College of Civil Engineering, Hunan University, Changsha, China.
PLoS One. 2022 Oct 5;17(10):e0275644. doi: 10.1371/journal.pone.0275644. eCollection 2022.
The colloidal particle transport process in all porous media from laboratory to nature is affected by gravity. In this paper, a mathematical model of colloidal particle migration in a saturated porous medium with the gravity effect is established by combining the gap velocity (advection) with the settling velocity (gravity effect), and an analytical solution of the particle migration problem with time variation of the particle injection intensity is obtained using an integral transformation. The correctness and rationality of the analytical solution are verified by comparing the experimental and theoretical results of the particle migration problem in the point-source transient injection mode. The analytical solution can easily analyze the colloid transport experimental data in a variety of seepage directions. Analysis of the influence of seepage velocities in three different seepage directions on particle transport parameters shows: under the same seepage direction, the peak value of the breakthrough curve increased with an increase in the seepage velocity. The dispersion, adsorption coefficient, and deposition rate decreased with an increase in the seepage velocity. Under the same seepage velocity, the peak value of the breakthrough curve from large to small was vertically downward (VD)> horizontal (H)> vertically upward (VU), the order of dispersion from large to small was vertically downward (VD)>horizontal (H) >vertically upward (VU), the order of the adsorption coefficient and deposition rate of particles from large to small was vertically upward (VU)> horizontal (H) >vertically downward (VD), and the smaller the seepage velocity, the greater the relative differences in the peak value of the breakthrough curve, dispersion, the particle adsorption coefficient, and the deposition rate in the different seepage directions. Therefore, gravity is an important mechanism of particle migration in saturated porous media. The larger the particle size and density were, the smaller the seepage velocity was and the more obvious the effect of gravity. The findings of this study can help for better understanding of colloidal transport properties in porous media under the coupled effects of gravity and hydrodynamics.
胶体颗粒在所有多孔介质中的输运过程都受到重力的影响。本文通过结合间隙速度（对流）和沉降速度（重力效应），建立了一个具有重力效应的饱和多孔介质中胶体颗粒迁移的数学模型，并通过积分变换得到了颗粒注入强度随时间变化的颗粒迁移问题的解析解。通过比较点源瞬态注入模式下的颗粒迁移问题的实验和理论结果，验证了解析解的正确性和合理性。该解析解可以方便地分析各种渗流方向下的胶体输运实验数据。分析了在三种不同渗流方向下的渗流速度对颗粒输运参数的影响，结果表明：在相同的渗流方向下，穿透曲线上的峰值随渗流速度的增加而增加。随着渗流速度的增加，分散系数、吸附系数和沉积速率减小。在相同的渗流速度下，穿透曲线峰值从大到小依次为垂直向下（VD）>水平（H）>垂直向上（VU），分散系数从大到小依次为垂直向下（VD）>水平（H）>垂直向上（VU），颗粒的吸附系数和沉积速率从大到小依次为垂直向上（VU）>水平（H）>垂直向下（VD），渗流速度越小，不同渗流方向上穿透曲线峰值、分散度、颗粒吸附系数和沉积速率的相对差异越大。因此，重力是饱和多孔介质中颗粒迁移的重要机制。颗粒粒径和密度越大，渗流速度越小，重力的影响越明显。本研究的结果有助于更好地理解重力和水动力耦合作用下多孔介质中胶体的输运特性。
