Due to the increased use of nanoparticles in everyday applications, there is a need for theoretical descriptions of particle transport and attachment in porous media. It should be possible to develop a one dimensional model to describe nanoparticle retention during capillary transport of liquid mixtures in porous media.

Water-glycerol-nanoparticle mixtures were prepared and the penetration process in porous Al₂O₃ samples of varying pore size is measured using NMR imaging. The liquid and particle front can be measured by utilizing $T_2$ relaxation effects from the paramagnetic nanoparticles.

A good agreement between experimental data and the predicted particle retention by the developed theory is found. Using the model, the binding constant for Fe₂O₃ nanoparticles on sintered Al₂O₃ samples and the maximum surface coverage are determined. Furthermore, we show that the penetrating liquid front follows a square root of time behavior as predicted by Darcy’s law. However, scaling with the liquid parameters is no longer sufficient to map different liquid mixtures onto a single master curve. The Darcy model should be extended to address the two formed domains (with and without particles) and their interaction, to give an accurate prediction for the penetrating liquid front.

由于纳米粒子在日常应用中的使用增加，因此需要对多孔介质中粒子传输和附着的理论描述。应该有可能发展出一维模型来描述在多孔介质中液体混合物的毛细管运输过程中纳米颗粒的保留。

制备水-甘油-纳米颗粒混合物，并使用NMR成像测量在孔径变化的多孔Al ₂ O ₃样品中的渗透过程。液体和颗粒的前缘可以通过利用${Ť}_{\mathrm{2个}}$ 顺磁性纳米粒子的弛豫效应。

发现实验数据和通过发达的理论预测的颗粒保留之间的良好一致性。使用该模型，确定Fe ₂ O ₃纳米颗粒在烧结Al ₂ O ₃样品上的结合常数和最大表面覆盖率。此外，我们证明了渗透液体前沿遵循达西定律所预测的时间行为的平方根。但是，用液体参数缩放不再足以将不同的液体混合物映射到单个主曲线上。达西模型应该扩展为处理两个形成的区域（有和没有粒子）及其相互作用，从而为渗透性液体前沿提供准确的预测。