菲克扩散(第一)定律【Fick's (First) Law of Binary Diffussion】

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

$$\pmb j_A=-\rho \mathscr{D} _{AB} {\nabla } w_A$$
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

$$w_{Ax}=-\dfrac {d w_A} {dx}$$

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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

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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

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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

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参考文献

1. R. Byron Bird, Warren E. stewart, Edwin N. Lightfoot.* Transport phenomena:Revised second edition* John Wiely &Sons, Inc.