Lattice Model for Spontaneous Imbibition in Porous Media: The Role of Effective Tension and Universality Class
Heiko Rieger,
Zeinab Sadjadi
Recently, anomalous scaling properties of front broadening during spontaneous imbibition of water in Vycor
glass, a nanoporous 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.
[1] D. S. Lee, Z. Sadjadi and H. Rieger Lattice Model for Spontaneous Imbibition in Porous Media: The Role of Effective Tension and Universality Class |
Phys. Rev. E 90, 013016 (2014)
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[condmat], [pdf]
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