional conventional dielectrophoretic force to the particle using different electric frequency, which is more helpful for particle positioning in the experiment.

並列關鍵字

Viscous resistive torque ； Wall effects ； Dielectrophoresis ； Electrorotation ； Dual-frequency operation ； Optical tweezers

參考文獻

[44] 黃佳慶, “利用光鉗與廣義介電泳量測近牆效應下圓球的黏性阻力矩,” 國立臺灣大學應用力學研究所碩士論文, 2012.

[35] Becker, F. F., Wang, X.-B., Huang, Y., Pethig, R., Vykoukal, J., and Gascoyne, P. R. C., “Separation of human breast cancer cells form blood by differential dielectric affinity,” Proceedings of the National Academy of Sciences of the United States of America, 92, 860-864, 1995.

[1] Pohl, H. A., “The motion and precipitation of suspensoids in divergent electric field,” J. Appl. Phys, 22,, 869-871, 1951.

[3] Jones, T. B., Electromechanics of particles, Cambridge University Press, Cambridge, 1995

[4] Jones, T. B. , “Basic theory of dielectrophoresis and electrorotation,” IEEE Engineering in Medicine and Biology, 22, 33-42, 2003.

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牆效應對球狀粒子黏性阻力矩的影響

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