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 H = S 4 l 0 1 − γ N 1 − ( γ N ) m + 1 (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.

This paper theoretically and numerically investigates the hydraulic resistance, mixing efficiency, and comprehensive mixing and hydraulic performance characterized by the outlet mixing efficiency to hydraulic resistance ratio of the symmetric T-shaped rectangular microchannel mixer with uniform channel height. The influences of multi-parameters including width ratio of inlet channel and outlet channel, channel height, and two different inlet conditions of inlet velocity and inlet flowrate on the hydraulic and mixing performance of the micromixer are investigated. This work found that the comprehensive performance first increases and then decreases with the increasing channel width ratio of inlet channel and outlet channel, indicating the existence of an optimal channel width ratio to reach the best comprehensive mixing and hydraulic performance. This result is similar to the conclusion of classical Murray’s law and can be considered as an extension of classical Murray’s law in the field of microscale mixing. The effects of the channel height, channel length ratio and different inlet conditions on the optimal width ratio are analyzed.

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This paper proposes a mixer with an elastic vortex generator consisting of a branched elastic flag connected to the rear of a cylinder in the mixing channel and studies the effects of the branching angle of the branching elastic flag and Reynolds number based on the cylinder diameter Red on the mixing modes of the fluid flow in the mixer. One free diffusion-induced mixing mode and two different vortex-induced mixing modes are found, and a phase diagram regarding the mixing modes of the fluid flow behind the elastic vortex generator is established. It is found that the elastic vortex generator is helpful for the transition of the mixing mode from free diffusion-induced mixing to vortex-induced mixing with the increasing branching angle. Furthermore, the rising Reynolds number results in the transition of mixing mode from free diffusion-induced mixing to vortex-induced mixing. In addition, the present work quantitatively studies the effects of the branching angle of the branched elastic flag and Reynolds number on the pressure loss and the outlet mixing efficiency of the mixer. It is found that the increase in pressure loss and the outlet mixing efficiency are 141.41% and 613.70% as the branching angle increases from 0° to 180° when Red = 90. In addition, the pressure loss and outlet mixing efficiency of the mixer with the branched elastic flag of branching angle θ = 180° can be 227.66% and 601.36% higher than those of the fluid flow around the cylinder without the elastic flag in the mixing channel when Red = 50.

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