Mechanistic Breakage of Cellulose During Media Milling and its Modeling

本論文主旨在探討纖維素於介質研磨下之破碎機制與其破碎模型的建立。實驗以棉花纖維素為原料，藉由不同研磨時間下產物之體積與粒數粒徑分布變化的趨勢，配合掃描式電子顯微影像判斷纖維素於介質研磨下之破碎機制，並以beta分布函數的組合描述體積粒徑分布的近似函數，最後利用粒數平衡之觀念建立纖維素經介質研磨之破碎模型，模擬不同進料經研磨後產物之粒徑分布。 15 g纖維素原料連同3000 mL去離子水。採用粒徑0.3 mm之釔鋯珠作為研磨介質，經過15分鐘的研磨後，纖維素的體積粒徑分布和粒數粒徑分布皆以由單峰分布轉為雙峰分布，以1 um分成大粒子與小粒子兩子分布。1 um以下之小粒子所佔體積為2.67 %，粒數為99.96 %，表示纖維素經研磨後會產生大量的小粒子，且其總體積隨研磨時間而增加，由掃描式電子顯微影像中也可得到相同之結果。此外大粒子子分布之標準差皆會隨研磨時間而下降，分布逐形狀隨時間漸趨狹窄，推測纖維素經介質研磨後將以將以表面侵蝕的機制進行破碎降解。 以beta分布函數的組合描述粒徑分布，所得結果之相關係數皆 大於0.975。令破碎速率函速與破碎分布函數皆符合指數形式，將上述三函數代入粒數平衡方程式中，可將方程式由偏微分積分式轉換為聯立常微分方程式組，建立破碎模型。將原料體積增加為3000 mL，使研磨過程達到準穩態後，以所建立之模型模擬不同粒徑分布之纖維素，經一單位時間的研磨後產物之粒徑分布，所得結果誤差皆小於20 %。模擬結果中，由破碎分布函數之性質可知纖維素經破碎後將產生大量的小粒子，可間接證實纖維素的破碎是以表面侵蝕的機制進行。In this research, the breakage mechanism and its modeling of cellulose during media milling is investigated. The breakage mechanism of raw cotton cellulose is identified by comparing volume and number particle size distribution (PSD) of product at various time and their SEM photographs. The PSD is described by combining multiple beta distribution and the population balance equation is used to model the breakage kinetics of cellulose. This model can be used to simulate the PSD of various product, which the initial PSD are different. The volume and number PSD of cellulose are convert into bimodal distribution and the fine sub-population and coarse sub-population are divided by 1 um after 15 min milling. The volume percentage of particle smaller than 1 um is 2.67 and the number percentage is 99.96 , it represent that there are a large number of fine particle after milling and the total volume increase with time. The same results are obtained by SEM photographs. Additionally, the standard deviation of coarse sub-population is decreased and the shape of distribution is narrowed. According to the results above, the breakage mechanism of cellulose is characterized in terms of surface-erosion during media milling. Bimodal PSD was described by combining multiple beta distribution and all the correlation coefficient are larger than 0.975. Assuming specific breakage rate and breakage distribution function obey power-form and substituting all the functions into population balance equation, the partial integro-differential equation is transferred into ordinary differential equations and the breakage kinetics is then modeled. In order approach the milling process to quasi-steady state, the volume of feed is enlarge to 3000 mL and the breakage model is applied to experimental data available from various PSD of feed milling during on space time, the maximum error is less than 20%. The simulation results indicate that cellulose produce a great quantity of fine particle after breakage and it can be used to confirm the surface-erosion mechanism indirectly.目 錄 壹、前言 1 貳、文獻回顧 3 2.1. 研磨技術 3 2.1.1. 簡介 3 2.1.2. 濕式研磨的原理 7 2.1.3. 影響研磨降解的因素 7 2.1.3.1. 轉速 7 2.1.3.2. 進料固型物濃度 9 2.1.3.3. 介質填充量 9 2.1.3.4. 介質大小 9 2.1.3.5. 乳化劑的添加 11 2.2. 粒徑量測技術 11 2.2.1. 粒徑之定義及其分布之圖示法 11 2.2.2. 粒徑分析儀之分類 14 2.2.3. 雷射光散射法 17 2.3. 研磨降解模型分析 22 2.3.1. 粒子破碎機制 22 2.3.2. 粒數平衡 23 2.3.3. 粒數平衡方程式 24 2.3.4. 破碎速率函數及破碎分布函數之近似解 27 2.3.4.1. G-H模型 27 2.3.4.2. 線性時變模型 30 2.3.4.3. 馬可夫鏈模型 34 參、材料與方法 39 3.1. 材料 39 3.2. 設備 39 3.3. 實驗流程及步驟 42 3.3.1. 原料濃度 43 3.3.2. 介質研磨 43 3.3.3. 粒徑分析 44 3.3.4. 數據分析 44 肆、理論分析 45 4.1. 粒徑分布近似函數 45 4.1.1. Beta分布 45 4.1.2. 多峰分布 47 4.2. 粒數平衡模型 48 伍、結果與討論 54 5.1. 原料性質 54 5.2. 纖維素之破碎機制 54 5.2.1. 粒徑分布變化 56 5.2.2. 纖維素經介質研磨後之型態 62 5.3. 纖維素之破碎模型 67 5.3.1. 準穩態進料方式之建立 67 5.3.2. 粒徑分布函數與Beta分布函數的近似結果 70 5.3.3. 粒數平衡模型之模擬結果 72 陸、結論 80 柒、參考文獻 82 捌、附錄 85 A. Beta分布函數模擬結果 85 B. 符號索引 90 B.1. 英文字符號 90 B.2. 希臘字符號 9