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

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