The interface of viscous-Rivlin-Ericksen fluids is analyzed through the linear theory of stability analysis when mass and heat is transferring across the interface. The Rivlin-Ericksen fluid lies in the upper region while the lower region of the interface contains viscous fluid. The gravitational acceleration destabilizes the top-heavy arrangement and interface instability is governed by Rayleigh-Taylor instability. The two-dimensional interface is considered, and the viscous potential flow theory is employed to establish the relationship between perturbation's growth and wave number. This relationship is analyzed, and the perturbation's growth is plotted for various flow parameters. A marginal stability condition is obtained, and it is given in terms of heat transport coefficient and wave number. The marginal stability criterion is analyzed using the well-known Newton-Raphson method. The heat and mass transfer phenomenon drives the unstable interface towards stability. It is pointed out that the viscoelastic coefficient influences the interface to be stable while the thickness of the viscoelastic fluid makes the interface unstable. Atwood numbers and Weber numbers show destabilizing behavior.
The interface of a viscous fluid and [Formula: see text]-water nanofluid is analyzed through linear instability analysis in a spherical configuration. The viscous fluid lies inside the sphere while the outside region contains nanofluid. In this model, the viscosity of the nanofluid is considered a function of the base fluid viscosity, nanoparticles volume fraction, fractal aggregates, and nanoparticles shape. The perturbed flow is taken as irrotational, and the linear perturbation equations are solved through viscous irrotational theory. The perturbations growth rate can be computed through a 2-degree polynomial and the coefficients of this polynomial are the functions of the Atwood number, Richardson number, Weber number, Reynolds number, etc. The nanofluid interface is found more stable than the viscous fluid interface. The density of nanofluids raises the amplitude of disturbances while the nanofluid's viscosity has a reverse effect.
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