Reservoir end wall effects on bivariate ion and fluid transport in micro/nano-nozzles for effective electroosmotic mixing

Abstract

The aim of this study was to develop an efficient convection diffusion-based mathematical model for the species transport and mixing in different shaped (i.e., nozzle, diffuser, diffuser–nozzle, nozzle–diffuser) micro/nano-channels connected to large reservoirs. Both analytical and numerical studies are performed to illustrate the impact of inertial and contact angles for the generation of complex flow patterns due to different aspect ratio specified transformations. The hydrodynamics of the ion and fluid transport are analyzed through the Poisson–Nernst–Plank-based Navier–Stokes model subjected to specified system of forces endured by the reservoir fluids. The numerical results for pressure velocity correlations are obtained when the transport mechanism of the domain is changed from nozzle to diffuser. Mixing efficiency is evaluated for different geometric configurations and compared with a rectangular slit channel when the parallel reservoirs are connected. The role of Debye–Hückel parameter, conical angles or slope, and reservoir height/width on the transport of ions and enhancement of mixing are discussed. The mixing efficiency is found to attain a higher value after considering the reservoir connected to a nozzle without involving any hurdles or heterogeneous zeta potential along the channel wall. Closed-form analytical solutions of the electric potential are obtained through the linearized Poisson–Boltzmann model and further incorporated for the pressure evaluation. The axial and transverse velocities are evaluated from the modified Navier–Stokes equation including electric body force term and are validated with the experimental results. Effective nonlinear coupling responses of ion transport are found to be more pronounced in nozzle compared with diffuser resulting a higher mixing. Also, the solutions of velocity resulting in a low torque satisfy the equilibrium conditions and are optimized in terms of adversion of frictional factor and viscous dissipation resulting in an effective mixing. The findings manifest the species patterns with high accuracy and versatility, which could possibly help to handle the technical challenges associated with the design of pumpless actuated microfluidic devices.