Wicking and flooding of liquids on vertical porous sheets

When one brings a wet paintbrush into contact with a vertical watercolor paper, the paint may wick into the porous sheet completely or run down to ruin the art. We study a simple model of this spreading dynamics of liquids on hydrophilic porous sheets under the effects of gravity, using a capillary as a liquid source and thin fabrics of non-woven polyethylene terephthalate. Upon finding the maximum flow rate, Q_w, that can be absorbed into the fabric, we show that the model can be used to obtain an estimate of the in-plane permeability of fabrics in a simpler manner than the conventional schemes. The shape of a wetting area that grows when the flow rate exceeds Q_w to lead to rivulet formation is also theoretically given. The nose shape of the wetting front is shown to be time-invariant, while its profile depends on the properties of the liquid and the fabric. This study can be applied to understand and improve the liquid absorption behavior of hygiene items, heating, ventilation, and air-conditioning equipments, and fuel cell membranes in addition to elucidating the mundane painting activity.