Lawrence Berkeley National Laboratory

Hysteresis in the relation between water saturation and matric potential is generally regarded as a basic aspect of unsaturated porous media. However, the nature of an upper length scale limit for saturation hysteresis has not been previously addressed. Since hysteresis depends on whether or not capillary rise occurs at the grain scale, this criterion was used to predict required combinations of grain size, surface tension, fluid-fluid density differences, and acceleration in monodisperse systems. The Haines number (Ha), composed of the aforementioned variables, is proposed as a dimensionless number useful for separating hysteretic (Ha 15) behavior. Vanishing of hysteresis was predicted to occur for grain sizes greater than 10.4 +- 0.5 mm, for water-air systems under the acceleration of ordinary gravity, based on Miller-Miller scaling and Haines' original model for hysteresis. Disappearance of hysteresis was tested through measurements of drainage and wetting curves of sands and gravels and occurs between grain sizes of 10 and 14 mm (standard conditions). The influence of surface tension was tested through measurements of moisture retention in 7 mm gravel, without and with a surfactant (sodium dodecylbenzenesulfonate (SDBS)). The ordinary water system (Ha = 7) exhibited hysteresis, while the SDBS system (Ha = 18) did not. The experiments completed in this study indicate that hysteresis in moisture retention relations has an upper limit at Ha = 16 +- 2 and show that hysteresis is not a fundamental feature of unsaturated porous media.