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.
Interfacial instability is a fundamental fluid-dynamic phenomenon that arises when disturbances develop and grow at the interface separating two fluid layers. Such instabilities are encountered in numerous natural and engineering processes, including petroleum recovery, polymer processing, coating technologies, microfluidic systems, thermal management devices, and multiphase transport applications. The evolution of interfacial disturbances strongly influences momentum transfer, heat transfer, mass transport, and mixing efficiency, making stability analysis an important area of research in fluid mechanics and transport phenomena.
Among the various instability mechanisms, Kelvin–Helmholtz instability occurs due to velocity differences between adjacent fluid layers, whereas Rayleigh–Taylor instability develops when a denser fluid overlies a lighter fluid under the influence of gravity. Capillary instability is primarily governed by surface tension effects, while cylindrical instability frequently arises in confined and rotating geometries. These instability mechanisms have attracted considerable attention because of their relevance to both fundamental fluid dynamics and practical engineering applications. Cylindrical interfacial instability, in particular, is central to a wide range of industrial processes, including polymer extrusion, fibre spinning, coating technologies, inkjet printing, enhanced oil recovery, and biomedical transport systems, where controlled disturbance growth directly affects product quality and process efficiency.
In many practical situations, interfacial stability is significantly influenced by heat transfer, mass transfer, electric fields, magnetic fields, and geometric confinement. Thermal gradients and concentration differences can alter fluid density, viscosity, and surface tension distributions, thereby modifying the onset and growth of instability. Consequently, the interaction between transport phenomena and fluid rheology gives rise to complex multiphysics behavior that continues to motivate theoretical, numerical, and experimental investigations. While instability phenomena in Newtonian fluids have been extensively studied, increasing attention has been directed toward viscoelastic and non-Newtonian fluids because of their widespread industrial importance. Rivlin and Ericksen introduced constitutive equations for a class of viscoelastic fluids now known as Rivlin–Ericksen fluids. These fluids exhibit both viscous and elastic characteristics and are capable of describing material behavior that cannot be adequately represented by classical Newtonian models. In Rivlin–Ericksen fluids, the conventional viscous contribution is modified through the incorporation of viscoelastic effects, resulting in a more realistic description of complex fluid behavior.
The stability of cylindrical fluid interfaces is a classical problem in fluid mechanics with applications in liquid jets, coating processes, fiber manufacturing, atomization, and multiphase flows. Interfacial behavior is controlled by the interaction of surface tension, inertia, viscosity, gravity, and density differences. Early experimental observations by Plateau showed that a cylindrical liquid column becomes unstable when disturbances exceed a critical wavelength. Rayleigh later provided the theoretical explanation by demonstrating that surface tension governs the amplification of axisymmetric disturbances, establishing the basis of classical capillary instability theory. Rayleigh–Taylor instability occurs when a heavier fluid is supported above a lighter fluid, allowing gravitational forces to amplify interfacial disturbances. Analytical investigations based on viscous potential flow theory demonstrated that heat transfer, mass transfer, and viscosity substantially modify disturbance growth and may stabilize configurations that are unstable under purely hydrodynamic conditions. Further investigations considering rotational disturbances revealed that interface curvature, viscosity ratio, and perturbation wave number strongly influence the transition between two-dimensional and three-dimensional instability modes, particularly for cylindrical geometries.
Kelvin–Helmholtz instability develops due to velocity differences across the interface between two fluid layers and is strongly influenced by viscosity, density ratio, and surface tension. Studies based on viscous potential flow theory have shown that these parameters govern disturbance propagation, critical velocity, and the growth of interfacial disturbances in cylindrical fluid systems. Further investigations have demonstrated that variations in Reynolds number, viscosity ratio, surface tension, and fluid properties significantly modify the stability characteristics and wave evolution of cylindrical interfaces. Planar interfacial instability provides a basic framework for studying Kelvin–Helmholtz and Rayleigh–Taylor instabilities. However, cylindrical geometry introduces curvature and additional disturbance modes that are absent in planar systems. For a planar interface, the disturbance is usually described by a single wavenumber, and the base-state curvature is zero. In a cylindrical configuration, the interface has a finite radius, and disturbances depend on both the axial wavenumber and azimuthal mode number. Consequently, both axisymmetric and non-axisymmetric modes can occur. For the axisymmetric case, the classical Rayleigh–Plateau mechanism produces instability under a curvature-dependent condition that has no direct planar counterpart. The planar result can be recovered from the cylindrical formulation in the large-radius limit. For finite radius, additional modes, including sinuous, flute, and helical disturbances, may occur. Recent studies of viscoelastic cylindrical jets further show that the dominant instability mechanism depends on the azimuthal mode, with Rayleigh–Plateau effects being important for axisymmetric disturbances and Kelvin–Helmholtz effects becoming more significant for non-axisymmetric modes.
Viscous potential flow theory has evolved into an effective analytical approach for studying interfacial instability problems by accounting for viscous normal stresses while maintaining the simplicity of an irrotational flow description. Unlike classical inviscid formulations, viscous potential flow offers improved predictions of disturbance growth and wave propagation, making it particularly suitable for cylindrical interfacial configurations encountered in engineering and physical systems. The applicability of this approach has gradually expanded toward porous media environments, where permeability, porosity, and density variations introduce additional mechanisms that influence interface stability. Earlier investigations revealed that porous resistance may either suppress or promote instability depending on the fluid properties and transport processes involved. Further studies considering nanofluids and porous cylindrical domains demonstrated that permeability, surface tension, and nanoparticle concentration collectively govern the evolution of interfacial disturbances. In recent years, increasing attention has been directed toward incorporating viscoelastic constitutive models within the viscous potential flow framework. Fluids described by Rivlin–Ericksen and Walters’ B models have been extensively employed to capture elastic effects arising in polymeric, biological, and industrial applications. Existing analyses indicate that viscoelasticity generally acts as a stabilizing mechanism, whereas heat transfer, mass transfer, and electromagnetic forces may alter the instability characteristics depending on the relative importance of thermal, solutal, and electrical transport phenomena.
Heat and mass transfer mechanisms significantly influence the evolution of interfacial disturbances by modifying density distributions, transport properties, and energy exchange processes. In many engineering applications, thermal diffusion and species transport coexist with viscous, electromagnetic, and porous-medium effects, resulting in complex instability behaviour. Magnetohydrodynamic and electrohydrodynamic effects have received considerable attention due to their ability to control interfacial disturbances through external fields. Analytical investigations based on viscous potential flow theory have demonstrated that magnetic fields, thermal gradients, and mass transfer generally suppress disturbance growth and enhance interface stability in cylindrical configurations. Furthermore, coupled analyses incorporating porous media and electromagnetic forces have shown that permeability, magnetic intensity, and transport coefficients strongly affect neutral stability boundaries and instability growth rates. Recent studies have focused on non-Newtonian and viscoelastic fluids, where thermal and solutal transport processes interact with elastic stresses. Investigations involving power-law and viscoelastic liquids indicate that heat transfer often acts as a stabilizing mechanism, whereas concentration gradients may either stabilize or destabilize the interface depending on fluid rheology and flow conditions. Several researchers have reported that increasing heat transfer rates generally delay the onset of instability and reduce disturbance amplification. However, in certain viscoelastic and power-law fluid systems, heat and mass transfer may promote destabilization owing to enhanced transport interactions and elastic effects. These findings highlight the dual role of thermal and solutal transport in governing interfacial dynamics and emphasize the necessity of considering coupled transport mechanisms in instability analyses.
Electric fields influence the interface primarily through Maxwell stresses. Depending on the field orientation, electrical properties, and permittivity contrast of the fluids, these stresses can either stabilize or destabilize interfacial disturbances. The reviewed electrohydrodynamic studies indicate that an increase in the permittivity ratio can reduce disturbance growth. However, reported results also show that a tangential electric field can promote instability under certain conditions in planar liquid layers. Therefore, the effect of an electric field is not universally stabilizing or destabilizing, but depends strongly on the field configuration and properties of the interacting fluids. For cylindrical interfaces, these electromagnetic effects become more complex because magnetic and electric stresses interact with interface curvature, radial confinement, and azimuthal disturbance modes. The combined influence of field orientation, fluid properties, and cylindrical geometry may consequently alter the instability threshold and growth rate. The interaction between heat and mass transfer and rotational motion has also emerged as an active research area. Studies performed for annular geometries and swirling cylindrical interfaces indicate that rotational effects suppress perturbation growth, while simultaneous heat and mass transfer further enhance system stability. Such investigations provide valuable insight into the complex coupling among viscoelasticity, swirling motion, transport phenomena, and electromagnetic effects encountered in industrial mixing devices, thermal systems, and multiphase engineering applications.
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, Finite Difference Method, Finite Element Method, and Boundary Element Method, remain almost entirely unexplored for this class of problems. The 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. The reviewed studies show that viscosity, viscoelasticity, thermal transport, mass diffusion, and external body forces significantly influence disturbance growth and interfacial stability. Across this body of work, cylindrical interface stability emerges as the product of coupled effects: fluid rheology, geometry, surface tension, transport processes, and external fields act together rather than in isolation. No single parameter determines the outcome on its own: predicted stability depends jointly on the constitutive model, disturbance wavelength, cylindrical geometry, transport coefficients, and boundary conditions, so a result obtained for one configuration cannot be assumed to generalize to another.
Subject of Research: A systematic review of cylindrical interfacial instability in viscous and Rivlin–Ericksen viscoelastic fluids under heat, mass transfer, porous media, electromagnetic, and rotational effects.
Article Title: A review of cylindrical interfacial instability in viscous and Rivlin–Ericksen viscoelastic fluids under multiphysics effects
Article References: C, K., & Shukla, P. (2026). A review of cylindrical interfacial instability in viscous and Rivlin–Ericksen viscoelastic fluids under multiphysics effects. Frontiers in Mechanical Engineering, 12, Article 1952180. https://doi.org/10.3389/fmech.2026.1952180
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DOI: 10.3389/fmech.2026.1952180
Keywords: interfacial instability, Kelvin–Helmholtz instability, Rayleigh–Taylor instability, Rivlin–Ericksen fluid, viscoelastic fluid, viscous potential flow, cylindrical interface, heat transfer, mass transfer, porous media, electromagnetic fields, fluid mechanics
News Source: Denise Maddox. (November 7, 2026). Review finds viscoelastic interface instability research stuck in linear theory. Scienmag.
