CHEN Xiaotong; GUO ZhaoLi

doi:10.7498/aps.74.20250288

Abstract

The structural randomness of porous medium presents significant challenges for accurately simulating colloidal transport. The Boltzmann transport equation (BTE) provides a reliable way for simulating 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 dependent 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 explain 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 using the model.The model is effective at small mixing filtration coefficients λl. By comparing the outlet concentration profiles of different models, the influences of this mechanism on the advection velocity delay and capture efficiency are elucidated. The model solves some of the paradoxes of traditional colloidal transport models, and under specific conditions, it is consistent with previous models.

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Corresponding author: GUO ZhaoLi, zlguo@hust.edu.cn

Funds: Project supported by the Interdisciplinary Research Support Program of Huazhong University of Science and Technology (Grant No. 2023JCYJ002).

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	α = 1	α < 1
$ {{Pe}}^{-1} $	$ {({l}{/}{L}){{C}}_{{v}}^{2}}_{}^{} $	$ ({l}{/}{L}){{C}}_{{v}}^{2} $
θ	$ 2{ \lambda l}{{C}}_{{v}}^{2} $	$ 2{ \lambda l}\left\{\left(1+{{C}}_{{v}}^{2}\right)\left[2\varPhi\left(\displaystyle \frac{1}{{{C}}_{{v}}}\right)-1\right]+\displaystyle \frac{2{{C}}_{{v}}}{\sqrt{{2\pi}}}\text{exp}\left(-\frac{1}{2{{C}}_{{v}}^{2}}\right)\right\} $
Ω	$ \lambda{ L}{(1}-{ \lambda l}{{C}}_{{v}}^{2}) $	$\lambda L \left[ \left[ 2\varPhi\left( \dfrac{1}{C_v} \right) - 1 \right] + \dfrac{2C_v}{\sqrt{2\pi}} \exp\left( -\dfrac{1}{2C_v^2} \right) - \lambda l \left( C_v^2 + 1 - \left\{ \left[ 2\varPhi\left( \dfrac{1}{C_v} \right) - 1 \right] + \dfrac{2C_v}{\sqrt{2\pi}} \exp\left( -\dfrac{1}{2C_v^2} \right) \right\}^2 \right) \right] $
注:$ \varPhi \left( x \right) = \displaystyle \int_{ - \infty }^x {\frac{{\exp \left( { - {y^2}/2} \right)}}{{\sqrt {2{\pi{}}} }}} {\text{d}}y. $

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Vol. 74, Issue 12 - 2025-06-20

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