Infiltration into inclined fibrous sheets

Abstract

The flow from line and point sources through an inclined fibrous sheet is studied experimentally and theoretically for wicking from a saturated region and flow from a constant-flux source. Wicking from a saturated line generates a wetted region whose length grows diffusively, linearly or tends to a constant, depending on whether the sheet is horizontal or inclined downwards or upwards. A constant-flux line source generates a wetted region which ultimately grows linearly with time, and is characterized by a capillary fringe whose thickness depends on the relative strength of the source, gravitational and capillary forces. Good quantitative agreement is observed between experiments and similarity solutions.

Capillary-driven and constant-flux source flows issuing from a point on a horizontal sheet generate a wetted patch whose radius grows diffusively in time. The flow is characterized by the relative strength of the source and spreading induced by the action of capillary forces, $\gamma$. As $\gamma$ increases, the fraction of the wetted region which is saturated increases. Wicking from a saturated point corresponds to $\gamma\,{=}\, \gamma_c$, and spreads at a slower rate than from a line source. For $\gamma \,{<}\,\gamma_c$, the flow is partially saturated everywhere. Good agreement is observed between measured moisture profiles, rates of spreading, and similarity solutions.

Numerical solutions are developed for point sources on inclined sheets. The moisture profile is characterized by a steady region circumscribed by a narrow boundary layer across which the moisture content rapidly changes. An approximate analytical solution describes the increase in the size of the wetted region with time and source strength; these conclusions are confirmed by numerical calculations. Experimental measurements of the downslope length are observed to be slightly in excess of theoretical predictions, though the dependence on time, inclination and flow rate obtained theoretically is confirmed. Experimental measurements of cross-slope width are in agreement with numerical results and solutions for short and long times. The effect of a percolation threshold is observed to ultimately arrest cross-slope transport, placing a limitation on the long-time analysis.