Abstract:The stability of the liquid/vapor interface between two concentric revolving cylinders is examined. The transfer of heat/mass is allowed at the interface. Both the cylinders rotate with different angular velocities. The fluids inside the annular region are taken as incompressible and viscous. The theory of viscous potential flow analysis is used to add the viscous effects. The normal mode technique is used to calculate the growth of perturbations. If we rotate the inner cylinder, it is seen that asymmetric dis… Show more
“…This shows that MHT has a stabilizing influence. This outcome has been proven by several previous researchers; for instance, see Agarwal and Awasthi 49 . Figure 13 The transition curve with the variation .…”
The current article examines a nonlinear axisymmetric streaming flow obeying the Rivlin–Ericksen viscoelastic model and overloaded by suspended dust particles. The fluids are separated by an infinite vertical cylindrical interface. A uniform axial magnetic field as well as mass and heat transmission (MHT) act everywhere the cylindrical flows. For the sake of simplicity, the viscous potential theory (VPT) is adopted to ease the analysis. The study finds its significance in wastewater treatment, petroleum transport as well as various practical engineering applications. The methodology of the nonlinear approach is conditional primarily on utilizing the linear fundamental equations of motion along with the appropriate nonlinear applicable boundary conditions (BCs). A dimensionless procedure reveals a group of physical dimensionless numerals. The linear stability requirements are estimated by means of the Routh–Hurwitz statement. The application of Taylor’s theory with the multiple time scales provides a Ginzburg–Landau equation, which regulates the nonlinear stability criterion. Therefore, the theoretical nonlinear stability standards are determined. A collection of graphs is drawn throughout the linear as well as the nonlinear approaches. In light of the Homotopy perturbation method (HPM), an estimated uniform solution to the surface displacement is anticipated. This solution is verified by means of a numerical approach. The influence of different natural factors on the stability configuration is addressed. When the density number of the suspended inner dust particles is less than the density number of the suspended outer dust particles, and vice versa, it is found that the structure is reflected to be stable. Furthermore, as the pure outer viscosity of the liquid increases, the stable range contracts, this means that this parameter has a destabilizing effect. Additionally, the magnetic field and the transfer of heat don’t affect the nature of viscoelasticity.
“…This shows that MHT has a stabilizing influence. This outcome has been proven by several previous researchers; for instance, see Agarwal and Awasthi 49 . Figure 13 The transition curve with the variation .…”
The current article examines a nonlinear axisymmetric streaming flow obeying the Rivlin–Ericksen viscoelastic model and overloaded by suspended dust particles. The fluids are separated by an infinite vertical cylindrical interface. A uniform axial magnetic field as well as mass and heat transmission (MHT) act everywhere the cylindrical flows. For the sake of simplicity, the viscous potential theory (VPT) is adopted to ease the analysis. The study finds its significance in wastewater treatment, petroleum transport as well as various practical engineering applications. The methodology of the nonlinear approach is conditional primarily on utilizing the linear fundamental equations of motion along with the appropriate nonlinear applicable boundary conditions (BCs). A dimensionless procedure reveals a group of physical dimensionless numerals. The linear stability requirements are estimated by means of the Routh–Hurwitz statement. The application of Taylor’s theory with the multiple time scales provides a Ginzburg–Landau equation, which regulates the nonlinear stability criterion. Therefore, the theoretical nonlinear stability standards are determined. A collection of graphs is drawn throughout the linear as well as the nonlinear approaches. In light of the Homotopy perturbation method (HPM), an estimated uniform solution to the surface displacement is anticipated. This solution is verified by means of a numerical approach. The influence of different natural factors on the stability configuration is addressed. When the density number of the suspended inner dust particles is less than the density number of the suspended outer dust particles, and vice versa, it is found that the structure is reflected to be stable. Furthermore, as the pure outer viscosity of the liquid increases, the stable range contracts, this means that this parameter has a destabilizing effect. Additionally, the magnetic field and the transfer of heat don’t affect the nature of viscoelasticity.
“…[7] investigated the swirl impact on mass/heat transfer at the liquid-vapor interface. When both cylinders were rotating, the liquid-vapor interface in an annulus and studied its instability was considered [8]. In Refs.…”
The mutual influences of the electric field, rotation, and heat transmission find applications in controlled drug delivery systems, precise microfluidic manipulation, and advanced materials’ processing techniques due to their ability to tailor fluid behavior and surface morphology with enhanced precision and efficiency. Capillary instability has widespread relevance in various natural and industrial processes, ranging from the breakup of liquid jets and the formation of droplets in inkjet printing to the dynamics of thin liquid films and the behavior of liquid bridges in microgravity environments. This study examines the swirling impact on the instability arising from the capillary effects at the boundary of Rivlin–Ericksen and viscous liquids, influenced by an axial electric field, heat, and mass transmission. Capillary instability arises when the cohesive forces at the interface between two fluids are disrupted by perturbations, leading to the formation of characteristic patterns such as waves or droplets. The influence of gravity and fluid flow velocity is disregarded in the context of capillary instability analyses. The annular region is formed by two cylinders: one containing a viscous fluid and the other a Rivlin–Ericksen viscoelastic fluid. The Rivlin–Ericksen model is pivotal for comprehending the characteristics of viscoelastic fluids, widely utilized in industrial and biological contexts. It precisely characterizes their rheological complexities, encompassing elasticity and viscosity, critical for forecasting flow dynamics in polymer processing, food production, and drug delivery. Moreover, its applications extend to biomedical engineering, offering insights crucial for medical device design and understanding biological phenomena like blood flow. The inside cylinder remains stationary, and the outside cylinder rotates at a steady pace. A numerically analyzed quadratic growth rate is obtained from perturbed equations using potential flow theory and the Rivlin–Ericksen fluid model. The findings demonstrate enhanced stability due to the heat and mass transfer and increased stability from swirling. Notably, the heat transfer stabilizes the interface, while the density ratio and centrifuge number also impact stability. An axial electric field exhibits a dual effect, with certain permittivity and conductivity ratios causing perturbation growth decay or expansion.
“…They observed that the system's instability is augmented when small Weber numbers are considered and gets suppressed at larger Weber numbers due to confinement. Lastly, Awasthi et al [13][14][15][16][17] scrutinized the stability of the various interfaces subject to heat and mass transfer between two concentric cylinders. They discovered that when the inner cylinder rotates, asymmetric disturbances destabilize the interface, whereas rotation of the outer cylinder induces stability.…”
The multifaceted applications of swirling interfaces featuring heat and mass transfer extend across diverse industries, encompassing energy, manufacturing, healthcare, and environmental protection. The present study is concerned with examining the swirling impact on the capillary instability occurring at the interface between a Walter’s B viscoelastic fluid and a viscous fluid, under the influence of heat and mass transfer. The setup consists of two rigid cylinders that form an annular region filled with viscous fluid on the inner side and Walter’s B viscoelastic fluid on the outer side. The outer cylinder rotates at a constant angular velocity, while the inner cylinder remains stationary. The study employs the Walter’s B viscoelastic model, which conforms to the potential flow theory for viscoelastic fluids. The proposed flow theory disregards tangential stresses and balances the difference in normal viscous stresses with the surface force at the free boundary. The perturbed equations yield a quadratic equation in growth rate, which is numerically analyzed. The results show that heat and mass transfer enhance the interface’s stability and swirling makes it more stable. Moreover, it is noteworthy that the Weber number exerts a stabilizing influence on the interface, while the density ratio also plays a role in promoting its stability. The centrifuge number exhibits a counteractive effect by impeding interface growth, thus contributing to its stabilization.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
