Physics of two-phase flow on rough surfaces

In the vadose zone, fluid, such as water or contaminants, moves within unsaturated rock fractures. Glass is commonly used to model rock when investigating characteristics of droplet movement in rock fractures. This is a theoretical investigation of the effect of surface roughness on water droplet speeds. We found that the speed of droplets moving down glass fractures is significantly different than the speed down rock fractures. It has been experimentally observed that the physical condition of the surface is more responsible for wetting behavior than the chemistry. We investigate the physics of fluid movement over rough surfaces as applied to water droplet movement within a fracture. Chemical heterogeneity is ignored. Three theoretical constructs are added to the Navier-Stokes analysis to account for the surface roughness: Wenzel's roughness factor, a slip condition on the scale of the roughness, and a spreading force that accompanies the movement of the contact line. Prior work shows how a dynamic contact angle changes the velocity when smooth glass fractures are used; this possibility is discussed for rough fractures.