Rayleigh-Taylor Instability of a Cylindrical Interface Between Two Inviscid Fluids

Abstract

A theoretical analysis for the instability of a fluid film around a cylinder in an immiscible fluid is presented. A general dispersion equation, relating wave number to growth rate, is derived with consideration of the effects of the cylindrical interface and a finite film thickness. Application of the dispersion equation to the breakup of a liquid film around a cylindrical body in still air leads to a prediction of the dominant wavelength by λ = 2π2 / (1/ R2 + ρ1g/q), where R is the radius of the cylinder, ρ1 is the density of the liquid, g is the acceleration due to gravity, σ is the surface tension. Experiments showed good agreement with the present analysis. The dominant wavelength decreases with a decrease in the radius of the cylindrical body. A previous report on the breakup of a liquid film around a horizontal cylindrical body is shown to be in error.