2 Experimental Setup

[681.1.6.1] The experimental setup of [15] consists of a vertical cylindrical, $72\,\textrm{cm}$ long column, whose side walls are impermeable, filled with a homogeneous, isotropic and incompressible porous medium, an unconsolidated sandy material comprising approximately 97.5, 0.8 and 1.7% sand-, silt-, and clay-sized particles respectively. [681.1.6.2] The two fluids considered here are water and air and water is the wetting fluid. [681.1.6.3] The top of the column is connected to the atmosphere so that only air can enter the top of the column. [681.1.6.4] The bottom of the column is connected to a water tank and only water can enter from the bottom. [681.1.6.5] The pressure in the tank is adjustable. [681.1.6.6] Initially, the porous column is completely water saturated and the pressure ${P_{{\mathbb{W}}}}$ in the water tank is chosen such that it compensates the water column ${P_{{\mathbb{W}}}}(t=0)=72\,{\rm cmH_{2}O}(=7.06\textrm{k}\textrm{Pa})$ . [681.1.6.7] Hence, the capillary fringe is located at the top of the column. [681.1.6.8] The pressures in this section are given in cm column of water because this translates one to one to the position of the water table in the column. [681.1.6.9] Below in Section 5 SI units are used. [681.1.6.10] Figure 1 gives a conceptual picture of the experiment.

Figure 1: Conceptual picture of the experimental setup and the pressure protocols in the upper and lower reservoir vs. time.

[681.1.6.11] The column is drained by lowering the pressure in the reservoir by ${\Delta P}=5\,{\rm cmH_{2}O}$ every ${\Delta t}=10\,\textrm{min}$ 13 times until the water pressure reaches ${P_{{\mathbb{W}}}}=7{\rm cmH_{2}O}$ . [681.1.6.12] After a relaxation period of ${\Delta t}=50\,\textrm{min}$ , the water pressure is raised again in seven steps by ${\Delta P}=5\,{\rm cmH_{2}O}$ every ${\Delta t}=10\,\textrm{min}$ and the column is imbibed again. [681.1.6.13] After ${\Delta t}=50\,\textrm{min}$ , the water pressure is again lowered by ${\Delta P}=5\,{\rm cmH_{2}O}$ every ${\Delta t}=10\,\textrm{min}$ for 5 times and the column is drained again. [681.1.6.14] Finally, ${\Delta t}=50\,\textrm{min}$ later, the water pressure is raised again by ${\Delta P}=5\,{\rm cmH_{2}O}$ steps every ${\Delta t}=10\,\textrm{min}$ until it reaches its initial value ${P_{{\mathbb{W}}}}(t>8\,\textrm{h})=72\,{\rm cmH_{2}O}$ . [681.1.6.15] However, the original water content in the column is not recovered because a fraction of air remains trapped in the medium [7].

[681.1.7.1] In the laboratory, water saturation and water pressure have been measured at height $x=0.4\,\textrm{m}$ , $x=0.5\,\textrm{m}$ , $x=0.6\,\textrm{m}$ and $x=0.7\,\textrm{m}$ from the bottom of the column. [681.1.7.2] It may safely be assumed that the air pressure is essentially hydrostatic and atmospheric for two reasons: Firstly, because of the high viscosity and density contrast ( $\mu _{{\mathbb{W}}}=0.001\,\textrm{kg}\,\textrm{m}^{{-1}}\sec^{{-1}}$ , $\mu _{{\mathbb{O}}}=18\times 10^{{-6}}\,\textrm{kg}\,\textrm{m}^{{-1}}\sec^{{-1}}$ and $\varrho _{{\mathbb{W}}}=1000\,\textrm{kg}\,\textrm{m}^{{-3}}$ , $\varrho _{{\mathbb{O}}}=1.2\,\textrm{kg}\,\textrm{m}^{{-3}}$ ), and secondly, because the column is short. [681.1.7.3] It is therefore concluded that the measurement of water saturation and water pressure suffices to determine the capillary pressure saturation relationship.

Authors:	F. Doster and R. Hilfer
originally published in:	Water Resources Research, Vol. 50, pages 681-686 (2014)
originally submitted:	January 28th, 2014