A unified scaling model for flow through a lattice of microfabricated posts

A scaling model is presented for low Reynolds number viscous flow within an array of microfabricated posts. Such posts are widely used in several lab-on-a-chip applications such as heat pipes, antibody arrays and biomolecule separation columns. Finite element simulations are used to develop a predictive model for pressure driven viscous flow through posts. The results indicate that the flow rate per unit width scales as ∼h^1.17g^1.33/d^0.5 where h is the post height, d post diameter and g is the spacing between the posts. These results compare favorably to theoretical limits. The scaling is extended to capillary pressure driven viscous flows. This unified model is the first report of a scaling that incorporates both viscous and capillary forces in the microfabricated post geometry. The model is consistent with Washburn dynamics and was experimentally validated to within 8% using wetting on microfabricated silicon posts.