Critical Value Of Wave Number Research Articles

Study of heat and mass transport on the instability of a swirling viscoelastic liquid film.

In this article, we examine the response of transport of mass and heat at the viscous gas-viscoelastic liquid interface, while the instability of the interface is defined by capillary instability. The fluids are enclosed in an annular region bounded by two rigid cylinders. The Oldroyd B-type viscoelastic fluid is considered and the outer cylinder is swirling with a uniform angular velocity. The governing mathematical equations are work out through the viscoelastic-viscous potential flow theory. The well-known normal mode procedure is utilized and a critical value of wave-number is calculated to determine the stability/instability norm for the interface. Various plots showing the effect of swirling, heat/mass transfer, etc. have been made and illustrated physically. The addition of swirl prevents the development of disturbance waves. We achieve that the transport of mass/heat at the interface reduces the amplitudes of perturbations.

STUDY ON ELECTROHYDRODYNAMIC CAPILLARY INSTABILITY OF VISCOELASTIC FLUIDS WITH RADIAL ELECTRIC FIELD

We study the linear analysis of electrohydrodynamic capillary instability of the interface between a viscous fluid and viscoelastic fluid of Maxwell type, when the phases are enclosed between two horizontal cylindrical surfaces coaxial with the interface, and when fluids are subjected to the radial electric field. Here, we use an irrotational theory known as viscous potential flow (VPF) theory in which viscosity enters through normal stress balance but shearing stresses are assumed to be zero. A quadratic dispersion relation that accounts for the growth of axisymmetric waves is obtained and stability criterion is given in terms of a critical value of wave number as well as electric field. It is observed that the radial electric field has dual effect on the stability of the system.

Evaporative capillary instability for flow in porous media under the influence of axial electric field

We study the linear analysis of electrohydrodynamic capillary instability of the interface between two viscous, incompressible and electrically conducting fluids in a fully saturated porous medium, when the phases are enclosed between two horizontal cylindrical surfaces coaxial with the interface and, when there is mass and heat transfer across the interface. The fluids are subjected to a constant electric field in the axial direction. Here, we use an irrotational theory in which the motion and pressure are irrotational and the viscosity enters through the jump in the viscous normal stress in the normal stress balance at the interface. A quadratic dispersion relation that accounts for the growth of axisymmetric waves is obtained and stability criterion is given in terms of a critical value of wave number as well as electric field. It is observed that heat transfer has stabilizing effect on the stability of the considered system while medium porosity destabilizes the interface. The axial electric field has dual effect on the stability analysis.

Viscous potential flow analysis of magnetohydrodynamic Rayleigh–Taylor instability with heat and mass transfer

The effect of tangential magnetic field on the linear analysis of Rayleigh–Taylor instability of two viscous, incompressible and electrically conducting fluids is studied when there is heat and mass transfer across the interface. We use an irrotational theory known as viscous potential flow theory; in which viscosity enters through normal stress balance but shearing stresses are assumed to be zero. A quadratic dispersion relation that accounts for the growth of disturbance waves is obtained and stability criterion is given in terms of a critical value of wave number as well as applied magnetic field. We observe that heat and mass transfer and magnetic field both stabilize the interface while vapour thickness has destabilizing effect.

Electrohydrodynamic capillary instability with heat and mass transfer

We study the linear analysis of capillary instability of a cylindrical interface between two viscous and dielectric fluids, when the fluids are subjected to a constant axial electric field and, when there is heat and mass transfer across the interface. We use viscous correction for the viscous potential flow theory in which the discontinuities in the irrotational tangential velocity and shear stress are eliminated in the global energy balance by taking viscous contributions to the irrotational pressure. A quadratic dispersion relation that accounts for the growth of axisymmetric waves is obtained and stability criterion is given in terms of a critical value of wave number as well as electric field. It is observed that heat transfer and electric field both have stabilizing effect while vapor fraction has destabilizing effect on the stability of the system.

PRESSURE CORRECTIONS FOR THE VISCOELASTIC POTENTIAL FLOW ANALYSIS OF ELECTROHYDRODYNAMIC CAPILLARY INSTABILITY

Pressure corrections for the viscoelastic potential flow analysis of capillary instability in the presence of axial electric field has been carried out. In viscoelastic potential flow theory, viscosity enters through normal stress balance and the effects of shearing stresses are completely neglected. We include the viscous pressure in the normal stress balance along with irrotational pressure and it is assumed that this viscous pressure will resolve the discontinuity of the tangential stresses at the interface for two fluids. A dispersion relation is derived for the case of axially imposed electric field and stability is discussed in terms of various parameters such as electric field, Deborah number, Ohnesorge number, permittivity ratio and conductivity ratio etc. Stability criterion is given in terms of critical value of wave number as well as critical value of applied electric field. The system is unstable when electric field is less than the critical value of electric field, otherwise it is stable. It has been found that irrotational shearing stresses have stabilizing effect on the stability of the system.

Viscous potential flow analysis of capillary instability with heat and mass transfer through porous media

The capillary instability of the cylindrical interface separating two viscous and incompressible fluids through porous medium is studied using viscous potential flow theory, when there is heat and mass transfer across the interface. The fluids are considered to be viscous and incompressible with different kinematic viscosities. A dispersion relation that accounts for the growth of axisymmetric waves is derived and stability is discussed theoretically as well as numerically. Stability criterion is given in terms of critical value of wave number. Various graphs have been drawn to show the effect of various physical parameters such as heat transfer capillary number, viscosity ratio, permeability and porosity on the stability of the system. It has been observed that porous media and heat transfer both have stabilizing effect while porosity has destabilizing effect on the stability of the system.

STUDY ON ELECTROHYDRODYNAMIC CAPILLARY INSTABILITY OF VISCOELASTIC FLUIDS IN PRESENCE OF AXIAL ELECTRIC FIELD

Linear viscoelastic potential flow analysis of capillary instability in presence of axial electric field has been studied. A dispersion relation is derived for the case of axially imposed electric field and stability is discussed in terms of various parameters such as electric field, Deborah number, Ohnesorge number, permittivity ratio and conductivity ratio etc. Stability criterion is given in the terms of critical value of wave number as well as critical value of applied electric field. The system is unstable when electric field is less than the critical value of electric field, otherwise it is stable. It has been found that in presence of the electric field the growth rates for viscoelastic fluid are higher than viscous fluid. Various graphs have been plotted for growth rate and critical electric field.

Parametric instability of the interface between two viscous magnetic fluids

The flat interface solution between two magnetic fluids can be parametrically excited by periodically oscillating magnetic field H 0(1+m cos(ωt)) oriented in direction normal to the fluids. The stability problem for the interface of two magnetic viscous fluids has been formulated. Beyond a critical value of wave number k C and a critical value m C of amplitude of excitation, the plane interface becomes unstable and standing waves appear. The solutions for standing waves are found to exist within stability bands in ( k, m) plane for a given value of external frequency ω and steady magnetic field H 0.

Numerical Study of the Unstable Modes of a Hyperbolic-Tangent Barotropic Shear Flow

Abstract An unbounded hyperbolic-tangent barotropic shear flow is assumed. The complex phase speeds and eigenfunction structure of unstable modes are studied numerically. A reversal of the planetary and shear vorticity gradient is required for these modes to exist. For sufficiently small wavenumber, the unstable modes, which can be associated with the modes of a discontinuous shear layer, are found on both sides of the neutral solution curve in wavenumber-shear parameter space. For sufficiently large wavenumbers, the unstable modes are contiguous to the neutral solution. For an intermediate range of wavenumbers, there are two sets of unstable modes (one contiguous to the neutral solution and one not); one set merges with the zero β unstable mode and one set vanishes for sufficiently small β (or large shear). Above some critical value of wavenumber, the set of modes at fixed wavenumber merging with the neutral solution is contiguous to the neutral boundary, whereas below the critical wavenumber value this ...