Electroosmotic effect on two immiscible (conducting–non-conducting) fluids flowing in the porous channel under magnetic field

Abstract

In this article, we investigate the motion of two-phase immiscible fluids in the channel with the porous medium in the presence of a magnetic field. Depending on the different levels of permeability, the channel is classified into two regions. The lower region (region-I) consists of non-conducting modified Casson fluid and the upper region (region-II) consist of conducting Newtonian fluid. The external electric field is applied in the region-II and the electroosmotic effect is produced at the wall and the interface region. Due to the interfacial effect, the non-conducting fluid was driven by conducting fluid. To compute the flow dynamic and electric potential nature, the momentum equation and Poisson–Boltzmann equation have been solved analytically in the state of periodic vibrations. The impact of physiological parameters such as Debye–Hückel parameter, electric field, magnetic field, Darcy numbers, viscosity ratio, Casson parameter and Womersley number has been investigated and the various behaviours were characterised. Based on numerical computations performed on the aforementioned parameters, we found that the Casson parameter, Darcy numbers and electric double layer (EDL) effects are predominant features. In the velocity profiles, we identified the flow of the fluid was enhanced by the augmented values of Darcy numbers, electric field (wall zeta potential), Debye–Hückel parameter and Casson parameter. The retardation flow occurred for the higher values of the magnetic field, viscosity ratio and electric field (interface zeta potential). Based on the conditional cases, the Womersley number possesses inconsistent behaviour. The depletion nature was found in the percentage flow rate of the Casson parameter. By increasing the value of the electric field and Casson parameter, the magnitude of wall shear stress to Darcy number increases and decreases for higher values of the magnetic field, viscosity ratio and pulsatile Reynolds number. It is first noticed that for any value of M1 and M2, Darcy number (Da2) plays a dual role in the upper wall shear stress. The present study leads to the pumping effect of gas pipelines or designing the microfluidic devices which are manipulated in biosensors/biochips.