Numerical Study of Interface Tracking for the Unsteady Flow of Two Immiscible Micropolar and Newtonian Fluids Through a Horizontal Channel with an Unstable Interface

The dynamics of the interaction between immiscible fluids is relevant to numerous complex flows in nature and industry, including lubrication coating processes, oil extraction, physicochemical separation techniques, etc. One most essential components flow fluid interface, which must be consistently monitored. In this article, unsteady two i.e., an Eringen micropolar Newtonian liquid considered a horizontal channel. Despite no-slip hyper-stick shear stress condition at channel edge, it accepted that interface dynamic, migrating from one position next possibly get absolute change; as result, CS (continuum surface) model integrated with single moment equation based on VOF (volume fluid) approach trace interface. are under three applied pressure gradients (constant, decaying, periodic) analyzed seamless over entire modified cubic b-spline differential quadrature method (MCB-DQM) used solve modeled coupled partial equations for evolution. advection tracking time, wave number, amplitude illustrated through graphs. It observed presence parameters affects time. novelty current study previous studies (which smooth unstable movement fluid, steady stream fluids, monitoring different modes) extended generalized consider time-dependent namely moving . For decaying gradient case, requires more time achieve steady-state , peak waves resembles those constant case. becomes extensive when applied. stable quickly parameter decreased case weaker encourage faster stabilization With periodic takes stabilize, crest significantly higher compared cases. simulations demonstrate excellent ability MCB-DQM analyze interfacial flows.