以水平集法研究具化學反應的兩種黏彈流體間的混合行為

Abstract

本研究旨在探討兩股可產生化學交聯反應的非牛頓流體於靜態混合器中之混合行為，並以DGEBA(diglycidyl ether of bisphenol A，雙酚A型雙環氧基醚)為代表性流體(主劑)，搭配混合於增稠液(聚丙二醇(PPG)為基底、添加10%氟化矽所形成之懸浮液)的TETA(三乙烯四胺，triethylenetetramine)作為固化劑，建立一套可同時模擬流體混合與交聯反應(DGEBA與TETA反應後由液態轉變為固態)的數值模型。 研究中採用 COMSOL Multiphysics 軟體，整合水平集法(Level Set Method)與化學反應模組，進行三維模擬計算，追蹤不同流體間界面變化並模擬交聯反應動力學，藉以分析不同混合器幾何設計下之混合效率與反應表現。混合效率的優劣常以變異係數(Coefficient of Variation, 简稱COV)表示，其值介於1與0之間，愈接近0者其效率愈高。本文共採用三種方式來估算COV值，分別是水平集函數、物種濃度c、及含化學反應的c，並分別稱為之COV、COVc、及COVc-Chem。透過對一含6個混合元件的慣用圓形截面SMX混合器，本文以DGEBA與含TETA的增稠液進行計算。在混合器入口截面上述三項COV值均為1，在出口截面上分别算得COV = 0.62、COVc = 0.17、及COVc-Chem = 0.11，因的計算只含對流效應、並未納入擴散效應，故以 COVc 及 COVc-Chem 較能反映混合行為、且化學反應有加強混合的效果。按計算結果，SMX 混合器能有效促進流體界面拉伸與折疊，提升整體混合效率、並使交聯反應更趨均勻。 本文亦對以下狀况進行了研究。如改變兩股待混合流體的黏度差異，本研究的計算顯示差異大者混合較佳。至於兩流體中反應物的當量比效應，以符合理論當量比者能獲致最佳混合；但若偏離理論值不大，其影響有限，此因混合器自具的混合能力明顯高於化學反應所促進者。比較方形與圓形截面混合器中的混合，以圓形截面者較優、固化程度亦較佳。 綜合而言，本研究成功建立了一套整合混合與化學交聯反應的數值模擬計算，並提供一種可量化比較不同混合器性能的方法。

The goal of this thesis is to study the mixing of two non-Newtonian fluids which could perform cross-linking chemical reaction (curing) in static mixer, and develop an associated numerical model for simulation. The DGEBA (diglycidyl ether of bisphenol A) and TETA (triethylenetetramine) suspended in shear-thickening fluid were chosen as the primary target fluids in this study. The COMSOL Multiphysics was employed, using the Level Set Method together with the chemical reaction module, for capturing the interface between two fluids and the curing process. The mixing efficiency was then studied for different geometries of the mixers. The mixing efficiency was characterized by the coefficient of variation (COV), and its value is between 1 and 0. Better mixing when COV is closer to zero. We have estimated three values for COV, based on the level-set function (), the concentration of selected species (c), and the concentration under chemical reaction, and are called COV, COVc, and COVc-Chem, respectively. Through the simulation of DGEBA and TETA in shear-thickening fluid in a general SMX mixer with circular cross section and 6 mixing elements, we found COV = 0.62, COVc = 0.17, and COVc-Chem = 0.11 at the exit plane, with the corresponding values equal 1 at the inlet of the mixer. Also, average degree of cure reaches 0.6 at the exit plane. COV is not so adequate for characterizing the mixing as the calculation of  accounts only the convection without diffusion. Thus, COVc and COVc-Chem are more appropriate for studying mixing, and mixing is enhanced via chemical reaction. According to the calculation, the interface between those two fluids for mixing are stretched and folded through the design geometry of mixer, and thus mixing is enhanced and more curing occurs. Some findings concerning mixing are obtained through the present study. Mixing is enhanced when the viscosity contrast between those two fluids is increased. Mixing is optimized when the molar amounts of reactants are at their theoretical equivalent ratio. Mixing and degree of cure in mixer with circular cross section is better than those with square cross section. In summary, a numerical model for simulation is developed successfully for accessing mixing and curing of two non-Newtonian fluids in static mixer.