Towards an approximate solution of highly viscous electro-osmotic flows in inclined Channel: Applications in petroleum and gas engineering

Abstract

Electro-osmotic flows (EoF) through an inclined channel are investigated in this article. Differential type non-Newtonian fluid model has been used to form highly viscous bi-phase fluid flows. Two different kinds of metallic particles are considered for disperse phase. The application of external electric fields and gravitational force are the main sources of multiphase flows under the magnetic environment. Nonlinear differential equations are formulated taking the stress tensor of fourth-grade fluid, Poisson equation, and Debye length approximation into account, respectively. An approximate solution is obtained for the nonlinear flow problems. Comparative analyses have also been performed with the previous investigations via tables and graphs and, were found to be in great agreement. A comprehensive parametric study is carried out, as well, which reveals that there is a definite difference between the momentum of the fluid phase and the particles phase. The contribution of the Helmholtz–Smoluchowski parameter in each phase is quite supportive. However, the effects of the transverse magnetic field and electro-osmotic parameter are in full coherence. Moreover, traditional multiphase flows can be derived for the limiting case. Finally, this theoretical study explicitly describes the applications in petroleum and gas engineering.