圓管型電動力擠壓流之分析

Abstract

生物體內具有許多因受到應力而發生形變之彈性組織，彈性組織內部的流體將因彈性組織發生形變因受到擠壓而開始流動。本研究主要目的是分析彈性組織受到應力進而發生形變時，內部流體因彈性組織變形而誘導出之電動力效應(electrokinetic effect)的能量轉換效能。由於內部流體因彈性組織發生形變而產生流動，傳統壓力驅動流(pressure-driven flow)並無法詳盡描述內部流體流動之情況，因此吾人透過質量守恆定律將此流場以擠壓流(squeeze flow)之形式進行描述。並利用以上之模型求解出圓管型電動力擠壓流之解析解，包括速度場、生成電流、軸向電位分佈以及能量轉換效率等。參數分析部分則討論當流道幾何以及外部電阻發生改變時，並於固定壁面收縮速度或施予固定壁面作用力之情況下，探討機械能轉換為電能時，能量轉換效能所發生之變化。除此之外，增加流道並聯數量與加入線性納維滑移條件(linear Navier slip condition)可分別有效提升總電流與能量轉換效率。由最終之結果顯示，增加滑移長度可有效使得能量轉換效率提升，而最大轉換效率可達約 30 % ，且最大轉換效率相近於平板型電動力擠壓流之能 量轉換效率。

Many elastic biological tissues undergo deformation due to an external stress. Hence, flow will be induced by deformation of the tissues. In this thesis, we aim to analyze and investigate the performance of mechanical to electrical electrokinetic energy conversion. Because the flow is induced by deformation of the tissues, the pressure-driven flow cannot describe the flow entirely. Therefore, we introduce the mass conservation law into our analysis to construct a model for squeeze flow. Under this model and some assumptions, we can obtain the analytical expressions, including velocity field, total current, streaming potentials, and efficiency. Parametric analyses are conducted to investigate the variation in the electrokinetic energy conversion performance with respect to variation in the channel radius or channel length. In addition, increasing the number of channels and applying the linear Navier slip condition will enhance the strength of total current and improve the energy conversion efficiency, respectively. The results show that maximum efficiency goes above 30% while employing infinite slip lengths and that the efficiency of the circular cylindrical geometries is close to that of planar geometries.