3.4 模擬結果分析
3.4.3 滑動係數之影響
由前述研究可知不同滑動係數造成在壁面有不同之剪切應力值，而過 去文獻中指出，流體界面間之剪切應力為鋸齒型不穩定現象生成之主要因 素，故除了滑動係數對壁面剪切應力之影響外，本論文亦藉由改變壁面滑 動係數來探討壁面光滑度對於界面之剪切應力影響，以期能改善鋸齒形 (zig-zag)不穩定現象。
因左右壁面邊界設定不會影響壁面之剪切應力(τyx)，故此小節之滑動 邊界設定僅改變進料區塊上下壁面之滑動係數做比較，以避免流體界面接 觸線(contact line)因滑動係數過小而產生往上偏移的情況，其餘設定則同上 述研究，邊界設定如圖3-43。
Y Z
流體界面 對稱面 滑動邊界
滑動邊界
滑動邊界
圖3-43 進料區塊邊界設定示意圖 表 3-13 不同滑動係數設定之分析比較
Slip Coefficien t(Power law slip model) noslip 5×105 1×105 Wall Shear Stress (kPa) 22.1 19.6 9.3 Interfacial Shear Stress (kPa) 9.06 8.40 4.89
Outlet DN1 (kPa) 5.52 4.64 1.35
第三章 結果與討論
0 5 10 15 20 25
-0.50 -0.25 0.00 0.25 0.50
Y Coordinate (y/L)
Shear Stress τ yx(kPa)
Interface Position (noslip, 5x105)
No-slip condition Fslip= 5x105 Fslip= 1x105
Interface Position (1x105)
圖 3-44 不同滑動係數設定之界面剪切應力比較圖
表 3-13 及圖 3-44 為不同滑動係數設定下之界面剪切應力比較，可看 出當滑動係數越低，流體剪切應力(τyx)越低，而其界面剪切應力值亦越 低，可避免鋸齒形不穩定產生。上述現象是因滑動係數越低表示流體於壁 面越易產生滑移，而由前述研究可知當壁面滑動係數大則壁面之剪切應力 越小，此現象亦間接影響流體界面之剪切應力，使其隨著滑動係數減小而 降低。
圖 3-45 至圖 3-47 分別為不同滑動係數設定時上下層流體於流體界面 附近之第一正向應力差(N1)變化圖，可看出隨著滑動係數下降，流體界面 附近之正向應力越低，而上下層流體之正向應力差亦隨著滑動係數而下 降，因此可推測此現象亦是因壁面滑移而造成。
第三章 結果與討論
First Normal Stress Difference N 1
Flow Distance (x/L) Fluid I
(kPa) Fluid II
no-slip condition
(QI/QII= 13.2, ηI/ηII= 2.5)
圖3-45 沿流動方向之第一正向應力差變化圖(no-slip condition)
0 2 4 6 8
Fi Sterence N 1
Flow Distance (x/L) Fluid I
(kPa) Fluid II
Fslip= 5x105
(QI/QII= 13.2, ηI/ηII= 2.5)
圖3-46 沿流動方向之第一正向應力差變化圖(Fslip＝5×105)
ress Diffrst Normal
第三章 結果與討論
First Normal Stress Difference N 1 (kPa)
Flow Distance (x/L) Fluid I
Flow Distance (x/L) no-slip condition
Fslip= 5x105 Fslip= 1x105
圖 3-48 沿流動方向之上下層流體DN1變化圖
第三章 結果與討論
由圖 3-48 可看出當滑動係數越低，上下層流體之正向應力差之差值 DN1越低，表示上下層流體於界面附近之正向應力值越相近，而藉此可避 免波浪形不穩定現象之形成。
由此小節之研究可知，藉由增加上下壁面之光滑度使流體在壁面產生 滑移，因流體所受壁面阻力減少，流體所受拉伸變形亦減小，而相較於粗 糙壁面，流體表現出不同之流動特性，雙層流體間之界面剪切應力值及正 向應力差皆因此降低，在共押出製程中可藉此避免流體界面不穩定現象發 生。
第四章 結論
四、結論
本論文進行進料區塊(feedblock)內流動之三維有限元素模擬，並於模 壁面使用滑動邊界設定，相較於其他文獻中使用外插法求取壁面接觸線之 模擬結果，本論文採用滑動邊界設定可得到較接近實驗值之模擬結果。而 相對於使用牛頓流體或泛牛頓流體模型，本論文採用 Giesekus 黏彈模型 (Giesekus viscoelastic model)將高分子塑料黏彈性質之影響考慮其中，更有 效的模擬出了高分子流體之黏彈流動特性。本論文亦針對共押出製程中之 三項主要製程問題及缺陷進行一系列之討論。
本論文針對 Giesekus 黏彈模型中代表流體第二正向應力差性質之流變 參數 α 進行一系列之討論，由本論文之研究可清楚看出第二正向應力差 (second normal stress difference)對於雙層共押出流體界面之影響，亦證實文 獻中之論點。當 Giesekus 黏彈模型中之流變參數 α 越大，流體之第二正向 應力差性質越明顯，且若上下層流體之 α 值相差越大，則此現象越更加明 顯，而此性質造成逐漸增加之界面包覆現象越為嚴重，大大影響界面之均 勻性。因此在進行高分子共押出時，需對於塑料之流變特性有相當的了 解，以避免界面不均勻性之問題產生。
本論文亦發現流量比對鋸齒形不穩定現象有極大影響，當流量比越低 時，上層流量增加進而推擠流體界面位置往下偏移，使上層流體(Fluid II) 厚度增加且流體界面遠離有較高剪切應力之壁面，因此流體界面之剪切應 力隨著流量比下降而降低。而當流量差異極大時，流體在匯流處因互相擠 壓而產生拉伸形變，在界面附近會造成上下流體有不同的正向應力(τxx)，
此不同之正向應力即為造成波浪形不穩定發生之原因。本論文發現流量比 越低，上層高分子塑料流量較高，上下流體正向應力之差異越低，藉此可 降低波浪形不穩定現象形成。但須注意的是低流量比時，界面彎曲包覆程
第四章 結論
度會較嚴重，而若整體押出量增加，會造成模具內剪切應力上升及流體黏 彈性質越顯著，造成界面鋸齒形不穩定現象及流體界面包覆現象越嚴重。
本論文藉由改變壁面滑動係數來探討壁面光滑度對於雙層流體間之正 向應力差及界面剪切應力之影響，研究發現隨著滑動係數減小，雙層流體 間之正向應力差及界面剪切應力皆隨著降低，因此藉由增加上下壁面之光 滑度使流體在壁面產生滑移，可減少共押出製程中進料區塊雙層流體間之 界面剪切應力值及正向應力差，以避免流體界面不穩定現象發生。
本論文與其他模擬文獻之比較，可看出相較於文獻中使用外插法求取 壁面接觸線之模擬結果，本論文採用滑動邊界設定可得到較接近實驗值之 模擬結果，但比較文獻實驗結果呈現之界面彎曲包覆仍有誤差，亦發現本 論文在 6.71L 處之流體界面形狀與實驗之 3.37L 處之流體界面相符合，因 此若能改善採用精確之流體流變參數及黏彈流動模型，以及更有效之出口 邊界條件，應能大大改善模擬精確度。
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