發(fā)布時間：2018-02-03 17:04

  本文關鍵詞： 菲克定律 無限擴散 有限擴散 拉普拉斯變換 復變函數(shù)　出處：《數(shù)學的實踐與認識》2017年01期 　論文類型：期刊論文

【摘要】：介紹了三維和一維擴散下的菲克定律,以及兩類涉及到擴散的實際問題,即求擴散粒子通過曲面的擴散通量和求解擴散粒子的濃度分布.通過拉普拉斯變換和復變函數(shù)相關數(shù)學理論,求解了菲克擴散定律在無限長介質和有限長介質兩種非穩(wěn)態(tài)擴散情況下的解.粒子在無限長介質中的非穩(wěn)態(tài)擴散和濃度分布可通過方程φ(z,t)=Φ·erfc(z/2DT~(1/2))表示.方程為余補高斯誤差函數(shù).粒子在有限長介質中的非穩(wěn)態(tài)擴散和濃度分布可通過方程φ(z,t)=Φ+Φ·4/π∑_(n=1)~(+∞)((-1)~n)/(2n-1)cos[z/L(n-1/2)π]e~((D_t)/(L~2)(n-1/2)~2π~2)表示.該方程為無限加和形式,當n≥100000時,φ可以精確到小數(shù)點后6位,在方程的圖像上不再能觀察出由n的取值造成的誤差.從方程的圖像可得到粒子在擴散介質中達到飽和的時間或粒子擴散到z=0處的時間等具有重要物理意義的參數(shù).
[Abstract]:The Fick's law under three dimensional and one dimensional diffusion and two kinds of practical problems related to diffusion are introduced. In other words, the diffusion flux of diffusion particles through the surface and the concentration distribution of diffusion particles can be solved by means of Laplace transformation and mathematical theory of complex function. The solution of Fick's diffusion law in two kinds of unsteady diffusion of infinite medium and finite length medium is solved. The unsteady diffusion and concentration distribution of particles in infinite medium can be obtained by the equation 蠁 ~ (z). The equation is a complementary Gao Si error function. The unsteady-state diffusion and concentration distribution of particles in a finite medium can be obtained by the equation 蠁 _ (z). Tr = 桅 桅 路4 / 蟺 鈭，

本文編號：1487900