Numerical study of time dependent flow of immiscible Saffman dusty (fluid-particle suspension) and Eringen micropolar fluids in a duct with a modified cubic B-spline Differential Quadrature method

Immiscible flows arise in many diverse applications mechanical, chemical, and environmental engineering. Such involve interfacial conditions often feature mass (species) diffusion. Motivated by non-Newtonian duct processing, the present article a comprehensive mathematical model computational simulation with modified cubic B-spline-Differential Quadrature method (MCB-DQM) is described for unsteady flow of two immiscible fluids - dusty (fluid-particle suspension) Eringen micropolar through horizontal channels. Mass transfer invoked due to particle concentration effects fluid. The stable liquid-liquid interface considered between fluids. Fluids are under three different pressure gradients- constant, decaying, periodic gradient characteristics scrutinized each case. coupled partial differential equations solved MCB-DQM physically realistic boundary conditions. Linear velocity, micro-rotation (Eringen angular velocity) visualized graphically key hydrodynamic solutal parameters i. e. Reynolds number, parameter, material volume fraction gradient, time, viscosity ratio, density ratio. simulations extend current understanding two-fluid hydrodynamics relevant chemical engineering separation processing systems.