The Optimal Branch Width Convergence Ratio to Maximize the Transport Efficiency of the Combined Electroosmotic and Pressure-Driven Flow within a Fractal Tree-like Convergent Microchannel

Abstract

Building upon the efficient transport capabilities observed in the fractal tree-like convergent structures found in nature, this paper numerically studies the transport process of the combined electroosmotic and pressure-driven flow within a fractal tree-like convergent microchannel (FTCMC) with uniform channel height. The present work finds that the flow rate of the combined flow first increases and then decreases with the increasing branch width convergence ratio under the fixed voltage difference and pressure gradient along the FTCMC, which means that there is an optimal branch width convergence ratio to maximize the transport efficiency of the combined flow within the FTCMC. The value of the optimal branch convergence ratio is highly dependent on the ratio of the voltage difference and pressure gradient to drive the combined flow. By adjusting the structural and dimensional parameters of the FTCMC, the dependencies of the optimal branch convergence ratio of the FTCMC on the branching level convergence ratio, the length ratio, the branching number, and the branching level are also investigated. The findings in the present work can be used for the optimization of FTCMC with high transport efficiency for combined electroosmotic and pressure-driven flow.

Analytical Solution for Transient Electroosmotic and Pressure-Driven Flows in Microtubes

“…It can also be potentially helpful especially in developi devices to mimic human vascular networks, and blood-air barriers in the human tory system to investigate lung disease progression, diagnosis, and treatment [8,12 While steady-state electroosmotic and/or pressure-driven flow has been tho investigated analytically [18][19][20][21][22][23], only a few researchers derive analytical solut transient EOF in channels or tubes [24][25][26][27][28]. Specifically, previous studies of time-d ent EOFs focused on different microchannel geometrics, typically using semi-an approaches or numerical methods [17,24,[29][30][31][32][33]. Therefore, what has not been de the analytical solution for transient electroosmotic and pressure-driven flows in a tube.…”

“…While steady-state electroosmotic and/or pressure-driven flow has been thoroughly investigated analytically [18][19][20][21][22][23], only a few researchers derive analytical solutions for transient EOF in channels or tubes [24][25][26][27][28]. Specifically, previous studies of time-dependent EOFs focused on different microchannel geometrics, typically using semi-analytical approaches or numerical methods [17,24,[29][30][31][32][33]. Therefore, what has not been derived is the analytical solution for transient electroosmotic and pressure-driven flows in a microtube.…”