A review of cylindrical interfacial instability in viscous and Rivlin–Ericksen viscoelastic fluids under multiphysics effects

Interfacial instability is important in many engineering and industrial applications involving viscous and viscoelastic fluid systems. This review systematically examines Kelvin–Helmholtz, Rayleigh–Taylor, capillary, and cylindrical instabilities, with particular emphasis on Rivlin–Ericksen viscoelastic fluids, based on a systematic search of seven databases covering publications from 1992 to 2026, from which 285 of 1,256 identified studies met the inclusion criteria. The influence of heat transfer, mass transfer, porous media, electric fields, and rotating cylindrical configurations on interfacial stability is critically discussed, and the governing equations, constitutive models, dispersion relations, and stability criteria reported in the literature are systematically summarized and compared. The reviewed studies show that viscosity, viscoelasticity, thermal transport, mass diffusion, and external body forces significantly influence disturbance growth and interfacial stability. A key finding of this review is that the vast majority of the reviewed literature including nearly all Rivlin–Ericksen fluid studies relies exclusively on analytical approaches, such as linear stability theory, normal-mode analysis, perturbation methods, and viscous potential flow formulations, which are restricted to small-amplitude disturbances and idealized geometries. Advanced computational techniques capable of resolving nonlinear, large-amplitude, and geometrically complex interfacial behavior including the Finite Volume Method (FVM), Finite Difference Method (FDM), Finite Element Method (FEM), and Boundary Element Method (BEM) remain almost entirely unexplored for this class of problems. This review identifies that gap as the principal barrier to progress in the field and outlines a path toward closing it, proposing future work centered on nonlinear analyses, coupled multiphysics models, and efficient FVM/FDM/BEM-based numerical simulations of complex viscoelastic interfacial flows.