Interfacial dynamics of two immiscible second-grade and couple stress fluids in rotating and counter-rotating scenarios

Abstract

Abstract This article aims to examine the dynamics of interfacial flow that occurs when a layer of second-grade fluid rotates over another layer of uniformly rotating immiscible couple stress fluid. Fluid models with different densities, pressures, velocities, and viscosities exhibit intriguing flow properties. Under the restriction of parameter σ 2 ρ = 1 , where σ = ω 2 / ω 1 (angular velocities ratio) and ρ = ρ 2 / ρ 1 (densities ratio), the occurrence of similarity solutions under coupling and viscoelastic effects across the interface for both cases of co-and-counter rotation is investigated. In contrast to the rotation of upper fluid, the couple stress fluid layer can counter-rotate. An advanced numerical method known as the Keller box is employed to thoroughly analyze the multiple aspects of the flow. The dominance of the couple stress fluid has been observed in shaping the dynamics of interfacial flow, significantly impacting phenomena such as the generation of inward/outward jets, Ekman pumping/suction, and the development of recirculation regions. Lower-layer far-field flow demonstrates transitions, oscillating between inflow and outflow, depending on parameters μ and σ . These findings illustrate an interesting interplay between rheological parameters, providing perspectives into the complicated behaviors of immiscible rotating fluids under different characteristics and useful implications for a variety of practical applications.