Rayleigh-Taylor Instability in Viscoelastic Fluids

TL;DR

This paper investigates the onset of Rayleigh-Taylor instability in viscoelastic fluids, analyzing stability conditions and effects of electric and magnetic fields, revealing differences from Newtonian fluids.

Contribution

It provides a theoretical analysis of Rayleigh-Taylor instability in viscoelastic fluids and explores how electric and magnetic fields influence stability.

Findings

Perturbations in stratified viscoelastic fluids grow exponentially without oscillation.

Electric or magnetic field gradients can nullify effective gravity in Newtonian fluids, stabilizing them.

Viscoelastic fluids remain unstable under similar field conditions, unlike Newtonian fluids.

Abstract

In this paper I analyze the onset of Rayleigh-Taylor instability between two linear viscoelastic fluids assuming that the perturbations at the interface are small. In the first half, the paper analyzes a stratified viscoelastic fluid in which I prove that the perturbations rise or fall exponentially without oscillating. The second half of the paper examines the effect of electric and magnetic fields on viscoelastic fluids. I show that it is possible to choose electric or magnetic field gradient such that the effective acceleration due to gravity is zero. If a heavy Newtonian fluid rests on top of a lighter Newtonian fluid such a choice of field gradient would have rendered the arrangement stable. If the fluids are viscoelastic, I show that a similar arrangement is unstable.