Scaling theory for spontaneous imbibition in random networks of elongated pores

TL;DR

This paper develops a scaling theory for spontaneous imbibition in elongated pore networks, explaining the arrest time distribution and roughness of the imbibition front, supported by simulations and experimental correlation.

Contribution

It introduces a novel scaling theory for imbibition in elongated pore networks, linking arrest times and front roughness with theoretical predictions and simulations.

Findings

Average front width scales linearly with height

Roughness exponent is exactly 1/2

Simulations confirm theoretical predictions

Abstract

We present a scaling theory for the long time behavior of spontaneous imbibition in porous media consisting of interconnected pores with a large length-to-width ratio. At pore junctions the meniscus propagation in one or more branches can come to a halt when the Laplace pressure of the meniscus exceeds the hydrostatic pressure within the junction. We derive the scaling relations for the emerging arrest time distribution and show that the average front width is proportional to the height, yielding a roughness exponent of exactly beta=1/2 and explaining recent experimental results for nano-porous Vycor glass (NVG). Extensive simulations of a pore network model confirm these predictions.