Small-Scale Features of Gravity-Driven Flow in Unsaturated Fractures

Abstract

Liquid flow through unsaturated fractures often proceeds as fingers or preferential flow paths. During the invasion of liquid fingers into an initially dry, nonhorizontal fracture, fingers may drain, forming a narrow thread of liquid called a rivulet that connects to a wider portion of liquid at the advancing front, defined as a blob. Experimental studies using idealized fractures were performed to investigate the effects of wettability, surface roughness, and aperture size on several important features of gravity-driven flow in fractures: liquid drainage, blob migration, and rivulet flow. The experiments demonstrate that the critical length of the blob before drainage occurred was significantly longer on surfaces with intermediate wettability and on surfaces with roughness on the order of 100 μm than on a smooth, flat water-wetting surface. However, drainage did not occur on surfaces with smaller-scale roughness on the order of 10 μm. Blob velocities were also measured and were always less than the saturated gravity-driven flow velocity, even when a liquid with a static contact angle of zero was used. This reduction in velocity was attributed to contact angle hysteresis. Rivulet widths measured as a function of flow rate between glass and acrylic parallel plates were generally larger on the acrylic plates than the glass plates for a particular flow rate, demonstrating the sensitivity of rivulet flow to wettability. In addition, the cubic law overpredicted the measured rivulet widths, except for the widths measured between the acrylic plates at 20°. The effect of aperture variability on rivulet flow was also examined. At a critical aperture ranging between 0.25 and 0.37 mm, the liquid in the rivulet did not completely span the aperture, forming two streamlets of liquid on either side of the fracture.