Nonlinear EHD Instability of Two-Superposed Walters’ B Fluids Moving through Porous Media

The current work examines the application of the viscous potential flow to the Kelvin-Helmholtz instability (KHI) of a planar interface between two visco-elastic Walters’ B fluids. The fluids are fully saturated in porous media in the presence of heat and mass transfer across the interface. Additionally, the structure is pervaded via a uniform, normal electrical field in the absence of superficial charges. The nonlinear scheme basically depends on analyzing the linear principal equation of motion, and then applying the appropriate nonlinear boundary-conditions. The current organization creates a nonlinear characteristic equation describing the amplitude performance of the surface waves. The classical Routh–Hrutwitz theory is employed to judge the linear stability criteria. Once more, the implication of the multiple time scale with the aid of Taylor theory yields a Ginzburg–Landau equation, which controls the nonlinear stability criteria. Furthermore, the Poincaré–Lindstedt technique is implemented to achieve an analytic estimated bounded solution for the surface deflection. Many special cases draw upon appropriate data selections. Finally, all theoretical findings are numerically confirmed in such a way that ensures the effectiveness of various physical parameters.

Instability of a Radially Moving Cylindrical Surface: A Viscous Potential Flow Approach

The effect of viscosity on the unstable interface of the cylindrical jet is analyzed through viscous potential flow approach. The jet is moving radially and jet interface is experiencing Rayleigh–Taylor type instability. Previous studies have completely ignored the viscosity effect while considering the instability of a radially moving cylindrical jet. The fluids inside and outside jet are incompressible as well as viscous. The theoretical analysis provides us a second-order ordinary differential equation to establish the instability/stability criterion. The radial velocity and acceleration both have significant impact on the stability of the jet. We found that as viscosity enters to the analysis, perturbations grow rapidly. In addition, the acquired stability criterion is applied to the cylindrical jets in HYLIFE-II which is basically an inertial confinement fusion reactor.

Capillary Instability of Viscoelastic Liquid Film With Heat and Mass Transfer

This paper examines the effect of transfer of heat and mass on the capillary instability between a viscoelastic liquid and a viscous gas. The viscoelastic liquid obeys the Oldroyd B-model. These two fluid layers considered in coaxial cylinders and viscoelastic–viscous potential flow theory are used for investigation. To study the stability of the interface, the normal-mode procedure is employed and a cubic dispersion equation in terms of growth rate has been obtained. We observe that the viscoelastic liquid–viscous gas interface is more unstable than the viscous liquid–viscous gas interface. Additionally, we show that the unstable axisymmetric wave modes are stabilized by allowing heat transfer at the interface.

Microbubble dynamics in a viscous compressible liquid near a rigid boundary

This paper is concerned with microbubble dynamics in a viscous compressible liquid near a rigid boundary. The compressible effects are modelled using the weakly compressible theory of Wang & Blake (2010, Non-spherical bubble dynamics in a compressible liquid. Part 1. Travelling acoustic wave. J. Fluid Mech., 730, 245–272), since the Mach number associated is small. The viscous effects are approximated using the viscous potential flow theory of Joseph & Wang (2004, The dissipation approximation and viscous potential flow. J. Fluid Mech., 505, 365–377), because the flow field is characterized as being an irrotational flow in the bulk volume but with a thin viscous boundary layer at the bubble surface. Consequently, the phenomenon is modelled using the boundary integral method, in which the compressible and viscous effects are incorporated into the model through including corresponding additional terms in the far field condition and the dynamic boundary condition at the bubble surface, respectively. The numerical results are shown in good agreement with the Keller–Miksis equation, experiments and computations based on the Navier–Stokes equations. The bubble oscillation, topological transform, jet development and penetration through the bubble and the energy of the bubble system are simulated and analysed in terms of the compressible and viscous effects.

Rayleigh–Taylor Instability of Swirling Annular Layer With Mass Transfer

The interfacial instability of Rayleigh–Taylor type at the cylindrical boundary involving the liquid phase and vapor phase of a fluid has been considered when the vapor is warmer than the liquid. We use viscous potential flow theory to include the viscosity at the interface. To examine the stability of the arrangement, the normal-mode analysis is performed together with the effect of heat as well as mass transfer and free swirl. The physical system consists of an annular fluid layer restricted in a cylinder with vapor phase in the core. This work investigates the effect of a variety of variables on the instability of the interface. It is found that when the heat transfer constant increases, the range of stability increases. Also, the range of stability increases faster in the presence of swirling.