Lattice Model for Spontaneous Imbibition in Porous Media: The Role of Effective Tension and Universality Class

Abstract

Recently anomalous scaling properties of front broadening during spontaneous imbibition of water in Vycor glass, a nano-porous medium, were reported: the mean height and the width of the propagating front increase with time $t$ both proportional to $t^{1/2}$. Here we propose a simple lattice imbibition model and elucidate quantitatively how the correlation range of the hydrostatic pressure and the disorder strength of the pore radii affect the scaling properties of the imbibition front. We introduce an effective tension of liquid across neighboring pores, which depends on the aspect ratio of each pore, and show that it leads to a dynamical crossover: both the mean height and the roughness grow faster in the presence of tension in the intermediate-time regime but eventually saturate in the long-time regime. The universality class of the long-time behavior is discussed by examining the associated scaling exponents and their relation to directed percolation.

arXiv comment11 pages, 13 figures

References in corpus (8)

• Imbibition in Disordered Media
• Anomalous Front Broadening During Spontaneous Imbibition in a Matrix with Elongated Pores
• Avalanches and the Directed Percolation Depinning Model: Experiments, Simulations and Theory
• Liquid Conservation and Non-local Interface Dynamics in Imbibition
• Simulating temporal evolution of pressure in two-phase flow in porous media
• Anisotropic Interface Depinning - Numerical Results
• Scaling theory for spontaneous imbibition in random networks of elongated pores
• Pipe network model for scaling of dynamic interfaces in porous media

Cited by in corpus (2)

• Soft matter in hard confinement: phase transition thermodynamics, structure, texture, diffusion and flow in nanoporous media - topical review
• Capillary rise dynamics of liquid hydrocarbons in mesoporous silica as explored by gravimetry, optical and neutron imaging: Nano-rheology and determination of pore size distributions from the shape of imbibition fronts