多尺度共旋描述方法對模擬電流變液有效黏性之影響

Influences of multi-scale co-rotational descriptions on modeling the effective viscosity of electrorheological liquids

陳韋良(Wei-Liang Chen)

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(2012年)

https://doi.org/10.6342/NTU.2012.10994

摘要

基於懸浮在黏性流體中之懸浮微粒群其Quincke電旋轉運動所引發之負電流變現象為現今電流變學領域之一新興研究主題。自1980年代開始，Cebers與Lemaire等團隊即積極研究並建立基於單尺度單一顆懸浮微粒Quincke電旋轉動力分析對巨觀有效黏性影響之理論。此套理論雖廣為學界所接受，但近年以流變儀量測所得之實驗結果和Cebers與Lemaire之理論預測有所分歧。為此，Huang 與Huang et al.由連體力學中反對稱/矩應力之原理出發，引入多尺度共旋座標之描述方法以及連體角動量黏性擴散之損耗等觀點探討分析與模擬Quincke 電旋轉運動所引發的負電流變現象，其結果除推翻主流理論外，更大幅提升了理論預測的準確性。但，多尺度共旋座標之描述方法或是連體角動量黏性擴散之損耗何者對Quincke負電流變現象之準確預測影響較多仍尚不明朗，且角動量黏性擴散損耗之引入在學界中仍存有諸多爭議。
因此，吾人以平板庫頁流流場為幾何基礎，引入並利用多尺度共旋座標描述對單尺度微粒旋轉動力分析理論以及電流變液平衡極化與流體極化鬆弛方程進行修正，在忽略連體角動量黏性擴散之機制下，分析與探討Quincke負電流變平板流，其有效黏性相較於未引入多尺度共旋座標描述之單尺度微粒旋轉動力分析所得之有效黏性兩者之間的差異。結果發現，在忽略角動量黏性擴散之機制下，多尺度共旋與未含多尺度共旋兩種描述法之間雖有不小的差異，但引入多尺度共旋描述方法並未明顯提升Quincke負電流變平板流流變特性預測之準確性。
另一方面，Klingenberg與Zukoski發現正電流變現象之電流變液，其流體流變運動之特性具有類似於賓漢流體之相似特性。為延伸多尺度共旋座標描述法之研究，吾人借重Klingenberg與Zukosk實驗觀測所得之相關正電流變參數，並同時利用單尺度微粒旋轉動力分析與多尺度共旋描述方法對正電流變現象進行分析探討與比較。最後吾人發現，兩種尺度描述法所得之有效黏性增加之結果間亦有相當之差異。
經由以上研究，結果顯示，雖然引入多尺度共旋描述方法並無法有效提升電流變液流變特性與有效黏性預測之準確度，本論文所得之新的分析結果仍與傳統單尺度單微粒旋轉動力分析所得結果有相當的出入。此一結果暗示，若為了提升預測準確度，吾人亦須將角動量黏性擴散損耗以及懸浮微粒受電、流場作用所形成之微結構列入考量範圍，這也將成為本研究團隊未來的研究方向。

關鍵字

賓漢流體 ； 正電流變現象 ； 負電流變現象 ； Quincke電旋轉 ； 連體力學反對稱/矩應力 ； 有效黏性

並列摘要

The negative electrorheological (ER) phenomena induced by insulating dielectric solid micro-particle Quincke electrorotation suspended within a dielectric viscous liquid has become an emerging field of scientific research in recent years. In order to predict and describe the macroscopic hydrodynamics and electrorheological characteristics of this negative ER phenomena, Cebers and Lemaire et al. developed an electrorheological effective viscosity theory, which is based on a single-scale micro-particle electrorotational dynamics analysis. On the other hand, Huang and Huang et al. introduced a multi-scale co-rotational description for ER fluid polarization and emphasized the mechanism of angular momentum viscous diffusion loss (spin viscosity) under a continuum anti-symmetric/couple stress framework leading to a more accurate theoretical prediction on the negative ER characteristics as compared to the single-scale micro-particle electrorotational dynamics analysis. In this thesis, while neglecting angular momentum viscous diffusion loss (or couple stress), we combine the advantages of the previous two theories to study the influences of multi-scale co-rotational descriptions on improving the theoretical modeling of the Quincke rotation induced negative ER flow characteristics of particle-liquid suspensions.
On the other hand, the experimental observations of Klingenberg and Zukoski show that positive ER flow characteristics of the particle-liquid suspension in Couette flow geometries has Bingham plastic-like properties. As a further varification of the multi-scale co-rotational description, we next study the postive ER flow characteristics using both single-scale micro-particle electrorotational dynamics analysis, and multi-scale co-rotational description, with the electrical and viscometric properties given in Klingenberg and Zukoski. The investigations also emphasize on how the influences of multi-scale co-rotational descriptions improve the theoretical modeling of the rotation induced postive ER flow characteristics for particle-liquid suspensions.
Results show that as compared to the single-scale micro-particle electrorotational dynamics analysis, there is no significant improvement on the accuracy caused by introducing the co-rotational multi-scale descriptions in modeling and analyzing the rheological characteristics for both negative and positive ER phenomena in spite of the significant differences in the two sets of results. In other words, in order to improve the accuracy of the theoretical modeling and simulation of the ER effects induced by internal micro-particle rotation, we not only need to pay attention to the details of the co-rotational multi-scale descriptions of the fluid flow, but also need to consider the possible angular momentum viscous diffusion loss (or couple stress) that may exist in the ER flow field.

並列關鍵字

Bingham plastic fluid ； negative electrorheological phenomena ； postive electrorheological phenomena ； Quincke electrorotation ； continuum anti-symmetric /couple stress ； effective viscosity

參考文獻

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8. Huang, H.F., M. Zahn, and E. Lemaire, Continuum modeling of micro-particle electrorotation in Couette and Poiseuille flows-The zero spin viscosity limit. J. Electrostat. 68(2010) 345-359.