\[J = -D\frac{\partial c}{\partial x}\]
含义Meaning
扩散通量与浓度梯度成正比、方向相反（1855）。类似于热传导的傅里叶定律和电导的欧姆定律。
Diffusive flux is proportional to and opposite the concentration gradient (1855) — the analogue of Fourier’s and Ohm’s laws.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(J\) | 扩散通量diffusion flux | mol·m⁻²·s⁻¹ |
| \(D\) | 扩散系数（水中小分子约 10⁻⁹ m²/s）diffusion coefficient (~10⁻⁹ m²/s for small molecules in water) | m²·s⁻¹ |
推导Derivation
分子随机行走：在 x 处，左右两侧单位时间越过的分子数正比于各自浓度。
Random walk: molecules cross a plane from each side in proportion to the local concentration.
净通量 ∝ 左右浓度差 ∝ \(-\partial c/\partial x\)，比例系数即 D。
Net flux ∝ −∂c/∂x.
热力学上，驱动力是化学势梯度：\(J = -(Dc/RT)\,\partial\mu/\partial x\)。
Thermodynamically the driving force is the chemical-potential gradient.
适用条件与局限Assumptions & limitations
稀溶液、各向同性；浓溶液中 D 随浓度变化，多组分体系需用麦克斯韦–斯特藩方程。
Dilute, isotropic media; concentrated or multicomponent systems need concentration-dependent D or Maxwell–Stefan equations.