菲克扩散(第一)定律
Fick’s (First) Law of Binary Diffussion
物质扩散通量Diffusion flux表达通式
在单位时间内物质 A 通过垂直于扩散方向的单位截面积的扩散物质流量，$kg\cdot m^{−2} \cdot s^{−1}$，与该截面处的浓度梯度成正比。
其中
$\mathscr{D}_{AB }$ 是物质 A 在物质 B 中的传质系数，$ m^2\cdot s^{-1}$，
$ \rho $ 物质的密度， $kg·m^{−3}$,
$\nabla w_A$ 是物质 A 的浓度梯度，$kg·m^{−2}$.
浓度梯度 $w_{Ax}$表达式为
1.直角坐标系($ x, y, z $)
| 直角坐标系Cartesian coordinates ($\textit { x,y,z }$): | NO. |
|---|---|
| $j_{Ax}=-\rho \mathscr{D} _{AB}\dfrac {\partial w_A}{\partial x}$ | 1-1 |
| $j_{Ay}=-\rho \mathscr{D} _{AB}\dfrac {\partial w_A}{\partial y}$ | 1-2 |
| $j_{Az}=-\rho \mathscr{D} _{AB}\dfrac {\partial w_A}{\partial z}$ | 1-3 |
2.圆柱坐标系（$r,\theta, z$)
| 圆柱坐标系Cylindrical coordinates coordinates ($\textit {r, $\theta$, z }$): | NO. |
|---|---|
| $j_{Ar}=-\rho \mathscr{D} _{AB}\dfrac {\partial w_A}{\partial r}$ | 2-1 |
| $j_{A\theta}=-\rho \mathscr{D} _{AB} \dfrac {1}{r} \dfrac {\partial w_A}{\partial \theta}$ | 2-2 |
| $j_{Az}=-\rho \mathscr{D} _{AB}\dfrac {\partial w_A}{\partial z}$ | 2-3 |
3.球坐标系（$r, \theta, \phi $)
| 球坐标系Spherical coordinates（$\textit {r, $\theta$, $\phi$ }$): | NO. |
|---|---|
| $j_{Ar}=-\rho \mathscr{D} _{AB}\dfrac {\partial w_A}{\partial r}$ | 3-1 |
| $j_{A\theta}=-\rho \mathscr{D} _{AB} \dfrac {1}{r} \dfrac {\partial w_A}{\partial \theta}$ | 3-2 |
| $j_{A\phi}=-\rho \mathscr{D} _{AB} \dfrac {1}{r sin \theta} \dfrac {\partial w_A}{\partial \theta}$ | 3-3 |
参考文献
- R. Byron Bird, Warren E. stewart, Edwin N. Lightfoot. Transport phenomena:Revised second edition John Wiely &Sons, Inc.