Combined Electroosmotic And Pressure Driven Flow In Tree-Like Microchannel Network

The present work presents a simplified mathematical model to calculate the flowrate of the combined electroosmotic flow (EOF) and pressure driven laminar flow (PDLF) in the symmetric tree-like microchannel network under the assumptions of small zeta potential and thin electrical double layer. A numerical analysis of the combined EOF and PDLF in symmetric Y-shaped microchannel is also carried out to validate the mathematical model. The analytical results and numerical results are found to be in good agreement with each other. Using the mathematical model, the present work further investigates the effect of diameter ratio of the tree-like network on the flowrate of the combined EOF and PDLF to recognize a possible conclusion being similar to the Murray’s law. Based on the present work, it is found that the symmetric tree-like network has an optimal diameter ratio to achieve the maximum flowrate for the combined EOF and PDLF when the total microchannel volume is constant; however, this optimal diameter ratio for the combined flow disobeys the generalized Murray’s law in a simple form of power function of the branching number N, and it is not only related on the branching number, but also depends on the branching level and channel length ratio of the tree-like network. Furthermore, the optimal diameter ratio shows a monotonous transition from N−1/3 for the pure PDLF to N−1/2 for the pure EOF with the increasing ratio of the driven voltage and driven pressure. The present work discusses the effects of these parameters on the optimal diameter ratio for the combined EOF and PDLF.