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由于多孔介质结构的随机性，很难对其内的胶体粒子输运过程进行建模。Boltzmann输运方程为模拟随机空间中胶体粒子的微观动力学提供了一种可靠的途径。本文通过Chapman-Enskog（CE）分析，从胶体粒子的Boltzmann方程导出了宏观输运模型。该模型具有对流-扩散方程形式，包括依赖粒子速度分布的扩散项、速度延迟项以及反映微观捕获机制的捕获项。我们还给出了三个输运系数的显式表达。该宏观模型部分解决了传统胶体输运模型的悖论，并且在特定条件下与以往模型一致。
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关键词:
- 多孔介质 /
- 胶体输运 /
- 捕获 /
- Boltzmann方程
The structural randomness of porous media presents significant challenges to accurately simulating colloidal transport. The Boltzmann transport equation (BTE) provides a reliable way to simulate the microscopic dynamics of colloidal particles in random space.
By using the Chapman-Enskog (CE) method, a macroscopic advection-diffusion transport model is derived from the BTE. It includes a diffusion term depending on the particle velocity distribution, a velocity delay term, and a capture term reflecting the microscopic capture mechanism, which tends to preferentially capture high-speed moving particles. These terms account for the delay and capture effects in colloidal transport. Meanwhile, the explicit expressions of the three transport coefficients are presented to provide a quantitative basis for the application of the model.
The model is effective at small mixing filtration coefficients λl. By comparing outlet concentration profiles of different models (Fig. 14), we clarify the impact of this mechanism on the advective velocity delay and capture efficiency. The model resolves some of the paradoxes of traditional colloidal transport models. And it agrees with previous models under specific conditions.-
Keywords:
- porous media /
- colloidal transport /
- capture /
- Boltzmann equation
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