Abstract
Abstract
The spread of fluid from a localized source on to a flat fibrous sheet is studied. The sheet is inclined at an angle, α, to the horizontal, and the areal flux of the fluid released is Q a. A new experimental study is described where the dimensions of the wetted region are measured as a function of time t, Q a and α (>0). The down-slope length, Y, grows according to Y ∼ (Q a t )2/3(sin α)1/3; for high discharge rates and low angles of inclination, the cross-slope width, X, grows as ∼ (Q a t )1/2, while for low discharge rates or high angles of inclination, the cross-slope transport is dominated by infiltration and X ∼ 2(2K sΦ∗t)1/2, where K s is the saturated permeability and Φ∗ is the characteristic value of capillary pressure. A scaling analysis of the underlying non-linear advection diffusion equation describing the infiltration process confirms many of the salient features of the flow observed. Good agreement is observed between the collapse of the numerical solutions and experimental results. The broader implications of these results for incontinence bed-pad research are briefly discussed.
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