Optimization of capillary flow through open-microchannel and open-micropillar arrays

We report semi-analytical models for capillary flow across surfaces covered by an array of open micropillars or open microchannels that incorporate first-order gravitational effects as well as the reduction of permeability due to meniscus curvature. We experimentally validate our models by measuring the vertical rise of a column of liquid across a series of vertical microstructured surfaces with varying characteristic dimensions, using Newtonian and non-Newtonian liquids. The data show that arrays of open microchannels deliver higher flow rates than comparable arrays of micropillars in most practical configurations. Furthermore, we experimentally demonstrate a flow maximum for open microchannels with respect to channel width that closely agrees with our analytical predictions. In addition, as an application example of the microstructures used in this study, we report electrospray emission from the edge of a chip covered by a microstructured surface that transports the liquid from a reservoir to the emission sites; the supply-limited regime of the current-voltage characteristics of these devices is in agreement with the literature on electrospray droplet emission.