Imbibition in porous membranes of complex shape: quasi-stationary flow in thin rectangular segments.

The sustained liquid flow of a typical lateral flow assay can be mimicked by two-dimensional shaped, thin porous membranes, specifically rectangular membranes appended to circular sectors. In designing these fan-shaped devices, we have been aided by analytical equations and finite-element simulations. We show both mathematically and experimentally how a continuous increase in unwetted pore volume causes a deviation from traditional imbibition, and leads to quasi-stationary flow in the rectangular element. These results are both theoretically and practically important because they indicate how medical diagnostic test strips may be fabricated without incorporating an absorbent pad.