Dynamics of water imbibition in multilayered paper channels

Microfluidic paper-based analytical devices ( ${\unicode{x03BC}}$ PADs) have gained considerable attention due to their ability to transport fluids without external pumps. Fluid motion in ${\unicode{x03BC}}$ PADs is driven by capillary forces through the network of pores within paper substrates. However, the inherently low flow speeds resulting from the small pore sizes in paper often limit the performance of ${\unicode{x03BC}}$ PADs. Recent studies have introduced multilayered ${\unicode{x03BC}}$ PADs composed of stacked paper sheets, which enable significantly faster fluid transport through inter-layer channels. In this study, we present a combined theoretical and experimental investigation of water imbibition dynamics through channels formed by multiple paper layers. Upon contact with water, the paper layers absorb water and undergo swelling, altering channel geometry and consequently affecting flow dynamics. We develop a mathematical model that extends the classical Washburn equation to incorporate the effects of water absorption and swelling. The model predictions show excellent agreement with experimental observations of water flow through multilayered paper channels. The results elucidate how water absorption and swelling influence capillary imbibition, and suggest potential strategies for regulating flow rates in multilayered ${\unicode{x03BC}}$ PADs.