Imbibition in paper channels with engineered surface grooves

Paper-based microfluidic devices transport fluids by capillary imbibition and are widely used in low-cost point-of-care applications. Etching grooves onto the surface of the paper parallel to the flow is known to enhance wicking speeds, but the mechanisms and extent of speed-up are not well understood. We develop a model of vertical wicking in paper channels with etched grooves by coupling the flow in the paper matrix with that in the groove, and accounting for gravity and wettability effects. Using a lubrication-like theory for slender grooves, we show that speed up occurs due to the flow in the low-resistance groove acting as an additional source of fluid for transport in the paper matrix. At the same time, the flow in the groove is limited by its low wettability, and because driving capillary forces in the groove are counteracted by gravity. Perhaps counterintuitively, we find that the flow enhancement depends non-monotonically on the width of the groove. We also find that the addition of multiple grooves increases the flow speed but does so sub-linearly with the number of grooves. These findings are encapsulated in an analytical theory that generalizes the Lucas—Washburn wicking law to channels with etched grooves. The predictions of the theory for the wicking dynamics are shown to be in quantitative agreement with measurements of vertical imbibition in etched paper channels, and thus provide useful design guidelines for paper-based microfluidic devices.