Rayleigh-taylor instability of two viscoelastic superposed fluids

Abstract

The stability of the plane interface separating two viscoelastic superposed fluids of uniform densities has been studied. The stability analysis has been carried out, for mathematical simplicity, for two highly viscous fluids of equal kinematic viscosities. It is found that the system is stable for stable configuration and unstable for unstable configuration. The behaviour of growth rates with respect to stress relaxation time and strain retardation time parameters ate examined analytically. IntroduetionThe instability of the plane interface between two incompressible and viscous fluids of different densities when the lighter is accelerated into the heavier has been discussed b y CnA~DRAS~KHAR [2]. The influence of viscosity on the stability of the plane interface separating two incompressible superposed fluids of uniform densities, when the whole system is i m m e r s e d in a uniform horizontal magnetic field, is studied b y BHATIA [1]. H e has carried out the stability analysis for two fluids of equal kinematic viscosities and different uniform densities. SHARMA [4] studied the t h e r m a l instability of a layer of viscoelastic (OLDROYD) fluid acted on b y a uniform rotation. The rotation is found to have a destabilizing as well a s a stabilizing effect under certain conditions in contrast to t h a t of a Maxwell fluid where ir always has a destabilizing effect. The stabi-]ity of a layer of Oldroyd fluid heated from below and subject to a magnetic field has been studied b y SHARMA [5].Ir m a y be of some interest to s t u d y the stability of the plane interface separating two incompressible superposed viscoelastic fluids of uniform densities. This aspect forros the subject m a t t e r of the present p a p e r wherein we have carried out the stability analysis for two fluids of equal kinematic viscosities and different uniform densities.

Nonlinear surface wave instability for electrified Kelvin fluids

“…Consequently, the linear stability conditions are not available for arbitrary viscosity. The stability criteria were discussed in some special cases [16,23,24,26,55]. In contrast, the analysis for nonlinear scope allowed us to derive stability criteria owing to the well-known Ginzburg-Landau equation, Schrödinger equation, and diffusion equation.…”

“…The components of these stresses consist of hydrodynamic, pressure, viscous, stress, porosity effect, surface tension stress, and electrical stress terms. In order to establish the nonlinear governing equation, we substitute from (25), (26) and (30)-(33) into the condition of the normal stress tensor, using (12), keeping only terms of cubic order for the elevation ξ . Hence, we get…”

“…For non-Newtonian fluids with constant viscosities the dispersion relations were only recently calculated for a linear wave on a deep layer of Maxwell and Jeffrey fluids [24,25]. Sharma and Sharma [26] investigated the problem of the Rayleigh-Taylor instability of two viscoelastic-superposed fluids. Aitken and Wilson [27] studied the stability of an incompressible elastic fluid at rest above a free surface by carrying out a linear stability analysis.…”

Hydrodynamic and Hydromagnetic Stability of Viscous‐Viscoelastic Superposed Fluids in Presence of Suspended Particles

“…Kumar and M. Singh 5 together with (8)- (10). Assume that the perturbation h(h x , h y , h z ) in the magnetic field has also a space and time dependence of the form (12). μ e stands for the magnetic permeability.…”

“…An experimental demonstration by Toms and Strawbridge [11] reveals that 2 Physical Separation in Science and Engineering a dilute solution of methyl methacrylate in n-butyl acetate agrees well with the theoretical model of the Oldroyd fluid. R. C. Sharma and K. C. Sharma [12] studied the stability of the plane interface separating two Oldroydian viscoelastic superposed fluids of uniform densities.…”