平行板間導電溶液在垂直電場與水平壓力梯度作用下穩定特性分析

Abstract

本研究以數值方法模擬，研究在一平行板間固定流速的層流流場(laminar flow)通入一固定電場，對於此含有電場影響的流場的不穩定性分析。在本研究的物理模型很簡單的包括產生電場的兩電極板以及平行流道。在電場方面，是通入與流體流動方向垂直的電場。通入的流體，在此我們考慮通入的為會受電場影響的電解質水溶液，因此在電場通入時會產生導電梯度，且流體速度為固定值。而且考慮流體粒子由於布朗運動的擴散速度，以及流體帶電粒子因為電場的偏移速度，而讓理論分析為接近實際狀況。接著利用變換各種不同的操作條件，來探討流體的雷諾數、電場大小、以及導電梯度間的相互變化關係。結果顯示，在縱向波數分析方面，雷諾數的大小並不會改變其流體的穩定性，因此所有分析都與流體不流動時相同，而於Sc=10^4時，無論改變導電梯度值或是雷諾數值的情況下所需的Q(Q為用來顯示所需電場大小之參數)值都小於10^5即可使流場產生不穩定現象。而在橫向波數分析方面，結果顯示，改變其雷諾數、Sc或導電梯度，在某些情況下，其所產生的擾動會比縱向模式產生的擾動先行發生。

This study is based on numerical method to simulate a laminar flow accessing a regular electric field while flowing between parallel plates at a regular velocity of flow, and analyze the instability of it, which in this case was affected by the electric field. The mathematical model in this study simply includes two electrode plates which produce electric field and fluid between parallel plates. As for the electric field, it is a field of electronics accessing perpendicularly with the flow of the fluid. We suppose the accessing fluid was the electrolyte aqueous solution which shall be affected by the electric field; therefore it will produce the conductivity gradient at a fixed velocity of the flow while accessed by the electric field. This theoretical analysis is very close to reality while considering the rate of diffusion caused by Brownian motion of flow particle and the displacement velocity of the flow charged particle caused by the electric field. Now we shall discuss the relation between the Re. number, electric field, and conductivity gradient by switching all different kind of conditions on operations. As a result, the stability of the value of Re. number remains unchanged in terms of the analysis of the longitudinal wave number, so all the analyses stay the same as that of the static flow; the instability of the flowing field occurs while Sc=10^4 as long as the conductivity gradient value changes or Re. number value changes on condition of Q(Q is used for showing the necessary electric field ) is less than a value of10^5. In terms of the analysis of the transverse wave number, the result shows that if we change the value of Re., Sc., and the conductivity gradient, in some cases, the instability phenomenon of transverse mode would occur first, and the instability phenomenon of longitudinal mode will occur later.