Nano-particle dynamics during capillary suction

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 T₂ 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.