Electroviscous effects in pressure-driven flow of electrolyte liquid through an asymmetrically charged non-uniform microfluidic device

Background: Micro-scale systems depict a different flow behavior from the macro-scale systems due to more vital surface forces such as surface tension, electrical charges, magnetic field, etc., which significantly affect the micro-scale flow. Further, among others, electrokinetic phenomena play a significant role at the micro-scale for controlling practical microfluidic applications. Therefore, it is essential to understand the fluid dynamics in micron-sized channels to develop efficient and reliable microfluidic devices. Methods: The electroviscous effects in pressure-driven flow of electrolyte liquid through an asymmetrically charged contraction-expansion (4:1:4) slit microfluidic device have been investigated numerically. The mathematical model (i.e., Poisson's, Navier-Stokes, and Nernst-Planck equations) is solved using the finite element method to obtain the electrical potential, velocity, pressure, ion concentration fields, excess charge, an induced electric field strength for the following ranges of parameters: Reynolds number (Re = 0.01), Schmidt number (S-c = 1000), inverse Debye length (2 < K < 20), top wall surface charge density (4 < S-t < 16), surface charge density ratio (0 < S-r < 2) and contraction ratio (dc = 0.25). Significant Findings: Results show that the charge asymmetry (Sr) at the different walls of the microfluidic device plays a significant role on the induced electric field development and microfluidic hydrodynamics. The total potential (|AU|) and pressure drop (|AP|) maximally increase by 197.45% and 25.46%, respectively with asymmetry of the charge. The electroviscous correction factor (ratio of apparent to physical viscosity) maximally changes by 20.85% (at K = 2, St = 16 for 0 < S-r < 2), 34.16% (at S-t = 16, S-r = 2 for 2 < K < 20), and 39.13% (at K = 2, S-r = 2 for 0 < St < 16). Thus, charge asymmetry (0 < S-r < 2) remarkably influences the fluid flow in the microfluidic devices, which is used for controlling the microfluidic processes, such as, mixing efficiency, heat, and mass transfer rates. Further, a simpler analytical model is developed to predict the pressure drop in electroviscous flow considering asymmetrically charged surface, based on the Poiseuille flow in the individual uniform sections and pressure losses due to orifice, estimates the pressure drop 1-2% within the numerical results. The robustness of this model enables the use of present numerical results for design aspects in the microfluidic applications.