Spatial instability of a viscous liquid sheet

Abstract

The spatial instability theory is used to study the evolution of symmetrical and antisymmetrical disturbances of a moving viscous liquid sheet in an inviscid gas medium. The similarities and dissimilarities between spatial and temporal instabilities are delineated. Effects of properties such as viscosity, density, and surface tension on instability are examined. It is found that liquid viscosity always reduces the growth rate and dominant wave number for symmetrical disturbances. For antisymmetrical disturbances, liquid viscosity reduces the growth rate and dominant wave number at large Weber number, whereas liquid viscosity enhances instability at low Weber number. An increase in the gas-to-liquid density ratio always raises the growth rate of symmetrical disturbances. The growth rate of antisymmetrical disturbances initially increases with the density ratio, and then decreases when the density ratio exceeds Weber number. Surface tension always opposes the development of instability. Symmetrical disturbances control the instability for small Weber number, whereas antisymmetrical disturbances dominate for large Weber number. The dominant wave numbers associated with symmetrical disturbances are always greater than those of antisymmetrical disturbances.