Abstract
The linear analysis of Rayleigh-Taylor instability of the interface between two viscous and dielectric fluids in the presence of a tangential electric field has been carried out when there is heat and mass transfer across the interface. In our earlier work, the viscous potential flow analysis of Rayleigh-Taylor instability in presence of tangential electric field was studied. Here, we use another irrotational theory in which the discontinuities in the irrotational tangential velocity and shear stress are eliminated in the global energy balance. Stability criterion is given by critical value of applied electric field as well as critical wave number. Various graphs have been drawn to show the effect of various physical parameters such as electric field, heat transfer coefficient, and vapour fraction on the stability of the system. It has been observed that heat transfer and electric field both have stabilizing effect on the stability of the system.
Highlights
The potential flow of an incompressible fluid is a solution of the Navier-Stokes equation in which velocity u can be expressed as a gradient of potential function which satisfies Laplace’s equation
In 2002, Joseph et al [2] extended their study of Rayleigh-Taylor instability to viscoelastic fluids at high Weber number and concluded that the most unstable wave is a sensitive function of the retardation time, which fits into experimental data when the ratio of retardation time to that of relaxation time is of order 10−3
We observe that as the values of heat transfer coefficient increase, the stable region increases in the viscous corrections for the viscous potential flow (VCVPF) solution in comparison with the viscous potential flow (VPF) solution; this indicates that the effect of irrotational viscous pressure stabilizes the system in the presence of heat and mass transfer
Summary
The potential flow of an incompressible fluid is a solution of the Navier-Stokes equation in which velocity u can be expressed as a gradient of potential function which satisfies Laplace’s equation. The study of the electrohydrodynamic Rayleigh-Taylor instability of two inviscid fluids in the presence of tangential electric field was considered by Eldabe [10]. Mohamed et al [11] studied the nonlinear electrohydrodynamic Rayleigh-Taylor instability of inviscid fluids with heat and mass transfer in presence of a tangential electric field and observed that heat and mass transfer has stabilizing effects in the nonlinear analysis. The effect of tangential electric field on the Rayleigh-Taylor instability when there is heat and mass transfer across the interface was studied by Awasthi and Agrawal [12]. Awasthi [14] applied VCVPF theory on the Rayleigh-Taylor instability of two viscous fluids when there is heat and mass transfer across the interface and observed that the irrotational shearing stresses stabilize the interface. Various neutral curves are drawn to show the effect of various physical parameters such as electric field and heat transfer coefficient on the stability of the system
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