G.S. Agrawal

VISCOUS CONTRIBUTIONS TO THE PRESSURE FOR THE POTENTIAL FLOW ANALYSIS OF MAGNETOHYDRODYNAMIC KELVIN–HELMHOLTZ INSTABILITY

The present paper deals with the study of viscous contributions to the pressure for the viscous potential flow analysis of Kelvin–Helmholtz instability with tangential magnetic field at the interface of two viscous fluids. Viscosity enters through normal stress balance in the viscous potential flow theory and tangential stresses for two fluids are not continuous at the interface. Here, we have considered viscous pressure in the normal stress balance along with the irrotational pressure and it is assumed that the addition of this viscous pressure will resolve the discontinuity between the tangential stresses and the tangential velocities at the interface. The viscous pressure is derived by mechanical energy equation and this pressure correction applied to compute the growth rate of magnetohydrodynamic Kelvin–Helmholtz instability. A dispersion relation is obtained and stability criterion is given in the terms of critical value of relative velocity. It has been observed that the inclusion of irrotational shear stresses have stabilizing effect on the stability of the system.

Pressure Corrections for the Potential Flow Analysis of Kelvin-Helmholtz Instability

The present paper deals with the study of viscous contribution to the pressure for the viscous potential flow analysis of Kelvin-Helmholtz instability of two viscous fluids. Viscosity enters through normal stress balance in the viscous potential flow theory and tangential stresses for two fluids are not continuous at the interface. Here we have considered viscous pressure in the normal stress balance along with the irrotational pressure and it is assumed that the addition of this viscous pressure will resolve the discontinuity between the tangential stresses and the tangential velocities at the interface. The viscous pressure is derived by mechanical energy equation and this pressure correction applied to compute the growth rate of Kelvin-Helmholtz instability. A dispersion relation is obtained and a stability criterion is given in the terms of critical value of relative velocity. It has been observed that the inclusion of irrotational shearing stresses stabilizes 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.

Viscous Potential Flow Analysis of Rayleigh-Taylor Instability of Cylindrical Interface

The present paper deals with the study of Rayleigh-Taylor instability at the cylindrical interface using viscous potential flow theory. In the inviscid potential flow theory, the viscous term in Navier-Stokes equation vanishes as viscosity is zero. In viscous potential flow, the viscous term in Navier-Stokes equation vanishes as vorticity is zero but viscosity is not zero. Viscosity enters through normal stress balance in viscous potential flow theory and tangential stresses are not considered. A dispersion relation is derived and stability is discussed in terms of various parameters such as Ohnesorge number, density ratio etc. A condition for neutral stability is obtained and it is given in terms of critical value of the wave number. It is observed that the Ohnesorge number has destabilizing effect while inner fluid fraction has stabilizing effect on the stability of the system.