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底波拉数

底波拉數(Deborah number)是流變學中的一個无量纲量,用來描述材料在特定條件下的流動性。底波拉數最早是由以色列理工学院的教授馬庫斯·萊納英语Markus Reiner所提出,其名稱來自於聖經《士師記》5:5中,士師底波拉歌中的一句:

底波拉數是假設在時間足夠的條件下,即使是最堅硬的物體(例如山)也會流動。因此流動特性不是一個材料本身的固有属性,而是一種相對属性,此相對属性和二個有本質上完全不同的特徵時間有關。

底波拉數定義為馳豫時間及觀測時間尺度的比值。馳豫時間表示一材料反應施力或形變時所需要的時間,觀測時間尺度是指探索材料反應的實驗(或電腦模擬)的時間尺度。底波拉數中整合了材料的彈性粘滯度。若底波拉數越小,材料特性越接近流體,其運動越接近牛頓粘性流。若底波拉數越大,材料特性主要以彈性為主,底波拉數非常高時,材料特性接近固體[1] [2]

其方程式為:

其中

  • tc是指應力的馳豫時間(有時稱為馬克士威馳豫時間)
  • tp是指觀測的時間尺度

參考資料

[编辑]
  1. ^ Reiner, M., The Deborah Number, Physics Today, 1964, 17 (1): 62, doi:10.1063/1.3051374 
  2. ^ The Deborah Number 互联网档案馆存檔,存档日期2011-04-13.
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底波拉数
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