# 扩散作用

（重定向自简单扩散

## 唯象描述

### 菲克定律

${\displaystyle {\overrightarrow {J}}=-D\nabla c}$

${\displaystyle \iiint _{V}{\frac {\partial c}{\partial t}}dV=-\oint _{\mathbb {S} }{\overrightarrow {J}}\cdot \mathrm {d} \mathbf {a} =-\iiint _{V}\nabla \cdot {\overrightarrow {J}}dV=\iiint _{V}\nabla \cdot (D\nabla c)dV}$

${\displaystyle \iiint _{V}{\frac {\partial c}{\partial t}}dV=D\iiint _{V}\nabla ^{2}cdV}$

${\displaystyle {\frac {\partial c}{\partial t}}=D\nabla ^{2}c}$

### 热力学分析

#### 热动平衡条件

${\displaystyle dS={\Big (}{\frac {p_{A}}{T}}-{\frac {p_{B}}{T}}{\Big )}dV_{A}-{\Big (}{\frac {\mu _{A}}{T}}-{\frac {\mu _{B}}{T}}{\Big )}dN_{A}+{\Big (}{\frac {1}{T_{A}}}-{\frac {1}{T_{B}}}{\Big )}dU_{A}=0}$

${\displaystyle {\overrightarrow {J}}=-{\frac {Dc}{RT}}\nabla \mu }$

${\displaystyle {\overrightarrow {J}}=-D\nabla c}$

#### 昂萨格倒易关系

${\displaystyle {\overrightarrow {J}}_{i}=\sum _{j}L_{ij}X_{j}}$

${\displaystyle X_{k}=\nabla {\frac {\partial s(n)}{\partial n_{k}}}}$
${\displaystyle n_{k}}$被称为热力学广义坐标，对于扩散过程取${\displaystyle n}$为浓度即可。

## 相關條目

1. ^ Onsager, Lars. Reciprocal Relations in Irreversible Processes. I.. Physical Review. 1931, 37 (4): 405–426. doi:10.1103/physrev.37.405.
2. ^ ), Fu xian cai, (1920-; ), 傅献彩, (1920-. Wu li hua xue. shang ce. 5ban. Bei jing: Ren min jiao yu chu ban she https://www.worldcat.org/oclc/302366020. 2005. ISBN 9787040167696. OCLC 302366020. 缺少或|title=为空 (帮助)