Microchannel networks can be efficiently used for several applications. For example, they can be the main elements of micro chemical reactors or micro heat exchangers for cooling electronic chips. In such networks, the flow of liquid can be generated either by a pressure difference, by electro-osmosis or by both of them. The design of the network can be optimized in order to deliver a maximum flowrate. In this paper, an analytical study of a pressure driven and electro-osmotic flow in tree-shaped microchannel network is developed. The network is built with a series of rectangular microchannels with high aspect ratio. Each bifurcation connects a parent microchannel to a couple of twin child microchannels. The objective of this work is to determine the geometrical configuration which offers the highest flowrate. The efficiency of the tree-shaped network is compared to the efficiency of a series of parallel microchannels, for the same inlet and outlet values of electric potential and pressure and for the same network volume. Focusing on one bifurcation, the influence of the thickness of the electrical double layer is discussed. The optimal geometric dimensions, such as the ratio of the child over parent microchannel widths and the ratio of the parent over total microchannel lengths, are calculated. The influence of the number of bifurcations is also analyzed and optimal design rules are proposed.

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