Effective saturation profile
This protocol is extracted from research article:
Tracking time with ricequakes in partially soaked brittle porous media
Sci Adv, Oct 12, 2018; DOI: 10.1126/sciadv.aat6961

The equilibrated shape of wetting fronts in porous media partially soaked in fluid under gravity depends on many parameters (23), from the level of gravity to fluid viscosity, topology of the pores, and their connectivity in the solid medium. We take z = 0 as the lowest point of the wetting front, where the effective saturation is [Se(0) = 1]. From typical profiles reported in the literature, Se decays over distance z away from the lowest point of the front (34, 35). The typical length of decay is frequently related directly to the capillary gravity length (23)Embedded Image(10)where g is the gravity, ρ is the fluid density, and γ is the surface tension. A natural way to consider the saturation decay and take this length into account is to set the effective saturation profile as Se(z) = exp(−z/LG), assuming the puffed rice is a hydrophilic material (Fig. 4B). See supplementary text and fig. S1 for illustrations of the relevance of this profile for systems of highly porous particles. The carriage i whose top is at location z(i) therefore experiences effective saturation Embedded Image. Under the pressure level p* at the start of the wetting part of the experiments, we find the initial position of the center of the carriages Embedded Image. According to Valdes et al. (10), for the order of the p* ≈ 50 kPa in our experiments, K0 ≈ 15 MPa from shear wave measurements. This gives Embedded Image, and thus, the initial positions of the carriages can be calculated as Embedded Image. The initial effective saturation of carriage i is thereforeEmbedded Image(11)

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