Interplay of interface and rheological properties in the interfacial flow of two uniformly rotating immiscible Jeffrey and Newtonian fluids

• Published in: European physical journal plus Vol. 138; no. 10; p. 928
• Main Authors: Bashir, Sammar, Sajid, Muhammad, Sadiq, Muhammad Noveel
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 19.10.2023; Springer Nature B.V
• Subjects: Angular velocity; Applied and Technical Physics; Atomic; Complex Systems; Condensed Matter Physics; Continuous casting; Deborah number; Dynamic stability; Fluid flow; Heat transfer; Interface stability; Interfaces; Lubricants & lubrication; Mathematical and Computational Physics; Miscibility; Molecular; Newtonian fluids; Non-Newtonian fluids; Optical and Plasma Physics; Ordinary differential equations; Physics; Physics and Astronomy; Regular Article; Relaxation time; Reynolds number; Rheological properties; Rheology; Rotation; Similarity solutions; Suction; Theoretical; Velocity; Viscoelasticity
• ISSN: 2190-5444; 2190-5444
• DOI: 10.1140/epjp/s13360-023-04555-4

This research addresses the interfacial flow problem of two uniformly rotating immiscible Jeffrey and Newtonian fluids. The immiscible layers under consideration are two diverse fluid models having distinct densities ( ρ 1 & ρ 2 ), pressures ( p 1 & p 2 ), velocities ( V 1 & V 2 ), and viscosities ( μ 1 & μ 2 ). Counter-rotating flows occur when σ < 0 , indicating an angular velocities ratio ( σ = ω 2 / ω 1 ), while co-rotating flows are observed when σ > 0 . The lower layer has the ability to spin in the reverse direction to the upper layer. The presence of similarity solutions is observed across a plane interface located at z = 0 , subject to the restriction imposed by the parameter σ 2 ρ = 1 , where ρ = ρ 2 / ρ 1 (densities ratio). The resultant set of nonlinear ODEs is solved by applying a well-known finite-difference approach known as the Keller-Box method. The structural characteristics of the flow demonstrate notable resemblances between the upper layer and Ekman pumping, as well as the lower layer and Ekman suction, both below and above the interface. An intriguing phenomenon that occurs in counter-rotating flows is the creation of a steady recirculating region underneath the interface. The absolute size of this recirculation region increases by 55.6% relative to the viscous region. Our goal is to study how factors like the Deborah number and relaxation time affect interfacial stability and shape evolution. Our research on the interfacial dynamics of immiscible Jeffrey and Newtonian fluids aims to improve knowledge of complicated fluid flows and optimize industrial operations using such fluids.