This paper presents a theoretical and experimental investigation into the hydrodynamic focusing effect in rectangular microchannels. Two theoretical models for two-dimensional hydrodynamic focusing are proposed. The first model predicts the width of the focused stream in symmetric hydrodynamic focusing in microchannels of various aspect ratios. The second model predicts the location and the width of the focused stream in asymmetric hydrodynamic focusing in microchannels with a low or high aspect ratio. In both models, the theoretical results are shown to be in good agreement with the experimental data. Hence, the models provide a useful means of performing a theoretical analysis of flow control in microfluidic devices using hydrodynamic focusing effects. The ability of the proposed models to control the focused stream within a micro flow cytometer is verified in a series of experimental trials performed using polystyrene microparticles with a diameter of 20 µm. The experimental data show that the width of the focused stream can be reduced to the same order of magnitude as that of the particle size. Furthermore, it is shown that the microparticles can be successfully hydrodynamically focused and switched to the desired outlet port of the cytometer. Hence, the models presented in this study provide sufficient control to support cell/particle counting and sorting applications. (Some figures in this article are in colour only in the electronic version)

In this work, we designed and fabricated a three-dimensional hydrodynamic focusing microfluidic device. The device comprises a two-layer PDMS microchannel structure. There are four inlet ports and one outlet port. The fluids are all injected by syringe pumps. A sample flow stream was first vertically constrained into a narrow stream, and then horizontally focused on one small core region from a cross-section perspective, which is useful for cell/particle counting. We showed the numerical and experimental images of the focused stream shape from a cross-section perspective; experimental images were captured using a confocal fluorescence microscope. We also investigated the effect of channel aspect ratio on the vertical focusing effect using CFD simulations. The results showed that the sample flow can be focused successfully in the lower aspect ratio of the main channel (slightly greater than 0.5) in our design. Furthermore, the effect of the Reynolds number on the vertical focusing effect was also investigated. The numerical results showed that the rectangular-like shape of the focused stream from the cross-section perspective was deformed as the Reynolds number was high due to stronger secondary flows produced in the vertical focusing unit. This phenomenon was also demonstrated experimentally. The device only works well at low Reynolds numbers (approximately less than 5). The device can be integrated into an on-chip flow cytometer. (Some figures in this article are in colour only in the electronic version)

Numerical simulations based on the full Poisson–Nernst–Planck (PNP) equations are performed to investigate the reverse electrodialysis (RED) in negatively charged conical nanopores. The simulations consider three different salts (i.e., KCl, NaCl and LiCl) and examine the effects of the concentration gradient, surface charge density and diffusion coefficient on the current–voltage characteristics and energy conversion efficiency of the RED system. When diffusion takes place from the base side to the tip side, the transference number of counter-ion (t₊) can be enhanced due to an addition in the EDL overlap near the tip side. It results in the higher energy conversion efficiency of RED than the salt ion diffusion from the tip side to the base side, i.e., the RED performance of the conical nanopore is dependent on the direction of salt concentration gradient. In addition, the results show that the conversion efficiency increases as the diffusion coefficient of the positive ions (D₊) approaches that of the negative ions (D₋). For D₊ < D₋, the diffusion current and diffusion potential in negatively charged conical nanopores show negative on the current–voltage characteristics and the conversion efficiency increases as the concentration gradient is increased at small surface charge density. Finally, the calculated maximum power conversion efficiency reaches 45%.

Taking hydrodynamic slippage into account, we derived an exact expression for the figure of merit to evaluate the electrokinetic energy conversion efficiency and power of an ion-selective nanopore. In the absence of slip, and when the ratio of the radius and the Gouy-Chapmann length ( a / λ GC ) is approximately 10, the highest efficiency for an electrolyte consisting of simple monovalent ions was predicted to be approximately 9.7%. While this efficiency is low, it can be greatly improved to a potentially practical efficiency (>40%) when the slip ratio ( b / a ) is greater than 0.7.