Abstract
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.
Highlights
Over the past decades, microfluidic devices have attracted wide scientific attentions and been widely used in fields such as biological and chemical detections, drug delivery, and micromixing [1,2,3,4]
Surface charge generated at the solid wall-ionic liquid interface is a significant interfacial property to affect the microscale fluid flow [5,6,7,8,9,10]
This is because the surface charge at the solid–liquid interface can redistribute the charged ions in the ionic liquid and forms the electrical double layer (EDL) with local net charge density [5,6,7,8,9,10]
Summary
Microfluidic devices have attracted wide scientific attentions and been widely used in fields such as biological and chemical detections, drug delivery, and micromixing [1,2,3,4]. Surface charge generated at the solid wall-ionic liquid interface is a significant interfacial property to affect the microscale fluid flow [5,6,7,8,9,10]. This is because the surface charge at the solid–liquid interface can redistribute the charged ions in the ionic liquid and forms the electrical double layer (EDL) with local net charge density [5,6,7,8,9,10]. Shamloo et al [17] numerically studied the heat transfer performance of mixed electroosmotic and pressure-driven flow in straight microchannels with asymmetrical and symmetrical surface charge distributions
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