COMPUTATIONAL ANALYSIS OF GRAVITY AND PRESSURE-DRIVEN OBLIQUE FLOW OF MULTIPHASE FLUID THROUGH THE STEEP DIVERGENT MICROCHANNEL

Abstract

In this computational study, we investigate the gravity and pressure-driven electroosmotic multiphase flow of third-grade fluid through steep microchannel by using the semi-analytical technique. A two-dimensional mathematical model is proposed here for the supercritical bi-phase flow with the suspension of the nanometallic particles. A special type of non-Newtonian fluid (third-grade) is selected as a base fluid. The governing equations for the current flow problem are obtained through Poisson–Boltzmann equations, continuity equations, and Cauchy’s momentum equations. The Poisson–Boltzmann equation is simplified by using the Debye–Hückel approximation. The symbolic software MATHEMATICATM is used to obtain the closed-form expression of electric potential, fluid and particle velocities, pressure gradient, and volumetric flow rate, respectively. The computational results are discussed qualitatively under the impact of the physical parameters embedded in the study. The graphical plots of fluid and particle-phase velocities are generated against the different parameters used in this study by adopting the same software as discussed earlier. The electrokinetic forces are responsible for electroosmotic flow which is modeled through the Laplace and Poisson–Boltzmann equations. The externally applied potential and electrical double-layer potential is governed by the Laplace and Poisson–Boltzmann equations, respectively.