Electroosmotic Flow in Tree-Shaped Microchannel Networks

An analytical model of electroosmotic flow in tree-shaped microchannel networks is developed. The aim of the study is to determine the best network architecture to maximize the electroosmotic flowrate for a given electric field and a given total microchannel volume. The network consists of rectangular microchannels with high aspect ratio. The paper shows under what conditions the tree structure offers a higher flowrate than a series of parallel microchannels. The influence of the electric double layer (EDL) thickness is pointed out. As long as the EDL thickness is negligible compared with the microchannel width, the tree-shaped architecture does not present any particular interest. But as soon as the EDL thickness is significant, it is shown that the flowrate can be largely enhanced by increasing the number of bifurcations in the tree-shaped network. Two configurations of bifurcations (V-shaped and U-shaped) are considered and compared. Each bifurcation is composed of a parent microchannel connected to two identical daughter microchannels. The optimal value of the daughter over parent microchannels widths is calculated. The influence of the daughter over parent microchannels lengths and of the number of bifurcations is pointed out. Guidelines for the design of tree-shaped microchannel networks are finally proposed.