Assessing the rapid flow in multilayer paper-based microfluidic devices

A hot topic in paper-based microfluidics is the achievement of capillary-driven flows much faster than the ones theoretically allowed by the hydrodynamic permeability of common filter papers. Recent works have experimentally shown that the flow rates can be substantially improved by using multilayer paper systems instead of single-layer papers. The present work discusses a theoretical assessment of fluid transport in multilayer paper-based microfluidic devices. The proposed model effectively predicts a series of experimental observations, namely: the occurrence of fluid velocities 2 orders of magnitude larger than those measured in single-layer paper; the variation of fluid velocity as a function of the gap thickness, which presents a particular maximum; the effects of gravity on the filling dynamics, which is unexpected for single-layer paper; and the effect of the sample volume size, which leads to non-trivial filling dynamics. It is worth mentioning that these effects cannot be described by Lucas-Washburn model for single layers, because they arise from the interplay among the coupled flow domains in the multilayer system, together with the action of the gravitational force. The proposed model provides clues to understand the fundamentals behind the capillary-driven flow in multilayer systems, and hence to better design paper-based microfluidics devices for specified flow rates and time-stepped functions.