Cross-Sectional Dimension Dependence of Electroosmotic Flow in Fractal Treelike Rectangular Microchannel Network

The present work theoretically and numerically studies the electroosmotic flow (EOF) within a fractal treelike rectangular microchannel network with uniform channel height. To obtain minimum EOF fluidic resistance, the microchannel cross-sectional dimensions of the fractal network are optimized. It is found that the cross-sectional dimension dependence of EOF fluidic resistance within a symmetric fractal network is only dependent on the channel width when the total channel volume is constant, and the optimal microchannel widths to reach the minimum EOF fluidic resistance satisfy the scaling law of κ = N^-1 (where κ is the width ratio of the rectangular channels at two successive branching levels, N is the branching number); however, for the symmetric fractal network with constant total surface area , the optimal cross-sectional dimensions should simultaneously satisfy κ = N^-1 and (where H is the channel height, S is the total channel surface area, l₀ is the channel length at the original branching level, γ is the channel length ratio at two successive branching levels and m is the total branching level) to obtain the minimum EOF fluidic resistance. The optimal scaling laws established in present work can be used for the optimization design of the fractal rectangular microchannel network for EOF to reach maximum transport efficiency.