Analytical and numerical investigation of Rayleigh–Taylor instability in nanofluids

Abstract

This article is a maiden and naive attempt to formulate, analyse and investigate the Rayleigh–Taylor (RT) instability of two superimposed horizontal layers of nanofluids having different densities. Conservation equations are formulated and linearised by keeping in mind that density of the base fluids as well as nanoparticles is not constant. Linearised perturbed equations are sorted out by using the technique of normal modes and a dispersion relation incorporating the effects of surface tension, Atwood number and volume fraction of nanoparticles is obtained. Stable and unstable modes of RT instability are scrutinised using Routh–Hurtwitz criterion in the presence/absence of nanoparticles and presented graphically. Numerical calculations have been performed to explore the effect of surface tension, Atwood number and volume fraction of the nanoparticles. It is observed that in the presence/absence of nanoparticles, surface tension has a significant impact on stabilising the unstable mode of RT instability whereas Atwood number and volume fraction of nanoparticles hasten this instability. The graphical representations of these numerical investigations confirm the very explanation of RT instability under the effect of different parameters that have significant impact on the intensity of growth rate.